Voltage-gated K+ channels in Drosophila photoreceptors ...

VOLTAGE-GATED K +
CHANNELS IN DROSOPHILA
PHOTORECEPTORS
Biophysical study of neural coding
MIKKO
VÄHÄSÖYRINKI
Faculty of Science,
Department of Physical Sciences,
Division of Biophysics,
Biocenter Oulu,
University of Oulu
OULU 2004

MIKKO VÄHÄSÖYRINKI
VOLTAGE-GATED K + CHANNELS IN
DROSOPHILA PHOTORECEPTORS
Biophysical study of neural coding
Academic Dissertation to be presented with the assent of
the Faculty of Science, University of Oulu, for public
discussion in Oulunsali (Auditorium L5), Linnanmaa, on
December 11th, 2004, at 12 noon
OULUN YLIOPISTO, OULU 2004

Copyright © 2004
University of Oulu, 2004
Supervised by
Professor Matti Weckström
Reviewed by
Professor Kristian Donner
Professor Doekele Stavenga
ISBN 951-42-7598-5 (nid.)
ISBN 951-42-7599-3 (PDF) http://herkules.oulu.fi/isbn9514275993/
ISSN 0355-3191 http://herkules.oulu.fi/issn03553191/
OULU UNIVERSITY PRESS
OULU 2004

Vähäsöyrinki, Mikko, Voltage-gated K + channels in Drosophila photoreceptors
Biophysical study of neural coding
Faculty of Science, Department of Physical Sciences, Division of Biophysics, University of Oulu,
P.O.Box 3000, FIN-90014 University of Oulu, Finland, Biocenter Oulu, University of Oulu,
P.O.Box 5000, FIN-90014 University of Oulu, Finland
2004
Oulu, Finland
Abstract
The activity of neurons is critically dependent upon the suite of voltage-dependent ion channels
expressed in their membranes. In particular, voltage-gated K + channels are extremely diverse in their
function, contributing to the regulation of distinct aspects of neuronal activity by shaping the voltage
responses.
In this study the role of K + channels in neural coding is investigated in Drosophila photoreceptors
by using biophysical models with parameters derived from the electrophysiological experiments. Due
to their biophysical properties, the Shaker channels attenuate the fast transients and amplify the
slower signal components, enabling photoreceptors to use their voltage range more effectively. Slow
delayed rectifier channels, shown to be encoded by the Shab gene, activate at high light intensities,
thereby attenuating the light-induced depolarization and preventing response saturation. Activation
of Shab channels also reduces the membrane time constant making it possible to encode faster events.
Interactions between the voltage-gated K + channels and the currents generated by the light
induced conductance (LIC) were investigated during naturalistic stimulation in wild type and Shaker
mutant photoreceptors. It is shown that in addition to eliminating the Shaker current, the mutation
increased the Shab current and affected the current flowing through the LIC. Part of these changes
could be attributed to direct feedback from the Shaker channels via the membrane potential.
However, it is suggested that also other changes may occur in the LIC due to mutation in K + channels,
possibly during photoreceptor development.
Comparison of the Shaker and Shab mutant photoreceptors with the wild type revealed that a
concurrent decrease in the steady-state input resistance followed from deletion of the voltage-gated
K + channels. This allowed partial compensation of the compression and saturation caused by the loss
of Shaker channels and it maintained the characteristics of the light-voltage relationship in Shab
mutant photoreceptors. However, wild type properties were not fully restored in either mutant.
Indeed, decreased input resistance results in reduced efficiency of neural processing, assessed by the
metabolic cost of information.
Results of this study demonstrate the importance of the voltage-gated K + channels for neural
coding precision and highlight the robustness of neuronal information processing gained through
regulation of the electrical properties.
Keywords: Hodgkin-Huxley model, metabolic costs, naturalistic stimulus, robustness,
Shab, Shaker

To Alexandra

Acknowledgements
This study was carried out at the Department of Physics, Division of Biophysics in the
University of Oulu. I would like to thank my supervisor Professor Matti Weckström, also
the head of the Division of Biophysics and our research group, for his advices and
support during these early steps of mine in the intriguing world of science. I admire his
positive attitude towards life. I also highly appreciate the way he considers his employees
as friends and co-workers. I enjoyed numerous fruitful discussions we have had.
I would like to thank Dr. Jeremy Niven (Department of Zoology, University of
Cambridge, Cambridge, UK) with whom I have closely collaborated right from the
beginning. We have had many inspiring and productive periods of intensive working,
which produced the backbone for this study.
I would also like to thank Dr. Mikko Juusola (Physiological Laboratory, University of
Cambridge, Cambridge, UK) and Dr. Roger Hardie (Department of Anatomy, University
of Cambridge, Cambridge, UK). All the experimental data used in this study was
collected in their laboratories. Our enlightening discussions and especially their sharp
criticisms revealed possible weaknesses of many hypotheses, thereby significantly
improving the final outcome of this study. I am also grateful to Professor Andrew French
(Department of Physiology and Biophysics, Dalhousie University, Halifax, Nova Scotia,
Canada) for his fundamental role in the naturalistic stimuli project. I was very impressed
by his certainty of how things should be done and by his efficiency on getting these
things done.
I am also thankful for all the people not mentioned above, especially for the staff in
the Division of Biophysics, who have helped me in many issues during this study.
Finally, I would like to thank my family and friends for being there.
Oulu, 2004 Mikko Vähäsöyrinki

Abbreviations
ATP Adenosine triphosphate
Ca 2+ Calcium ion
Cl - Chloride ion
I-V relationship Current-voltage relationship
K + Potassium ion
k1(u) First-order Volterra kernel
k2(u,v) Second-order Volterra kernel
LIC Light induced conductance
LIC-V relationship Light induced conductance -voltage relationship
MSE Mean square error
Na + Sodium ion
NLN-model Parametric nonlinear-linear-nonlinear cascade model
LED Light emitting diode
Q10 Temperature quotient for a 10 °C temperature change
Shab Gene encoding slowly inactivating K + potassium current
Shab 1 Drosophila mutant; missense mutation in Shab gene causing
75% reduction in the Shab current
Shab 2 Drosophila mutant; missense mutation in Shab gene causing
71% reduction in the Shab current
Shab 3 Drosophila mutant; null mutation in Shab gene
Shaker Gene encoding A-type K + current
Shaker 14 Drosophila mutant; null mutation in the Shaker gene
producing non-functional Shaker K + channels
Shaker 14 Shab 3 Drosophila double mutant; null mutation in the Shaker and
Shab genes
SNR Signal-to-noise ratio
WT Wild-type Drosophila

List of original papers
All ideas and the final outcomes of these research projects in form of publications
resulted from successful collaboration. This makes it impossible to strictly associate
specific ideas or findings to certain person. From purely methodological point of view, I
developed biophysical models based on the experimental data recorded by the Dr. Jeremy
Niven, Dr. Mikko Juusola and Dr. Roger Hardie. This thesis is based on the following
articles, which are referred to in the text by their Roman numerals I-IV:
I Niven JE * , Vähäsöyrinki M * , Kauranen M, Hardie RC, Juusola M, Weckström M
(2003) The contribution of Shaker K + channels to the information capacity of
Drosophila photoreceptors. Nature 421, 630-634. *Shared first authorship
II Niven JE, Vähäsöyrinki M, Juusola M (2003) Shaker K + -channels are predicted to
reduce the metabolic cost of neural information in Drosophila photoreceptors. Proc R
Soc Lond B Biol Sci 270, Suppl 1:S58-61.
III Niven JE, Vähäsöyrinki M, Juusola M, French AS (2004) Interaction between lightinduced
currents, voltage-gated currents and input statistics in Drosophila
photoreceptors. J Neurophysiol 91, 2696-2706.
IV Vähäsöyrinki M * ., Niven, J.E * , Hardie, R.C., Weckström, M., Juusola, M. Role of
Shab K + channels in the information processing of Drosophila photoreceptors.
Submitted. *Shared first authorship

Contents
Abstract
Acknowledgements
Abbreviations
List of original papers
Contents
1 Introduction ................................................................................................................... 15
2 Review of the literature ................................................................................................. 16
2.1 Basis of neural information processing ..................................................................16
2.2 Hodgkin-Huxley model of the excitable membrane...............................................17
2.3 K + channels.............................................................................................................19
2.4 Efficiency of neural coding ....................................................................................20
2.5 Drosophila photoreceptors .....................................................................................20
3 Aims of the research ...................................................................................................... 22
4 Material and methods .................................................................................................... 24
4.1 Fly stocks................................................................................................................24
4.2 Optical neutralisation of the cornea........................................................................24
4.3 Electrophysiological experiments...........................................................................24
4.3.1 In vitro patch-clamp recordings from isolated photoreceptors ........................24
4.3.2 In vivo intracellular experiments.....................................................................25
4.4 Linear system analysis............................................................................................26
4.5 Nonlinear system analysis ......................................................................................27
4.6 Hodgkin-Huxley type photoreceptor models..........................................................29
4.6.1 Voltage-dependent properties of Shaker, slow delayed rectifier and novel
noninactivating K + channels.............................................................................29
4.6.2 Derivation of the other model parameters .......................................................32
4.6.3 MATLAB© implementation of the Hodgkin-Huxley type of photoreceptor
model................................................................................................................33
4.6.4 Reconstruction of the light induced conductance ............................................33
4.6.5 Model simulations ...........................................................................................34
4.6.6 Estimation of the metabolic costs....................................................................35

5 Summary of the results in the original papers ............................................................... 37
5.1 The contribution of Shaker K + channels to the information capacity
of Drosophila photoreceptors (I) ...........................................................................37
5.2 Metabolic cost of Shaker K + channels in Drosophila photoreceptors (II) ..............38
5.3 Interactions between light-induced currents, voltage-gated currents, and input
signal properties in Drosophila photoreceptors (III) .............................................39
5.4 Role of Shab K + channels in the information processing of Drosophila
photoreceptors (IV) ...............................................................................................40
6 Discussion ..................................................................................................................... 43
6.1 Modelling of Drosophila photoreceptors................................................................43
6.2 K + channels in Drosophila photoreceptors .............................................................44
6.3 The robustness of neural coding in Drosophila photoreceptors..............................44
6.4 Naturalistic stimulus...............................................................................................46
6.5 Efficiency of neural coding ....................................................................................47
6.6 Relevance of the findings .......................................................................................48
7 Conclusions ...................................................................................................................49
References
Appendix

1 Introduction
In nature the success of an individual depends upon accurately determining and executing
the appropriate behaviour based on the sensory information it gathers from its
surroundings. The most important cellular components of neural information processing
are ion channels found in the neural cell membrane. To understand why particular ion
channels are expressed in specific neurons requires detailed knowledge of their
contribution to information processing. Insect photoreceptors have provided a model
system for examining specific molecular mechanisms involved in information processing
with graded voltage signals, including signal transduction (the phototransduction
cascade) (Hardie & Raghu 2001, Hardie 2003) and membrane filtering (the photoinsensitive
membrane) (Weckström & Laughlin 1995). In Drosophila these mechanisms
can be studied in relative isolation by combining electrophysiological experiments with
genetic methods and mathematical modelling. Focus of this study is on the widely
expressed voltage-activated K + channels that are known to confer specific electrical
properties upon the membranes enabling neurons to process biologically relevant
information (Rudy 1988, Weckström & Laughlin 1995, Coetzee et al. 1999, Hille 2001,
Johnston et al. 2003).
Drosophila photoreceptors express voltage-activated K + channels in their photoinsensitive
membrane: Shaker and slow delayed rectifier channels being characterised as
the predominant ones (Hardie 1991a, Hardie et al. 1991, Hevers & Hardie 1995). What is
the contribution of these voltage-activated channels to the information processing in
Drosophila photoreceptors? How do the currents generated by these channels interact
with each other and with the currents generated by the light transduction machinery?
How do these channels affect the energy efficiency of neural code? How robust are
Drosophila photoreceptors to imposed changes in their ion channel composition? These
questions allow a systematic approach for estimating the contribution of voltage-gated K +
channels to the performance of Drosophila photoreceptors. Results of this study may
provide new insight to graded voltage signal processing by K + channels (e.g., in sensory
neurons and in dendrites) and to possible mechanisms of robustness in neural coding.

2 Review of the literature
2.1 Basis of neural information processing
Information is carried within and between neurons by complex electrical and chemical
signalling pathways. Every neuron has a separation of charges across its cell membrane
consisting of a thin cloud of positive and negative ions spread over the inner and outer
surfaces of the lipid bilayer membrane. The charge separation gives rise to a difference in
electrical potential across the membrane called the membrane potential, Vm:
Vm= Vin−Vout The membrane potential of a cell at rest is called the resting potential. A reduction of
charge separation, leading to less negative membrane potential, is called depolarisation.
An increase in charge separation, leading to a more negative membrane potential, is
called hyperpolarisation.
Electrical signals – receptor potentials, synaptic potentials, and action potentials – are
produced by the movements of ions into and out of the cells through ion channels
embedded in the cell membrane. The membrane’s overall selectivity for individual ion
species, mainly Na + , K + , Cl - and Ca 2+ , is determined by the relative proportions of the
various types of ion channels in the cell that are open. The ions are subject to two forces
driving them across the membrane: (1) a chemical driving force that depends on the
concentration gradient across the membrane and (2) an electrical driving force that
depends on the electrical potential differences across the membrane. The equilibrium
potential, Ei, for any ion can be calculated from the Nernst equation:
RT cin
Ei=− ln
(2)
zF cout
where R is the gas constant, T is the temperature, z is the valence of the ion, cin and cout
are the intra- and extracellular concentrations for the ions.
(1)

17
The equivalent electrical circuit of a neuron provides an intuitive understanding as
well as a quantitative description of how the current flows due to the movements of ions
generate voltage signals in neurons. The circuit model of a patch of the squid axon
(Hodgkin & Huxley 1952) is shown in figure 1.
Fig. 1. Equivalent electrical circuit of the squid axon. C m is the membrane capacitance, I i are
the currents and gi are the conductances.
ss
The steady-state potential, V m , for the equivalent circuit in Fig. 1 can be calculated with
the equation:
V
g E + g E + g E
=
ss Na Na K K L L
m
gNa + gK+ gL
where gi are the conductances and Ei are the Nernst potentials for sodium, potassium and
the leak, respectively. In the limit, if the conductance for one ion is much greater than that
for the other ions, Vm will approach the value of the Nernst potential of the corresponding
ion. During signalling the membrane voltage deviates from the steady-state and changes
constantly. The dynamics of a passive membrane can be defined by the time constant, τ:
τ= RC in m
where Rin is the input resistance and Cm is the capacitance of the membrane.
2.2 Hodgkin-Huxley model of the excitable membrane
In 1952 A.L. Hodgkin and A.F. Huxley published a series of papers in which they
investigated the flow of current through the membrane of the giant nerve fibre of the
(3)
(4)

18
squid (Hodgkin & Huxley 1952). Currents were recorded by using the voltage clamp
technique, where the membrane potential is stepped according to the experimental
protocol and kept constant with the feedback amplifier. Based on these experiments they
developed a biophysical model of the excitable membrane. Their electrical model
contained not only the passive membrane with fixed capacitance and resistance, but also
the contribution of active sodium and potassium ion channels, which change their
properties as a function of voltage.
In the Hodgkin-Huxley model (Fig. 1) the total current, I, can be written as a sum of
capacitive, Icap, and resistive currents, Ii. The capacitive current follows the equation:
dVm
Icap = Cm dt
(5)
where Cm is the membrane capacitance and Vm is the membrane potential. The resistive
currents, Ii, are described with the equation:
( )
I = g V −E
i i m i
where gi is the conductance for each ion. The equation for the membrane voltage, Vm, can
be derived by combining the current equations (5) and (6):
( − ) + ( − ) + ( − )
dV g V E g V E g V E
m Im
= −
dt C C
Na m Na K m K L m L
m m
where Im is the current injected by the experimenter.
Hodgkin and Huxley observed that during voltage clamp the sodium conductance first
rises with short delay and then falls again to a low value, processes they called activation
and inactivation, respectively. Based on these findings they developed an empirical
kinetic model that predicted correctly the major features of the experimental
observations. The kinetic behaviour of the opening and closing of the ion channels are
controlled by a varying number of independent membrane-bound particles. The state of
the gating particle, γk, is assumed to undergo first-order transitions between permissive
and non-permissive forms:
α
γ
1−
γ ←⎯⎯ ⎯⎯→ γ
k
β
k
γ
where αk and βk are the voltage dependent rate constants. The values for the gating
particles, describing the probability of the permissive state, γk, can be obtained from the
differential equation:
d
dt
γ k =αγ( 1−γ
k) − βγ
γ k
Based on the theory of gating particles, the conductance for each ion channel, gi, can be
calculated with the equation:
(6)
(7)
(8)
(9)

19
(10)
( )
where gimax is the maximum conductance and n is the number of gating particles, which,
while increasing from 1 to 2, 3, 4…, changes the rising phase of the conductance from
exponential to sigmoidal. Since the original publications, numerous models have been
developed following the Hodgkin-Huxley formalism for a variety of systems (Hille
2001). Hodgkin-Huxley type of models still form the reference for studying the role of
ion channels in electrical signalling (Meunier & Segev 2002).
n
gi = gimax∏⎡⎣γk V m,t
⎤⎦
k
2.3 K + channels
The history of the K + channels starts from the year 1902 when Julius Bernstein postulated
a selective potassium permeability in excitable cell membranes (Bernstein 1902).
Presently K + channels are known to be expressed in all animal cells, involving in
numerous functions (Hille 2001). Indeed, K + channels are generally considered to
represent the most diverse of the ion channel families (Rudy 1988), each type of neuron
expressing its own blend of channels to suit its special purposes. The best known example
is the axonal membrane expressing predominantly one major class of K + channels – the
delayed rectifier type – that repolarises the membrane after the action potential (Hodgkin
& Huxley 1952).
An A-type channel from Drosophila was the first K + channel to be cloned (Tempel et
al. 1987, Kamb et al. 1988, Pongs et al. 1988). The identification of this channel started
with mutant flies called Shaker, named after their tendency to shake legs while under
ether anesthesia. This one gene locus was found to code for a variety of K + channels by
mechanisms of alternative splicing (Iverson et al. 1988, Pongs et al. 1988, Schwarz et al.
1988, Timpe et al. 1988, Hardie et al. 1991) and heteromultimeric combinations (Isacoff
et al. 1990, McCormack et al. 1990). Later three other genes were identified in
Drosophila, complementing the K + channel family, named Shaker, Shal, Shab and Shaw,
coding for K + channels ranging from a rapidly inactivating A current to a slow delayed
rectifier current (Butler et al. 1989, Wei et al. 1990).
The equilibrium potential for the K + channels is typically slightly below the resting
potential of a neuron. Therefore, the opening of the K + channels draws the membrane
potential back to the direction of the resting potential, producing a stabilising effect. In
spiking neurons, the functions of K + channels include setting the resting potential,
keeping fast action potentials short, terminating periods of intense activity, timing the
inter-spike intervals during repetitive firing, and generally lowering the effectiveness of
excitatory inputs on a neuron when they are open (Hille 2001). In graded potential
neurons the potassium channels, in addition to their stabilising role, may tune the cell
membrane of sensory neurons into an optimal filter for the transduced signal (Laughlin &
Weckstrom 1993, Weckström & Laughlin 1995).

20
2.4 Efficiency of neural coding
Information theory quantifies our intuitive notions of gaining information and puts it on
the absolute scale (Rieke 1997, Dayan & Abbott 2001). The information capacity of a
system gives an upper limit for the number of states a signalling system can transmit in a
given time window. Energy as well as information capacity is an important consideration
in understanding neural processing. Potentially, energetic costs could limit absolute
numbers of neurons and synaptic connections in the neural systems and influence the
expression and distribution of ion channels (Laughlin et al. 1998).
Usage of energy can be linked to two fundamental measures of signal quality: signalto-noise
ratio (SNR) and bandwidth (a measure of speed of response) (Weckström &
Laughlin 1995). Improving the SNR increases the energy demands, because reliability
increases as the square root of the number of uncorrelated stochastic events that generate
signals. Each stochastic signalling event, such as opening an ion channel or releasing a
synaptic vesicle, requires extra energy. Raising the bandwidth means that the membrane
time constant must be reduced by increasing conductance. Increased conductance means
larger ion fluxes across the membrane that has to be compensated by ATP driven ion
transport. Evidence is accumulating that neurons economize by restricting the SNR and
bandwidth to the minimum required to get the job “done just right-enough” (Laughlin
2001).
2.5 Drosophila photoreceptors
The Drosophila eye is composed of ca. 800 ommatidia, each of them consisting of
sophisticated optics transmitting photons to sensory neurons (Stavenga 2003b, Stavenga
2003a, Stavenga 2004). Photoreceptors (Fig. 2) are the light detectors of visual systems
converting the energy of incoming photons into electrical signals by a process of
phototransduction (Hardie 2001). Discrete electrical events (bumps) can be recorded
under very dim illumination corresponding to single photon absorptions in the photosensitive
membrane (Wu & Pak 1975). The photoreceptors respond to light by graded
changes in their membrane potential consisting of numerous fused bumps.
Although the photoreceptor voltage responses are initiated by the currents generated in
the photo-sensitive membrane, the final shape of these responses is determined by the
properties of the photo-insensitive membrane containing voltage-gated K + channels
(Shaker and slow delayed rectifier channels being characterised as the predominant ones,
(Hardie 1991a, Hardie et al. 1991, Hevers & Hardie 1995). In Drosophila the
contribution of each type of K + channel to the performance can be studied in relative
isolation by combining electrophysiological experiments with genetic approaches and
modelling. This makes it a good model system to investigate the role of voltage-gated K +
channels in neural processing.

21
Fig. 2. Schematic introduction to the Drosophila photoreceptors. Scale bar in the electron
microscope picture in the right lower corner is 1 µm. Figure is modified from pictures
adapted from the Drosophila FlyBase (http://fly.ebi.ac.uk:7081/) and from (Hardie & Raghu
2001).

3 Aims of the research
The following questions were investigated to systematically estimate the contribution of
voltage-gated K + channels to the performance of Drosophila photoreceptors:
1. The contribution of the Shaker channels and its functional homologues (Rudy 1988,
Coetzee et al. 1999) to neuronal function remains unclear, although they are thought to
attenuate the amplitude of graded potentials and back-propagated action potentials in
dendrites (Laurent 1990, Hoffman & Johnston 1998, Magee et al. 1998), to influence
the firing frequency of spiking neurones (Connor & Stevens 1971) and to determine
the reliability of spike propagation (Debanne et al. 1997). What is the contribution of
Shaker K + channels to the information processing in Drosophila photoreceptors?
2. Sensory systems are thought to be tuned to the statistical properties of their natural
stimuli through evolutionary and/or developmental processes (Weckström & Laughlin
1995, Katz & Shatz 1996). Therefore, understanding how specific components
function within these sensory systems should benefit from using stimuli with
appropriate dynamic properties. How do the voltage-gated currents interact with each
other and with the light-induced currents in natural stimulus regimes in Drosophila
photoreceptors?
3. Despite their importance in regulating neural activity, many genetic deletions of
specific ion channels have caused relatively little changes in neuron performance
(Wickman et al. 1998, Brickley et al. 2001), even when pharmacological studies
suggest there should be severe phenotypes. This mismatch suggests that altered
channel expression may be compensated for by changes in other ion channels (Liu et
al. 1998, Namkung et al. 1998, MacLean et al. 2003). Do regulatory changes in the
electrical properties, potentially restoring the photoreceptor’s performance, follow
from deletion of the Shaker channels?
4. The efficient expenditure of a limited energy budget is a major factor influencing all
aspects of animal design. Therefore, energy is thought to have been an important
constraint upon the evolution of nervous systems (Laughlin 2001). Since neural
coding is metabolically expensive (Kety 1957, Ames 1997, Laughlin et al. 1998), the
metabolic cost of a particular conductance may be an important consideration. How do
the Shaker K + channels affect the energy efficiency of neural information in
Drosophila photoreceptors?

23
5. Voltage-gated K + channels have different biophysical properties and, therefore, their
role in shaping the voltage signals is likely to be different. What is the role of slow
delayed rectifier K + channels in neural processing of Drosophila photoreceptors? Are
potential changes in the electrical properties due to reduction in the slow delayed
rectifier conductance similar to that of the Shaker mutant photoreceptors or do they
possibly provide robustness for different aspects of function?

4 Material and methods
4.1 Fly stocks
Flies (Drosophila melanogaster) were raised on standard medium at 19°C in darkness.
The wild-type strain was red-eyed Drosophila melanogaster Oregon Red. The Shaker
channel mutation was Shaker 14 (a missense mutation in the core region resulting in nonfunctional
Shaker channels) (Kaplan & Trout 1961, Salkoff & Wyman 1981). Three
alleles of the Shab gene (Shab 1 , Shab 2 and Shab 3 ) were used either in ebony or wild-type
background. Shab 1 and Shab 2 are missense mutations whereas Shab 3 is a null allele
(Hegde et al. 1999). Shaker 14 Shab 3 double mutants lacked functional Shaker and Shab
channels. All the mutants were expressed in red-eyed flies.
4.2 Optical neutralisation of the cornea
For observing rhabdomeres in the intact eye, heads were mounted on microscope slides
using clear nail varnish and observed under a 63× oil immersion objective using
antidromic illumination for photography (Franceschini & Kirschfeld 1971).
4.3 Electrophysiological experiments
4.3.1 In vitro patch-clamp recordings from isolated photoreceptors
Whole-cell recordings from dissociated Drosophila photoreceptors were performed as
previously described (Hardie 1991a, Hardie 1991b, Hardie et al. 1991, Hardie et al.
2001). Dissociated ommatidia from recently eclosed adult flies were prepared and
transferred to the bottom of a recording chamber on an inverted Nikon Diaphot

25
microscope. The bath was composed of (in mM): 120 NaCl, 5 KCl, 10 TES, 4 MgCl2, 1.5
CaCl2, 25 proline and 5 alanine. The standard intracellular solution was (in mM): 140 K +
gluconate, 10 TES, 4 Mg ATP, 2 MgCl2, 1 NAD and 0.4 Na + -GTP. The pH of all
solutions was 7.15. Whole-cell voltage clamp recordings were made using electrodes
with a resistance of ~10-15MΩ. The series resistance values were generally below 25MΩ
and were routinely compensated to >80%. Data were collected and analyzed using an
Axopatch 1-D amplifier and pCLAMP 8 or 9 software (Axon Instruments, Foster City,
CA, USA).
Cells were stimulated via a green LED (560 nm), with maximum effective intensity of
~2x10 5 photons/s per photoreceptor. Relative intensities were calibrated using a linear
photodiode and converted to absolute intensities in terms of effectively absorbed photons
by counting quantum bumps at low intensities (Henderson et al. 2000). Bumps were
elicited either by continuous dim illumination or by repeated brief flashes containing on
average less than one effective photon and were detected and analysed off-line using
Minianalysis software (Synaptosoft) (Henderson et al. 2000). All the patch-clamp data
used in this study was provided by Dr. Roger Hardie (Department of Anatomy, University
of Cambridge, Cambridge, UK).
4.3.2 In vivo intracellular experiments
Intracellular recordings, stimulation and data acquisition have been described previously
in detail (Juusola & Hardie 2001a). Flies were fixed using wax in a custom built ceramic
holder and a small window was cut into the surface of the compound eye. Recordings
were made using quartz microelectrodes (resistances between 150 and 220 MΩ, filled
with 3 M KCl) placed to the retina through a small hole cut in the surface of the eye. As
indifferent electrode a second blunt microelectrode filled with fly Ringer was also placed
in the flies' head close to the eye. All recordings were made using a switch clamp
amplifier (SEC 10L, npi Electronic, Germany) in current-clamp mode. The temperature
of the flies was maintained at 25 °C throughout the experiments to within 1 °C accuracy
using a thermocouple feeding back to a Peltier device.
Impaled photoreceptors were stimulated by a high intensity green LED with peak
wavelength of 525 nm (3× 10 6 photons/s; Marl Optosource, UK). Data acquisition,
stimulus generation and signal analysis were performed by a purpose built MATLAB
interface (Biosyst, © Mikko Juusola). For the natural stimulus experiments, the light
intensity was derived from a published time series obtained from a light detector moving
through a natural environment (van Hateren 1997). Photoreceptors were considered for
analysis only if their resting membrane potential was less than -55mV and they had at
least a 45 mV saturating impulse response in dark-adapted conditions. All the
intracellular experiments were carried out by Dr. Jeremy Niven and Dr. Mikko Juusola in
the Physiological Laboratory at University of Cambridge, Cambridge, UK.

26
4.4 Linear system analysis
The goal of system analysis is to establish a cause-effect relationship that would allow the
prediction of the system response to any arbitrary stimulus. For linear systems the
property of superposition allows measurements from a restricted range of stimuli to
predict the response to any stimulus. Traditional linear system identification relies on
analysing responses to the impulse, step and Gaussian white noise stimuli (to determine
the frequency response function of a system). Gaussian white noise is a stationary, zeroaverage
random process, which has the fundamental property that any two samples of it
are statistically independent. Additionally, the power spectrum of ideal Gaussian white
noise is constant over all frequencies. Due to experimental limitations (limited signal
lengths) a band limited Gaussian white noise is used with a frequency band exceeding
that of the investigated system (Marmarelis & Marmarelis 1978).
Repeated presentations (10-30 times) of an identical pseudorandom Gaussian white
noise modulated current, i(t), or light contrast, c(t), evoke variable voltage responses due
both to recording noise and the stochastic nature of the underlying biological processes.
Averaging the responses gives the noise-free light contrast or current-evoked
photoreceptor voltage signal, sv(t). Subtraction of this signal from the individual
responses, rv(t)i, gives the noise component, nv(t)i, of each individual response period:
() = () − ()
n t r t s t
V i V i V
Errors due to residual noise in sV(t) are small and proportional to (noise power)/ n
(Kouvalainen et al. 1994).
To calculate the signal-to-noise ratio in the frequency domain, SNRv(f), signal and
noise were segmented into 50% overlapping stretches and windowed with a Blackman-
Harris fourth term window before their corresponding spectra, Sv(f) and Nv(f), were
calculated with an FFT algorithm. SNRv(f) is given by:
( )
2
Sf
SNR (12)
V ( f ) =
2
N( f)
From the SNRv(f) an estimate of the information capacity (bits/s), C, can be calculated
using Shannon's formula (Shannon 1948):
∞
∫
0
( 2 ⎡ ( ) ⎤)
C= log ⎣SNR f + 1⎦ df
The photoreceptor frequency response function, G(f), for the light contrast stimulus, c(t),
as well as membrane impedance, Z(f), for the current stimulus, i(t), can be calculated
with:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
* *
SV f ⋅C f SV f ⋅I
f
G( f) = and Z( f)
=
* *
Cf ⋅CfIf⋅If (11)
(13)
(14)

27
where asterisk stands for the complex conjugate of the corresponding Fourier transform.
How do the voltage-gated potassium channels affect the membrane impedance?
Activation of a channel means that more ion channels are opened, reducing the
impedance in the frequency range defined by the activation time constant, τ. The 3dB
corner frequency, f3dB, of this effect can be calculated with equation:
(15)
On the other hand, inactivation of the ion channels increases the impedance. Time
constants for the inactivation are usually much longer than those of the activation limiting
this effect to the low frequencies. If a significant proportion of the ion channels is open at
the steady-state, the inactivation may reduce the conductance below the steady-state
value. This causes the membrane impedance to exceed that of the steady-state at the
frequencies determined by the inactivation time constant. A schematic presentation of the
relationships between the membrane impedance and the dynamics of voltage-gated K +
1
f3dB
=
2πτ
channels is shown in Fig 3.
Fig. 3. The effect of voltage-gated K + channels on the membrane impedance
4.5 Nonlinear system analysis
For nonlinear systems the principle of superposition does not hold. Responses of neural
systems or components to one set of stimuli may not predict their responses to other
inputs (Rieke et al. 1995, van Hateren 1997, Lewen et al. 2001, Vickers et al. 2001,
Rinberg & Davidowitz 2002, Burton & Laughlin 2003, Chacron et al. 2003, Juusola & de
Polavieja 2003, Niven & Burrows 2003). For example, responses to white noise
stimulation of lateral geniculate nucleus neurons did not predict responses to naturalistic
stimuli (Dan et al. 1996). Kernels are a way to describe the pattern of the nonlinear

28
interaction among the past events with regard to the effect that this interaction has upon
the system response.
Nonlinear system identification in this study was based on estimating the kernels of a
Volterra series, K0, K1(u), K2(u,v), ... where u, v, ... are time lags (French & Marmarelis
1999) with light intensity as the input, x(t), as a function of time, t, and receptor potential
as the output, y(t).
∞ ∞ ∞
y( t) = K0 + ∫K1( u) x ( t − u) du + ∫∫K2(
u, v) x ( t −u) x ( t −v)
dudv
0 0 0
Several methods have been developed for kernel estimation. Earlier methods relied on
stimulating the unknown system with Gaussian white noise, but more recent methods
avoid this requirement (French & Marmarelis 1999). A completely general approach
based on the parallel cascade method (Korenberg 1991, Juusola et al. 2003) was used
having the linear filters of the cascades formed from Gaussian distributed random
numbers (French et al. 2001, Juusola et al. 2003). This method makes no initial
assumptions about the forms of the kernels or the nature of the input or output signals and
it can be applied to systems containing relatively high order of nonlinearities. However, it
is not necessary to construct all of the higher order kernels.
After kernel estimation, percentage mean square error (MSE) values (French &
Marmarelis 1999) were calculated for the zero and first-order kernels alone and for the
combined, zero-, first-, second and third-order kernels from:
2
(y(t) − y s(t))
MSE =
(17)
2 2
y(t) − (y(t))
where ys(t) is the Volterra series output and the bars indicate time averages. The kernel
estimates were used to predict the output of the nonlinear system to the input signal. All
predictions were based on recorded data that had not been used for system identification.
Based on the kernel analysis, a NLN (Nonlinear static-Linear dynamic-Nonlinear
static) cascade model (French et al. 1993) was developed to simulate the voltage
responses in Drosophila photoreceptors. The two nonlinear components were polynomial
functions and the linear component was the Wong and Knight photoreceptor model
(Wong et al. 1980):
1 ⎛ t ⎞
g(t) = ⎜ ⎟ e
n! τ ⎝τ ⎠
n
-t/ τNLN
NLN NLN
where n and τNLN are parameters to be fitted. To remove redundant parameters, only one
constant term was included in the model, as an offset in the output of the linear
component. Similarly, the first nonlinear component had a fixed first-order coefficient of
unity. The numbers of unknown parameters were therefore: N1-1 (first polynomial) + 3
(Wong and Knight model plus offset) + N2 (second polynomial), where N1 and N2 are the
order of the polynomials. The NLN cascade model was fitted by using the simulated
annealing method (Press et al. 1990). The first nonlinearity required a fifth-order
polynomial, whereas the second polynomial was third-order, giving a total count of 10
(16)
(18)

29
parameters. Nonlinear kernel analysis and NLN modelling were carried out in
collaboration with Prof. Andrew French (Department of Physiology and Biophysics,
Dalhousie University, Halifax, Nova Scotia, Canada).
4.6 Hodgkin-Huxley type photoreceptor models
A Hodgkin-Huxley type model of the photoreceptors was developed using MATLAB
software (Mathworks, USA). Photoreceptor models used in the original papers I-III
included Shaker and slow delayed rectifier voltage-gated potassium conductances, in
addition to K + and Cl - chloride leak conductances (the fast delayed rectifier conductance
was omitted because it is present only in some photoreceptors) (Hardie 1991a).
Photoreceptor models used in the original paper IV also included a slowly activating,
non-inactivating novel voltage-gated K + conductance and the partial failure of Shaker
channel inactivation (~11 %). The light-dependent conductance due to the
phototransduction cascade was modelled as an additional light leak conductance (light
adapted photoreceptors), as a simulation specific dynamic light conductance or as a
reconstructed light induced conductance (LIC; see 4.6.4). The electrical equivalent circuit
for the photoreceptor models is shown in Fig 4.
Fig. 4. Electrical circuit of the photoreceptor models. Abbreviations: Sh, Shaker channel; Dr,
delayed rectifier channel; Novel, novel K + channel; Kleak, potassium leak conductance; Cl,
chloride leak conductance; LIC, light gated conductance. The gNovel branch does not exist in
the photoreceptor models used in (I)-(III).
4.6.1 Voltage-dependent properties of Shaker, slow delayed rectifier and
novel noninactivating K + channels
Steady-state activation and inactivation curves for voltage-gated K + channels were fitted
with the Boltzmann function:
⎛ g ⎞ 1
⎜ ⎟=
⎝g⎠ 1+ e
∞
V50 −Vm
max s
(19)

30
where V50 is the voltage producing a steady-state conductance of 50 % of the maximum
value and s is the slope factor of the function. Steady-state activation and inactivation
curves for Shaker and slow delayed rectifier channels were obtained from previously
published data (Hardie 1991a, Hevers & Hardie 1995) (Figure 5a). The activation curve
for the novel voltage-gated K + conductance was fitted to experimental data from the
whole-cell recordings of Shaker 14 Shab 3 mutant photoreceptors (Figure 5b). The fraction
of Shaker channels failing to inactivate was determined from the whole-cell currents of
Shab 3 mutant photoreceptors (Fig 1c, IV).
Fig. 5. Steady-state activation and inactivation curves. (a) Shaker and slow delayed rectifier
(dashed line). (b) Experimental data points (star) and the fitted activation curve for the novel
K + conductance
The time constants of the activation and inactivation for the Shaker and slow delayed
rectifier channels were derived either from previously published data (Hardie 1991a,
Hevers & Hardie 1995) or from additional whole-cell recordings (I). The time constant of
activation for the novel K + conductance was derived from the whole-cell recordings of
Shaker 14 Shab 3 mutant photoreceptors (IV). Experimental data was fitted with the bell
shaped function:
1
τ= p (20)
2−Vm p p ( )
3 4⋅ p5 −Vm
p1⋅ e + p5−Vm p6
e −1
where pi are the free parameters for fitting (Fig. 6). The time constant of the slow delayed
rectifier inactivation is not significantly voltage-dependent (Hardie 1991a) and it was set
to 1200 ms in the model. All time constants were scaled down by a factor 1.35 (calculated
from the Q10 factor; (Juusola & Hardie 2001b), to take into account the temperature
difference between in vitro whole-cell (20 °C) and in vivo intracellular (25 °C)
recordings.

31
Fig. 6. Fitted activation and inactivation time constants for the experimental data (stars) (a)
Shaker activation, (b) Shaker inactivation, (c) Slow delayed rectifier activation, (d) Novel K +
conductance activation
Based on the original Hodgkin-Huxley formalism, following equations for the rate
constants, αk and βk were derived:
1
nk
⎡⎛g∞⎞ ⎤
(21)
⎢⎜ g ⎟
⎝ max ⎠
⎥
k
α
⎣ ⎦
k =
τk
( )
1
nk
⎡⎛g∞⎞ ⎤
⎢ g ⎥
⎣⎝ max ⎠k⎦
1−
⎜ ⎟
β k =
τ
k
here g∞g are the steady-state activation and inactivation curves of each voltage-
max k
gated conductance, nk and τk are the corresponding number of gating particles and the
time constants, respectively. Differential equations for the membrane voltage and gating
particles, in addition to the equation for the conductance, followed traditional Hodgkin-
Huxley formalism (equations (7)-(9), respectively). Parameters of the voltage-dependent
properties were fixed throughout the simulations and are given in Table 1.
(22)

32
Table 1. Voltage-dependent properties of the K + channels. Act and Inact refer to
activation and inactivation, respectively.
Variable
V50 (mV) -23.7
Shaker Shab Novel K + channel
Act Inact * Act Inact Act
1st -55.3
2nd -74.8
-1.0 -25.7 -14.0
S (mV) 12.8
1st -3.9
2nd -10.7
9.1 -6.4 10.6
n 3 1 2 1 1
* Shaker inactivation had two components
4.6.2 Derivation of the other model parameters
In the photoreceptor models, the maximum conductance for the voltage-gated K +
channels, the size of the leak conductances, the membrane capacitance and the current
input for the simulations are given as per area. To be able to compare the simulations with
the experiments, the value of the membrane area, Am, was defined. The membrane area
used in the model (1.571*10 -5 cm 2 ) was calculated according to average photoreceptor
dimensions (length 100 µm, diameter 5 µm).
The reversal potential for the potassium (-85 mV) and light leak conductances (+10
mV) were obtained from published data (Hardie 1991a, Reuss et al. 1997, Oberwinkler &
Stavenga 2000). The reversal potential for the Cl - leak conductance was obtained through
iteration (the reversal potential for the non-potassium leak and the sizes of these two
different leak conductances were adjusted until the experimental resting potential and
input resistance at rest were reproduced). A reversal potential of -30 mV was obtained,
which was concluded to represent the chloride ions (Hardie, unpublished data). The
reversal potentials of each ion and the membrane area were fixed parameters.
The properties of the photoreceptors, like the resting potential, the input resistance and
the capacitance of the cell, are highly variable from one recording to another. This is
because of the natural variability between the cells, but also because of the varying
quality of the experiments. All photoreceptor models were fitted based on the simulated
current injection experiments. To take into account the variation in photoreceptor
capacitance, first order exponentials were fitted to the voltage response of a small
hyperpolarising current injection and the specific membrane capacitance, cm, was
calculated with:
(23)
where τm is the membrane time constant, I the amplitude of current injection, Am the
membrane area and U the amplitude of the voltage response. The K + and Cl - τmI
cm
=
AmU leak
conductances were adjusted until experimental resting potential and input resistance
followed. The maximum conductance of each voltage-gated channel was adjusted to

33
reproduce the best fit with the experimental data. Exemplary values for these free
parameters are given in the Table 2.
Table 2. Example set of the free parameters.
Parameter Value
Resting potential -66 mV
Specific membrane capacitance * 4 µF/cm 2
Maximum Shaker conductance 0.8 mS/cm 2
Maximum Shab conductance 3.0 mS/cm 2
Maximum novel K + conductance 0.11 mS/cm 2
Potassium leak conductance 0.0855 mS/cm 2
Chloride leak conductance 0.0585 mS/cm 2
*
The contribution of the microvillar membrane is included in this parameter
4.6.3 MATLAB© implementation of the Hodgkin-Huxley type of
photoreceptor model
MATLAB © software provides all the basic and a vast variety of specialised functions (mfiles)
for example for the statistics, optimisation and signal processing. I used it as a
model development environment, because it also has efficient, in-built functions for
solving differential equations. As an example, m-files of the WT model used in current
injection simulations (Fig 4a, IV) are given in Appendix.
Normally, numerical integration of the differential equation models works well for the
smooth input (gradually changing, continuous derivatives). In this study it was necessary
to drive the models with highly irregular input, such as white noise. To ensure that the
models could be driven with these dynamic inputs, all the voltage-gated conductances
were set to zero thereby reducing the model to an analytically solvable RC-circuit.
Comparison of the simulations with the exact solution of the RC-circuit (step response
and frequency response function) validated that the numerical methods used for
simulations did not introduce significant errors.
4.6.4 Reconstruction of the light induced conductance
Assuming that the photo-insensitive membrane of the photoreceptor is accurately
modelled, it is possible to use the model for reconstructing the light induced conductance
(LIC) from the corresponding experimental voltage response. Although the voltagedependent
properties of the K + channels are characterized in darkness, these properties
were assumed to be insensitive to light. This was justified both by the comparison of
simulated voltage responses to current stimuli with experimental data, and by the
experimental results from Calliphora vicina photoreceptors (Weckström et al. 1991).

34
The absorption of a single photon happens in an all-or-none fashion, causing opening
of light-dependent channels followed by the influx of calcium and sodium ions in a
microvillus. This leads to rapid changes in ionic concentrations due to the small volume
of the microvillus. During light stimulation the photon flux activates numerous
microvilli, causing dynamic reversal potential fluctuations for the LIC in each microvillus
as it receives photons. These fluctuations were assumed to be independent, averaging to
the reversal potential of +10 mV (Reuss et al. 1997, Oberwinkler & Stavenga 2000).
Using this reversal potential, the LIC was modelled as a single conductance input to the
photo-insensitive membrane. This conductance was used to drive the model and its values
were iterated at each sample point until the experimental voltage response was
reproduced. A schematic presentation of the reconstruction procedure is shown in Fig. 6b
(IV) and the corresponding model m-files are given in the Appendix.
Predicted LICs always produced voltage responses that closely matched experimental
data. Small discrepancies were observed in simulations with the reconstructed LIC used
in the naturalistic stimuli simulations during the periods of darkness preceded by high
light intensities (Fig. 2, III). In such conditions, the experimental data contains clear afterhyperpolarisations,
as well as small depolarisations preceding the afterhyperpolarisations.
These are caused by the Na + /K + ATPase and the 3Na + /Ca 2+ exchanger
currents, respectively (Gerster 1997, Gerster et al. 1997, Oberwinkler & Stavenga 2000).
These discrepancies were concluded not to affect the results, based on their small size and
the nonlinear analysis (III).
4.6.5 Model simulations
To simulate the current injection experiments (for example, Fig. 4, I), models were driven
with the experimental current stimuli divided by the photoreceptor membrane area.
Modelling enabled the monitoring of each individual conductance during the simulations.
This feature was used to separate the effect of each voltage-gated conductance to the
voltage response (I-IV). Impedance functions for the models were determined by using
band-limited Gaussian white noise current input that was filtered by a fourth-order
Butterworth low pass filter with 500 Hz corner frequency (I). The frequency band of this
input was the same as in the experiments and it exceeds that of the photoreceptors
(Juusola & Hardie 2001a). The current-voltage (I-V) relationships for the models in (IV)
were determined by driving them with 70 evenly spaced, 100 ms current pulses, ranging
from -0.15 nA to 0.4 nA and sampling the membrane voltage at the end of each pulse.
To simulate photoreceptor responses in the light adaptation, light dependent leak was
added until the same amount of depolarization was achieved as in the experiments. The
log-normal shape of the light conductance pulses used in (I) and (II) were fitted to
experimentally derived light impulse responses and the size of the pulses was adjusted so
that the largest conductance pulse produced a saturated voltage response having
amplitude similar to those in the experiments (Juusola & Hardie 2001a). For the LICvoltage
(LIC-V) relationships in (IV), 100 ms LIC pulses of increasing amplitude were
used as the model input and the corresponding voltages were measured relative to the
dark resting potential and normalized by the amplitude of the saturating maximal

35
response. The simulated naturalistic stimuli experiments (III) and the determination of the
contrast gain (frequency response function between the white noise modulated light
contrast and the voltage response) for the photoreceptor models were carried out by using
the reconstructed LIC (IV).
In addition to experimentally fitted photoreceptor models, additional hypothetical
membrane models were also used in (I) and (IV). In (I) the hypothetical WT without
Shaker membrane model was used to study the effect of the Shaker inactivation to the
amplification observed in the impedance function (I, supplementary material). In (IV)
two hypothetical membrane models, WT with 30% Shab and WT without Shab, were
generated to investigate the role of regulation of the electrical properties of the photoinsensitive
membrane of Shab mutant photoreceptors.
4.6.6 Estimation of the metabolic costs
To estimate the metabolic costs, the electrical circuit model (Fig. 4) was extended to
include the Na + /K + ATPase and the Na + /K + /2Cl - co-transporter (Fig. 1, II). The activity of
the Na + /K + ATPase, the pump current (IP), determines the cost of maintaining the internal
K + concentration and external Na + concentration. A Na + /K + /2Cl - co-transporter, the
probable Cl - accumulating mechanism in neurones (Delpire 2000), maintains the internal
Cl - concentration. A fraction of the LIC (~20%) is carried by calcium ions (40% of the
current), which are exchanged in a 1:3 ratio for sodium ions by the Na + /Ca 2+ exchanger
(Reuss et al. 1997, Oberwinkler & Stavenga 2000). The Na + /K + ATPase hydrolyses one
ATP molecule for every three Na + ions expelled and two K + ions imported. Thus, if the
pump maintains the concentrations of these ions across the cell membrane, the pump
current can be derived from individual currents in the electrical circuit:
1 1
IP= ( IKSh+ IKdr + IKleak ) − IClleak
(24)
2 4
Since the membrane potential is stable in long term, the sum of all currents across the
model membrane must eventually equal zero:
IKSh + IKdr + IKleak + IClleak + IP+ ILIC= 0
These currents were adjusted to satisfy equation (25) using a simplex algorithm (function
called fminsearch in MATLAB © ) to minimise the changes for each current. Using these
adjusted values, the estimated number of ATP molecules hydrolysed per second can be
calculated:
ATP IN P A =
s F
(25)
(26)

36
The number of ATP molecules per bit of information was calculated by dividing the
estimated number of ATP molecules hydrolysed per second by the measured information
capacity, C (bits/s):
ATP IN P A F
=
bit C
(27)

5 Summary of the results in the original papers
5.1 The contribution of Shaker K + channels to the information
capacity of Drosophila photoreceptors (I)
The performance of a photoreceptor in coding a light signal may be quantitatively
described by its sensitivity, signal-to-noise ratio and frequency response, enabling
specific components of the signalling machinery, including ion channels, to be related to
specific aspects of cellular function (Weckström & Laughlin 1995). These quantitative
measures, combined with a mathematical model of the photoreceptors were used to
assess the contribution of the Shaker K + -conductance to photoreceptor performance.
The signalling efficiency of photoreceptors in wild type (WT) and Shaker 14 flies, was
studied by presenting sequences of dynamically modulated light with a mean contrast of
0.32, close to that of natural sceneries (Laughlin 1981), over the range of light intensities
to which the photoreceptors are normally exposed (Fig. 1B, I). The basic properties of the
phototransduction process were determined to be unaffected in Shaker mutant
photoreceptors. At all light background intensities, WT flies responded with a larger
signal (measured as the signal variance) than Shaker 14 flies (Fig. 1I, I). There was no
significant difference in the noise variance between Shaker 14 and WT flies over all light
intensities (p

38
induced by current injection opens additional Shaker channels that inactivate rapidly,
thereby increasing the membrane resistance beyond the resting value and producing a
larger voltage response to the same current step. The loss of the Shaker conductance
would be expected to result in a higher input resistance at rest, however, Shaker 14
photoreceptors had reduced resistances compared to those of WT photoreceptors
(Shaker 14 , 225 ± 26 MΩ at -64.3 ± 5.4 mV, N=13; WT, 411 ± 34 MΩ at -68.1 ± 3.2 mV,
N=21). Increase in the leak conductance was used to model the decrease in the Shaker 14
photoreceptor input resistance (Fig. 4H, I).
The input resistance affects the photoreceptor’s current to voltage gain. The
biophysical properties of the Shaker channels should lead to an increase in the spread of
the signal across the photoreceptor voltage range. The spread of the voltage responses of
the Shaker 14 photoreceptor was compressed compared to those of the WT, suggesting that
the WT photoreceptors were using the available voltage range more fully than Shaker 14
photoreceptors. Varying the size of the leak conductance in the WT and Shaker 14
photoreceptor models showed that the amount of leak conductance found experimentally,
i.e., the input resistance of the both photoreceptor types, optimised the available voltage
ranges (Fig. 5C,D; I).
5.2 Metabolic cost of Shaker K + channels in Drosophila
photoreceptors (II)
The contribution of the Shaker conductance to the cost of neural information was
estimated by comparing wild type (WT) and Shaker mutant photoreceptors. The currents
flowing through the ion channels either in steady-state or during light stimulation were
estimated with the Hodgkin-Huxley type of model (I). These currents were subsequently
used to derive metabolic costs by using an electrical circuit model of the photoreceptors
that also included the Na + /K + pump and the Na + /K + /2Cl - co-transporter (Fig. 2, II). The
estimated cost of maintaining the ionic gradients in both dark and light conditions was
greater in Shaker mutant than in the WT (Table 1, II). The increased rate of ATP
hydrolysis in Shaker photoreceptors coupled with their reduced information capacity led
to a ~2-fold increase in their bit cost when compared to their WT counterparts. The
calculated bit costs may be an underestimate for the Drosophila photoreceptors during
natural stimuli because of the lower information transmission rates and the energy
required for early steps in phototransduction (e.g., phosphorylation or amplification)
(Laughlin et al. 1998, Hardie 2001, Juusola & de Polavieja 2003). However, similar
calculations for Calliphora vicina photoreceptors (Laughlin et al. 1998) produce
estimates of metabolic cost close to experimentally determined values (Hamdorf et al.
1988), indicating that the estimates of the bit cost were valid.
The increased bit cost in Shaker 14 photoreceptors was due to reduced input resistance
following from the loss of the Shaker channels. In (I) the amount of leak conductance in
the model needed to reproduce the experimentally determined input resistances were
shown to maximise the available voltage range in Shaker 14 and WT photoreceptors. The
metabolic cost may also be an important factor affecting the regulation of the input
resistance. Both Shaker 14 and WT photoreceptors were optimised in terms of metabolic

39
cost and available voltage range (Fig. 2, II), however, WT photoreceptors incurred a
lower metabolic cost due to the Shaker conductance.
5.3 Interactions between light-induced currents, voltage-gated
currents, and input signal properties in Drosophila photoreceptors
(III)
In vivo intracellular recordings from WT and Shaker 14 photoreceptors were carried out
while presenting light modulated by a Natural Time Series of Intensities (NTSIs). The
naturalistic stimuli contained periods of both very low and high light intensity that were
reflected in the voltage responses of both the WT and mutant photoreceptors (Fig. 1A,
III). Differences in the voltage responses over the entire stimulus sequences are shown in
the response histograms (Fig. 1C, III), and the cumulative frequency distributions of
these histograms (Fig. 1D, III), which demonstrate that the voltage response of WT
photoreceptors was spread over a greater voltage range than the mutant.
A nonlinear analysis was used to characterize the effects of ion channels upon natural
stimulus coding in Drosophila photoreceptors (Figs. 2-4, III). First-order kernels, K1(u),
derived from WT and Shaker 14 voltage responses to naturalistic stimuli had the same
general form as flash responses in light-adapted Drosophila photoreceptors (Fig. 3A, III;
(Juusola & Hardie 2001a). All of the first-order kernels had a delay of approximately
6 ms, but the kernels derived from Shaker 14 voltage responses consistently were larger,
had faster time-to-peak (approximately 3-4 ms) and narrower half-width than those from
WT (Fig. 3A, III). These differences may be explained, at least partially, by the presence
or absence of Shaker channels. An increasing light intensity depolarizes WT
photoreceptors, rapidly activates Shaker channels, which partially shunts the LIC through
the increased membrane conductance. The Shaker K + channels then rapidly inactivate,
amplifying the effect of the LIC at later times in the photoreceptor voltage response.
Second-order kernels, K2(u,v), had positive peaks on the diagonals, having approximately
the same time courses as the first-order kernels (Fig. 3D,E, III).
The pattern of kernel forms suggested that the WT and Shaker 14 photoreceptor
responses could be described by a model in which a dynamic linear filter is followed by a
static nonlinearity (Korenberg & Hunter 1986, French & Korenberg 1989). The NLN
model was developed with a ‘Wong and Knight’ or gamma function model of
phototransduction (Wong et al. 1980) as the linear dynamic component surrounded by
two static nonlinearities (Figs. 2, 4, III). Shaker 14 photoreceptors differed most strongly
from WT photoreceptors in the second and third stages of the NLN model (Fig. 4, Table
2; III). The first static nonlinearity was a positive rectification and the linear components
were very similar to first-order Volterra kernels. The final static nonlinearity always had a
region of zero, or negative slope in the middle of an overall positive characteristic,
corresponding to an intermediate region where increasing light intensity produced no
change, or a slight hyperpolarisation, in the membrane potential. In Shaker 14
photoreceptors this effect occurred over a smaller stimulus range and at lower stimulus
levels, corresponding to less depolarized membrane potentials.

40
The Hodgkin-Huxley type models of the WT and Shaker 14 photoreceptors were used
to determine if possible differences in the LIC or voltage-gated K + channels contribute to
the observed differences between WT and Shaker 14 responses. These models were used to
reconstruct currents generated by the LIC, slow delayed rectifier currents and, in WT
photoreceptors, the Shaker current to the NTSI stimulus (Fig. 5A, D, F; III). Volterra
kernels between the naturalistic light stimulus and the LIC were calculated (Fig. 6, Table
3; III). Comparison of LIC kernels showed that the kernel of the Shaker mutant was
larger and faster than that of WT, which was also true for Volterra kernels from the
responses (Fig. 3, III). Similarity between the LIC and voltage response kernels suggests
that the LIC dominates the dynamic response.
The NLN model was developed also for the LIC (Fig. 7, Table 4; III). As for the
Volterra kernels, the linear Wong and Knight component, which may represent LIC
generation, was larger and had a faster time-to-peak in Shaker mutant photoreceptors
suggesting possible differences in the LIC of the two phenotypes. Association of the final
nonlinearity with the photo-insensitive membrane was supported by comparison of WT
and Shaker 14 NLN models for the LIC with those of the voltage response. The final
nonlinearity contains significant differences in the NLN models of the voltage responses
that are absent in the NLN models of the LICs suggesting that the final nonlinearity is
most affected by the properties of the photo-insensitive membrane.
Comparison of the slow delayed rectifier currents from WT and Shaker 14 models
revealed that in the absence of the Shaker current there was a marked increase in the slow
delayed rectifier current (Fig. 5D-G, III). Additionally, in WT the delayed rectifier current
was slower than in the Shaker 14 mutant (Fig. 5G, III). The Shaker channels effectively
shunt the photoreceptor currents, not only reducing the overall size of the slow delayed
rectifier current but also changing the time course of activation.
5.4 Role of Shab K + channels in the information processing of
Drosophila photoreceptors (IV)
Voltage clamp recordings of isolated photoreceptors from Shab 3 flies were performed to
show that the slow delayed rectifier was encoded by the Shab gene in Drosophila
photoreceptors. To ensure that mutation of the Shab gene did not affect photoreceptor
morphology we illuminated the photoreceptors antidromically to determine the structure
and spacing of their rhabdomeres. Each Shab 3 ommatidium contained a standard
configuration of photoreceptors with normal rhabdoms, and the phototransduction
cascade was shown to be unaffected in the mutant (Fig. 1, IV).
In vivo current injection experiments showed that Shab 3 photoreceptors had different
passive membrane properties from those of the WT (Fig. 2A,D; IV). As in the previous
studies (I-III), Hodgkin-Huxley type modelling was used to isolate the effect of the Shab
channels on the photo-insensitive membrane properties. Comparison between the model
simulations and the experimental Shab 3 photoreceptor responses suggested that, in
addition to changes in the passive membrane properties, an additional voltage-gated
conductance was present. To isolate this conductance, currents were recorded from
Shaker 14 Shab 3 double mutant photoreceptors in whole cell patch-clamp. In some

41
Shaker 14 Shab 3 double mutant photoreceptors the fast delayed rectifier voltage-gated
potassium current was present, showing that it was not encoded by the Shab gene (Fig.
3A, IV). An additional, novel, slowly activating, non-inactivating potassium current was
also present in Shaker 14 Shab 3 photoreceptors (Fig. 3A, IV) and, in those photoreceptors
lacking the fast delayed rectifier, appeared to be the only remaining voltage-gated
potassium current (Fig. 3B, IV). The voltage-dependent properties of this conductance
were characterized (Fig. 3C-E, IV) and it was incorporated into the photoreceptor
models. Close examination of Shab 3 photoreceptor whole cell currents (Fig. 1C, IV)
revealed a component that was not due to the novel voltage-gated K + conductance (Fig.
3A,B; IV). These residual currents followed from partial failure of the Shaker channel
inactivation (~11%), a feature, which was also incorporated to the models.
The I-V relationships of the WT and Shab mutant photoreceptors were simulated to
investigate if the altered passive membrane properties contribute to the maintenance of
the electrical properties. To model the changes in the passive membrane, an increase in
the leak conductances in the Shab photoreceptor models was needed to reproduce the
corresponding experimental data. The I-V relationships of the Shab photoreceptor models
were shown to closely match those of the WT over the physiological voltage range (-70
mV to -15 mV) (Fig. 4C-F, IV).
To quantify the reduction in input resistance suggested by the increased leak
conductances in the models, the mean input resistances in dark for the WT, Shab 1 and
Shab 3 flies were calculated (Fig. 5A, IV). Shab 1 and Shab 3 photoreceptors had
significantly reduced input resistances (-54% and -59% respectively), although Shab
channels are not activated at the photoreceptor resting potential (-66 mV). Photoreceptor
models were used to predict the corresponding input resistances in fully light-adapted
photoreceptors at -40 mV (Fig. 5A, IV). The Shab 1 and Shab 3 photoreceptor input
resistances in light were close to that of the WT photoreceptor despite the large
differences in the dark. Therefore, the light-voltage relationship of the WT, Shab 1 and
Shab 3 photoreceptors were compared over a wide range of light intensities. Over all
adapting light backgrounds, the mean steady-state membrane potentials of WT, Shab 1 and
Shab 3 photoreceptors showed a similar light dependency and were not significantly
different (Fig. 5B, IV).
The LIC input-voltage output relationships of the Shab 1 and Shab 3 photoreceptor
models as well as those of their hypothetical counterparts (reduced Shab conductance but
passive membrane properties same as in the WT models) were determined to study how
regulation of the electrical properties of the photo-insensitive membrane contribute to the
observed robustness in the light-voltage relationship (Fig. 5B, IV). In contrast to the
hypothetical models, the LIC-voltage relationships of the experimentally fitted ones
intersected with that of the WT at a LIC value producing a voltage response 50% of the
maximum (Fig. 5D, IV). Comparison of WT with the Shab 1 and Shab 3 photoreceptor
LIC-voltage relationships showed that the voltage-dependent Shab conductance produces
a more efficient use of the available voltage range compared to the voltage-independent
leak conductances used to model the regulatory reduction in the input resistance (Fig. 5D,
IV). However, due to this regulation, both Shab 1 and Shab 3 photoreceptors have an
increased spread of the voltages due to the LIC over the available voltage range in
comparison to their respective hypothetical models (Fig. 5C, IV).

42
The voltage responses of WT, Shab 1 and Shab 3 photoreceptors were recorded whilst
presenting repetitions of the white noise modulated light stimulus sequence to determine
how changes in the photo-insensitive membrane of the Shab mutant photoreceptors affect
the processing of dynamically fluctuating light stimuli. The LIC was reconstructed from
the Shab 3 photoreceptor recordings and used to determine the contrast gains of the WT,
Shab 1 and Shab 3 models. These contrast gains closely matched those of the
experimentally determined ones (Fig. 6D,E; IV), showing that regulation of the electrical
properties enables maintenance of the contrast gain in Shab 1 and Shab 3 photoreceptors.
Photoreceptor performance is constrained not only by signal gain but also by the
noise. To quantify the reliability of contrast coding, the mean information capacity of the
WT, Shab 1 and Shab 3 photoreceptors was calculated over the range of light intensity
backgrounds (Fig. 7C, IV). The mean information capacities were similar over almost all
light intensities for the WT, Shab 1 and Shab 3 photoreceptors. In particular, the
convergence of information capacities in high light intensities where changes in the
photo-insensitive membrane were shown to maintain light-voltage relationships in Shab
mutants (Fig 5, IV), demonstrates the robustness of contrast coding Drosophila
photoreceptors.

6 Discussion
6.1 Modelling of Drosophila photoreceptors
The Hodgkin-Huxley type of models used in this study are shown to be capable for
reproducing the experimentally determined photoreceptor responses, which justifies their
essential role in providing evidence for the conclusions presented. However, there are
limitations with this modelling approach that one has to consider. Hodgkin-Huxley type
of models are macroscopic descriptions of the ion channels on the isopotential cell
membrane, in contrast to the stochastic state-variable or electrically coupled
compartmental models (Koch 1999, Hille 2001). Stochastic modelling was not used
because of the success of the macroscopic approach in addition to the drastically
increased complexity and computational burden of stochastic models. Can Drosophila
photoreceptors be assumed as isopotential cells?
The photo-sensitive membrane of the Drosophila photoreceptor is formed from tightly
packed tubular microvilli (Fig 2) (Hardie & Raghu 2001). Despite of their small
dimensions, microvilli are shown to be electrically well coupled to the cell body (Postma
et al. 1999). Photoreceptors also have a relatively short axon lacking the sodium spike
generation. However, in vitro experiments have shown that the voltage-gated potassium
channels are located in the cell body membrane. This excludes the most common source
of inaccuracies in the Hodgkin-Huxley type of models, the errors in voltage dependent
channel properties due to the poor space clamp. The photoreceptor axons may still
possess different types of voltage-gated ion channels (Weckström et al. 1992). These
channels could potentially affect the voltage signals generated in the cell body, but based
on the experimental data and the model simulations this effect is very subtle and unlikely
to affect the results of this study.
The phototransduction and the concurrent generation of the currents due to the LIC
were not explicitly modelled in this study, although experimental data needed for
developing a detailed model has been accumulating during the recent years (Hardie 2001,
Hardie 2003). This restriction was kept in mind while planning the simulations to avoid
misinterpretations caused by inadequate modelling. In (III-IV) it was circumvented by
reconstructing the LIC from in vivo voltage responses.

44
6.2 K + channels in Drosophila photoreceptors
Drosophila photoreceptors can be assumed to be tuned during evolution according to
their visual ecology by adjusting the properties of the phototransduction and by matching
the photo-insensitive membrane to the transduced currents with voltage-gated K +
channels (Weckström & Laughlin 1995). The biophysical properties of these channels
determine their role in processing the voltage signals. Shaker channels activate rapidly in
voltages near the resting potential, followed by the fast inactivation. Therefore, Shaker
channels selectively attenuate the transient signal components while amplifying the
slower ones, which effectively spreads responses over the available voltage range (I).
Photoreceptors generate a maintained depolarization in response to increasing light
intensity. Due to their voltage dependency (Hardie 1991a, Hevers & Hardie 1995), Shab
channels open at high light intensities, thereby attenuating the light-induced
depolarization and preventing response saturation. Activation of Shab channels also
reduces the membrane time constant of the Drosophila photoreceptors allowing them to
encode faster events (IV).
Further insight into the role of each type of ion channel in Drosophila photoreceptors
may come from identification of the genes encoding fast delayed rectifier and novel K +
channels. It is shown that the novel non-inactivating K + channels and the fast delayed
rectifier channels are not encoded by either Shab or Shaker (IV) and are likely to be
formed from separate gene products, not heteromultimers (Covarrubias et al. 1991). The
most likely candidates are the remaining two members of the Shaker-like gene family in
Drosophila, Shal and Shaw (Butler et al. 1989, Wei et al. 1990). In vitro characterization
of these channels suggests that Shaw encodes non-inactivating potassium channel whilst
Shal encodes a fast activating-fast inactivating channel, which have similar kinetics to the
novel conductance and the fast delayed rectifier, respectively (Butler et al. 1989, Wei et
al. 1990).
6.3 The robustness of neural coding in Drosophila photoreceptors
The regulatory changes in other ion channels or in the passive membrane properties
following from imposed changes in the channel composition may be required for normal
neural function and could potentially ensure that neurons maintain relatively robust
response characteristics despite variable levels of channel expression (I, IV, (Goldman et
al. 2001, Marder & Prinz 2002, Niven 2004). The regulatory changes may also provide
insight to the function of the channel affected by the mutation. A decrease in the input
resistance of the Shaker mutant photoreceptors may compensate for the compressed
voltage range following from the mutation (I). Shab channels activate in depolarized
voltages being dominant K + conductance in light. Reduced input resistance of the Shab
mutant photoreceptors maintained a similar operating voltage, sensitivity and contrast
coding in light as the WT photoreceptors (IV). Although these changes for both the Shab
and Shaker mutant photoreceptors significantly improved their performance (I, IV),
several clear disadvantages may follow from loss of the voltage-gated channels. Both
Shaker and Shab mutant photoreceptors show a compressed voltage-range available for

45
coding the variations in light intensity. This may result in impaired performance in coding
the natural sceneries, which contain fast and large intensity fluctuations (III) (van Hateren
1997). The reduced input resistance is also energetically more expensive, especially at
rest, than the voltage-gated channels, which activate during the signalling events (II,
(Laughlin et al. 1998, Laughlin 2001).
What could be the nature of the regulatory mechanism decreasing the input resistance
in Drosophila photoreceptors? Regulation of the composition of ion channels of a neuron
was originally shown to be produced by learning tasks (Brons & Woody 1980, Alkon
1984, Moyer et al. 1996, Antonov et al. 2001). Subsequent studies in both invertebrate
and vertebrate neurons have demonstrated activity-dependent regulation of their electrical
properties taking place in hours to days after imposed changes in their activity
(LeMasson et al. 1993, Turrigiano et al. 1994, Turrigiano et al. 1995, Desai et al. 1999,
Golowasch et al. 1999, Aizenman et al. 2003). Persistent changes in electrical properties
can also be induced rapidly (Aizenman & Linden 2000) and in a graded manner for both
increases and decreases in activity (Egorov et al. 2002, Nelson et al. 2003). Recently, an
activity-independent mechanism was reported to take place in the absence of significant
changes in physiological activity (MacLean et al. 2003). Activity-dependent regulation is
thought to be mediated by changes in gene transcription (MacLean et al. 2003), whereas
the activity-independent regulation was suggested to be controlled by a
posttranscriptional mechanism. The results of this study show regulatory changes in
Shab 3 photoreceptors (IV), a null mutation of the Shab channels (Hegde et al. 1999);
Shab 1 and Shab 2 photoreceptors (IV), missense mutations of the Shab channels (Hegde et
al. 1999); as well as in the Shaker 14 photoreceptors (I), a null mutation producing
nonfunctional Shaker channels (Kaplan & Trout 1961, Salkoff & Wyman 1981). These
results suggest that the change in ion channel function would be sufficient to cause
concurrent regulation of the electrical properties. Therefore, by using the established
terminology, the regulation is activity-dependent in the Drosophila photoreceptors.
What could be the possible neuronal mechanism behind the decrease in the input
resistance? The decrease in the input resistances was modelled by increased leak
conductances. In Hodgkin-Huxley type of models the leak conductances are routinely
used to cover all the undefined processes to fit these models to the experimental data.
Thus, leak conductances can be considered as a descriptive representation of several
possible neuronal mechanisms, although a recent study demonstrated a maintenance of
the electrical properties by the compensatory increase in K + leak conductance in
celebellar granule cells after genetically removing a tonic synaptic conductance (Brickley
et al. 2001). If the leak conductances used in the modelling have cellular counterparts or
if they describe a more complicated process, remains to be determined in the future
works.
How could the regulation of the electrical properties be signalled in the Drosophila
photoreceptors? During a neuron’s development, a sequential acquisition of the
expression of different ion channel types may depend on the intracellular Ca 2+ that is
associated with spontaneous activity (Gu & Spitzer 1997). Substantial theoretical and
experimental evidence of Ca 2+ dependent regulation also in mature neurons makes Ca 2+ a
prime candidate for the induction mechanism of the robustness in electrical properties
(Zhang & Linden 2003). In Drosophila photoreceptors, 40% of current generated by the
LIC is carried by Ca 2+ ions leading to concentration changes in the cell body (Reuss et al.

46
1997, Postma et al. 1999, Hardie 2001). The logarithm of increase in cytosolic Ca 2+
concentration in the cell body has been shown to be linear with the logarithm of the light
intensity in vivo in Calliphora vicina photoreceptors (Oberwinkler & Stavenga 1998) and
similar concentrations have also been determined in vitro in Drosophila photoreceptors
(Hardie 1996). The changes in the K + conductance without a concurrent decrease in the
input resistance would alter the light-voltage relationship, potentially leading to changes
in the Ca 2+ concentration (I, IV). Changes in Ca 2+ concentrations could modify the
voltage-dependent properties of the ion channels through phosphorylation or direct
modulation by the calcium (Zhang & Linden 2003), or it could regulate their expression.
Therefore, Ca 2+ is suggested to play an essential role in the regulatory signalling of the
electrical properties.
6.4 Naturalistic stimulus
Natural visual inputs often contain strong temporal and spatial correlations, as well as
large intensity fluctuations (Burton & Moorhead 1981, Srinivasan et al. 1982, Field 1987,
Tolhurst et al. 1992, Ruderman & Bialek 1994) that may cause sparse, brief, intense
firing events (Vinje & Gallant 2000, Reinagel 2001, Vinje & Gallant 2002), and activate
components such as ion channels that strongly influence neural coding. However, sensory
systems are usually investigated using simpler, easily characterised stimuli, such as
pulses, steps or white noise (Zettler 1969, Laughlin 1978, French 1980, Juusola et al.
1994, Juusola & Hardie 2001a). These experiments have yielded considerable insights
into sensory systems but are unlikely to predict responses to natural stimuli.
Nonlinear analysis of the voltage responses of WT and Shaker mutant photoreceptors
to the naturalistic stimuli produced results that differed from those for white noise stimuli
published previously (I), (Juusola et al. 2003), suggesting that Shaker channels behave
differently under different stimulus regimes (Fig. 3, III). Differences between kernels
derived from naturalistic and white noise stimuli are due to the stimulus structure.
Naturalistic stimuli can contain prolonged dark periods interspersed with periods of high
light intensity, evoking large fluctuations in photoreceptor voltage (van Hateren 1997),
whereas dark and bright periods in band-limited Gaussian white noise stimuli of similar
duration are typically brief, allowing photoreceptor responses to be modulated around a
relatively constant mean voltage. Shaker channels behave differently under these two
stimulation regimes because their prominent activation and inactivation during voltage
transients are reduced by maintained depolarization.
The results in (III) suggest that mutation of the Shaker channels might affect the
currents generated by the LIC through a feedback mechanism. Such feedback could occur
due to changes in Ca 2+ concentration as discussed in 6.3. However, bump generation was
found to be unaffected in the Shaker 14 photoreceptors. Individual bumps are responses to
single photons, whereas the nonlinear analysis and modelling in (III) was done for the
responses to ~10 6 photons/s or more (III). As mean light intensity increases, average
bump size decreases markedly and time course is reduced (Wu & Pak 1975, Juusola &
Hardie 2001a). These changes in bump waveform may be due to Ca 2+ mediated
adaptation (Henderson et al. 2000), which is a feature of many invertebrate and

47
vertebrate photoreceptors (Hardie & Minke 1995, Montell 1999, Pugh et al. 1999, Burns
& Baylor 2001, Fain et al. 2001). Changes in light and dark adaptation mediated by Ca 2+
have been proposed to explain differences between photoreceptor responses within an
individual compound eye (Burton et al. 2001). Therefore, the changes in the currents
generated by the LIC could possibly follow from the altered dynamics in light adaptation.
This would extend previous findings that activity of the phototransduction cascade may
alter photoreceptor membrane properties (Burton 2002, Wolfram & Juusola 2004) by
showing that these interactions may be bidirectional.
As in the Shaker photoreceptors, Shab mutant photoreceptors may also respond
differently in the naturalistic stimuli regime. Indeed, the faster and larger impulse
responses in light adapted Shab 3 mutants could provide an explanation for the increased
high frequency content in the contrast gain (Fig 6D, IV). However, an in-depth study of a
possible tuning of the LIC properties after imposed changes in the photo-insensitive
membrane is needed to test the hypothesis and it remains to be investigated in future
works.
6.5 Efficiency of neural coding
The efficient expenditure of a limited energy budget is a major factor influencing all
aspects of animal design, therefore, energy is thought to have been an important
constraint upon the evolution of nervous systems (Laughlin 2001), including that of
humans (Aiello & Wheeler 1995). Potentially, energetic costs could limit absolute
numbers of neurones and synaptic connections (information channels) in the brain
(Laughlin et al. 1998), and influence the expression and distribution of ion channels and
second messenger pathways in individual neurones. Indeed, the human brain utilizes
energy at close to 20 Watts, accounting for 20% of the resting oxygen consumption of the
human body (Kety 1957), of which over half is required to fuel ion pumps (Ames 1997).
The success of an individual also depends upon accurately determining and executing
appropriate behaviour. Nervous systems are, therefore, also constrained by the need to
extract biologically germane, reliable information from the environment to generate such
adaptive behaviour (Meister & Berry 1999, de Polavieja 2002). The need for reliability,
in the presence of noise, constrains information processing in nervous systems setting
lower limits for the numbers of neurones and synaptic connections (Laughlin et al. 1998)
and influencing neuronal design. Although metabolic energy is clearly important in
determining neural function, the basic data on the quantitative relationships between
energy and information is lacking for the nervous system. Precisely how much energy
must a neuron consume to do a given amount of useful work, transmitting and processing
information? How does energy consumption scale with the quantity of information that
neurons handle?
Metabolic efficiency will only be an important determinant of the evolution and design
of a signalling system when metabolic costs impose a significant penalty on the parent
organism. The estimates of photoreceptor ATP consumption in this study compares with a
figure for the human brain that is widely considered to be significant and could have
shaped its evolution (Kety 1957, Laughlin 2001). The significance of retinal ATP

48
consumption is reinforced by comparative studies. Calliphora vicina photoreceptors
consume more energy, gram for gram, than active mammalian muscle (Laughlin et al.
1998).
Understanding the relationship between individual conductances and the metabolic
cost of information may also elucidate the function of other components in neural
signalling such as neuromodulators. For example, serotonin positively shifts the voltage
range of Shaker and Shab channels in Drosophila photoreceptors so that they are
completely inactive at rest (Hevers & Hardie 1995). This would remove a large
proportion of the K + conductance in the WT photoreceptors in the dark, significantly
reducing the metabolic cost of maintaining the resting potential. However, the shifted
voltage range would increase the metabolic cost of information at high light intensities,
suggesting serotonin should be released at night to minimize metabolic cost. Thus,
metabolic cost may be an important factor not only in determining which combinations of
ion channels are expressed in particular neurones but also in the plasticity within the
properties of these ion channels.
6.6 Relevance of the findings
This study is a systematic survey on how voltage-gated K + channels contribute to the
efficiency of neural processing in Drosophila photoreceptors. The functions discovered
are likely to be widespread in processing graded signals in sensory receptors and post
synaptic potentials in both vertebrates (Rudy 1988, Sheng et al. 1993, Wang et al. 1993,
Debanne et al. 1997, Hoffman et al. 1997, Magee et al. 1998, Coetzee et al. 1999) and
invertebrates (Connor & Stevens 1971, Laurent 1990, Hardie 1991a, Weckström &
Laughlin 1995).
This study also shows how regulatory changes in the electrical properties can restore
certain aspects of function after imposed changes to the ion channel composition. One
possible objective for these changes may be to maintain the operating point of the
Drosophila photoreceptors (I, IV). This would be well in accordance with the hypothesis
that regulation of the electrical properties could maximize information storage by keeping
the dynamic range of signalling within useful limits (Stemmler & Koch 1999, Turrigiano
& Nelson 2004).
Results of this study demonstrate the importance of the voltage-gated K + channels for
neural coding precision and highlight the effect of regulatory changes in the electrical
properties upon neuronal information processing. I believe this study improves our
understanding of the role of K + channels in neuronal signalling and provides new insight
on how the remarkable robustness of neuronal systems may be achieved.

7 Conclusions
1. Biophysical properties of the voltage-gated K + channels determine their role in
shaping the voltage signals in Drosophila photoreceptors. Shaker channels attenuate
the fast transients and amplify the slower signal components spreading the signals
efficiently over the available voltage range (I).
2. Shab channels activate at high light intensities, thereby attenuating the light-induced
depolarization and preventing response saturation. Activation of Shab channels also
reduces the membrane time constant of Drosophila photoreceptors allowing them to
encode faster events (IV).
3. Nonlinear analysis and the modelling of the WT and Shaker mutant photoreceptors
showed that, in addition to eliminating the Shaker current, the mutation also changed
the current flowing through the LIC and increased the Shab current. Part of these
changes could be attributed to direct feedback from the Shaker channels via the
membrane potential. However, other changes may occur in the LIC of Shaker mutants,
possibly during photoreceptor development (III).
4. Comparison of the Shaker and Shab mutant photoreceptors with the WT revealed that
a concurrent decrease in the steady-state input resistance followed from deletion of the
voltage-gated K + channels. This allowed partial compensation of the compression and
saturation caused by the loss of Shaker channels and it maintained the characteristics
of the light-voltage relationship in Shab mutant photoreceptors (I&IV).
5. Although the regulation of the electrical properties provided robustness to the
performance of the Drosophila photoreceptors, it did not fully restore wild type
properties in either mutant (I,III,IV). Indeed, it resulted in decreased efficacy of neural
processing, assessed by the metabolic cost of information (II).

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Appendix
Examples of the model m-files used in this study.
A1. M-file used for simulating the current injection experiments in Fig
4a, IV
%%% Script for current injection simulations %%%
global param param_1;
for Im=[0.00248 0.00802 0.0133 0.0188 -0.00248 -0.00802 -0.0133]
V0=-66; % mV, resting potential
h0=1/(1+exp((-25.7-V0)/-6.4));
n0=(1/(1+exp((-1-V0)/9.1)))^(1/2);
mKA0=(1/(1+exp((-23.7-V0)/12.8)))^(1/3);
hKA0=(0.8/(1+exp((-55.3-V0)/-3.9))+0.2/(1+exp((-74.8-V0)/-10.7)));
gnew0=1/(1+exp((-14-V0)/10.6));
yinit=[V0;h0;n0;mKA0;hKA0;gnew0]; % initial values for diff. equations
options=odeset(‘'OutputFcn','myparams'); % collects parameters
tspan=[0 300]; % timespan for the solution
param=[];
[t,y]=ode15s(@cur_clamp,tspan,yinit,options,Im);% ODE solver
% Plotting the results
figure(1); plot(t,y(:,1));title('Current injection simulation');
xlabel('ms)');ylabel('mV'); hold on;
figure(2); plot(t,param(:,1).*15710,'r');hold on; % Shaker
figure(2); plot(t,param(:,2).*15710,'b');hold on; % Shab
figure(2); plot(t,param(:,3).*15710,'g');hold on; % Novel potassium conductance
xlabel('ms)');ylabel('nS'); hold on;
end

%%% WT model %%%
function dy=cur_clamp(t,y,Im)
global param param_1;
Cm=4; % *10^-6 F/cm^2, membrane capacitance
gl=0.0585*10^-3; % S/cm^2, Chloride leak conductance
gl2=0.0855*10^-3; % S/cm^2, Potassium leak conductance
glic=0; % S/cm^2, Light leak conductance
gKsm=3*10^-3; % S/cm^2, Shab max conductance
gKAm=0.8*10^-3; % S/cm^2, Shaker max conductance
gnewm=0.11*10^-3; % S/cm^2, Novel K + channel max conductance
gKAmf=0.087*10^-3; % S/cm^2, partial failure in Shaker inactivation
Vl=-30; % mV, Chloride leak rev. potential
Vlic=10; % mV, LIC rev. potential
VK=-85; % mV, Potassium rev. potential
58
% Current injection protocol
c_start=100; % starting time
t_cur_on=100; % duration
t_cur_off=c_start+t_cur_on;
if tc_start+t_cur_on
I=0;
else
I=Im; % I=current injection
end
end
% Activation-inactivation -parameters
% Shaker
if abs(exp((-y(1)-59.639)/4.50122)-1)

59
bmKA=(1-((1/(1+exp((-23.7-y(1))/12.8))))^(1/3))/(1/(1.35*…
(0.008174*exp((-y(1)+1.61882)/24.6538)+0.058139*(-y(1)-59.639)/…
(exp((-y(1)-59.639)/4.50122)-1))));
end
if abs(exp((-y(1)+13.4859)/11.11)-1)

60
gKA=((y(4)^3)*y(5)*gKAm)+((y(4)^3)*gKAmf); % Shaker
gKs=(y(3)^2)*y(2)*gKsm; % Shab
gnew=y(6)*gnewm; % Novel K+ conductance
% Differential equations
dy=[-y(1)*((gKA+gKs+gl+glic+gl2+gnew)/(0.001*Cm))+(((gnew*VK)…
+(gKA*VK)+(gKs*VK)+(gl*Vl)+(glic*Vlic)+(gl2*VK))/(0.001*Cm))+(I/(0.001*Cm))
-y(2)*(ah+bh)+ah
-y(3)*(an+bn)+an
-y(4)*(amKA+bmKA)+amKA
-y(5)*(ahKA+bhKA)+ahKA
-y(6)*(anew+bnew)+anew];
param_1=[gKA,gKs,gnew];
%%% Assisting function %%%
function status=myparams(t,y,flag);
% Date: 12/02/1998,Oulu; Han Chunlei. Modified 17.6.2001 by Mikko Vähäsöyrinki.
% This is for extracting the parameters from ODE solvers,
% the INPUT is PARAM_1; OUTPUT is PARAM;
% code is based on the m-file of ODEPLOT.M.
global param param_1;
if nargin < 3 | isempty(flag)
param=[param;param_1];
else
switch(flag)
case 'init'
param=[param;param_1];
case 'done'
end
end
status = 0;

61
A2. M-file for reconstructing the LIC from experimental voltage
response, IV
%%% Reconstructing the LIC from Shab3 photoreceptor response %%%
% Commented to the extent are not covered in A1
global goal param param_1; % goal is the experimental voltage response
% created in the workspace
V0=-40;
mKA0=(1/(1+exp((-23.7-V0)/12.8)))^(1/3);
hKA0=(0.8/(1+exp((-55.3-V0)/-3.9))+0.2/(1+exp((-74.8-V0)/-10.7)));
gnew0=1/(1+exp((-14-V0)/10.6)));
yinit=[V0;mKA0;hKA0;gnew0];
options=odeset('maxstep',0.5,'OutputFcn','Myparams');
tspan=[0:1:9999];
g=(0.1793*10^-3)*ones(10000,1); % initial value vector for the LIC
counter=0;
while counter < 30 % Number of the iterations, solution converges usually fast
param=[];
[t,y]=ode113(@s3_lic_fit,tspan,yinit,options,g);
for ind=1:1:length(goal),
diff=goal(ind)-y(ind,1);
err=abs(diff/goal(ind));
if err > 0.00005 % Calculates the error in each point
if y(ind,1) >= 0 % and the LIC values are iterated if the error
delta=diff/goal(ind); % exceeds the set value
else
delta=-diff/goal(ind);
end
g(ind)=g(ind)*(1+delta);
end
end
counter=counter+1;
end
% Plotting the results
figure(1);plot(t,y(:,1),t,goal); title('Voltage');xlabel('ms'); ylabel('mV');
figure(2); plot(t,param*15710); title('LIC'); xlabel('ms'); ylabel('nS');

%%% Shab3 model %%%
function dy=s3_lic_fit(t,y,g)
global goal param param_1;
Cm=2.44;
gl=0.171*10^-3;%
gl2=0.2055*10^-3;
gKAm=0.8*10^-3;
gnewm=0.11*10^-3;
gKAmf=0.087*10^-3;
Vl=-30;
Vlic=10;
VK=-85;
glic=g(length(param)+1);
I=0;
if abs(exp((-y(1)-59.639)/4.50122)-1)

end
anew=((1/(1+exp((-14-y(1))/10.6)))^(1/1))/((13+(6232/(30*sqrt(pi/2)))*…
exp(-2*((y(1)+19.4)/30).^2))/1.35);
bnew=((1-(1/(1+exp((-14-y(1))/10.6))))^(1/1))/((13+(6232/(30*sqrt(pi/2)))*…
exp(-2*((y(1)+19.4)/30).^2))/1.35);
63
gKA=((y(2)^3)*y(3)*gKAm)+((y(2)^3)*gKAmf);
gnew=y(4)*gnewm;
dy=[-y(1)*((gKA+gl+glic+gl2+gnew)/(0.001*Cm))+(((gKA*VK)+(gl*Vl)+…
(glic*Vlic)+(gl2*VK)+(gnew*VK))/(0.001*Cm))+(I/(0.001*Cm))
-y(2)*(amKA+bmKA)+amKA
-y(3)*(ahKA+bhKA)+ahKA
-y(4)*(anew+bnew)+anew];
param_1=[glic];