Topologically Defined Neuronal Networks Controlled by Silicon Chips

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CHAPTER 2. NETWORKS OF DEFINED TOPOGRAPHY The topographic structures in this study consisted of pits with 70µm and 80µm diameter for taking up the cells and 14µm wide connecting grooves, see fig. 2.8A. Their overall height ranged from 10µm to 40µm. Note the perfectly vertical walls shown in the inset, they are essential for controlling neuronal outgrowth and confining cells to the pits. Although a structure height of 10µm is sufficient to reliably guide growing neurites and retain them in the grown geometry, somata are sometimes pulled out of the pits, as they are too shallow, especially to confine large cell bodies. By increasing the resist thickness to 30µm-40µm even large somata are kept in place, but at the cost of a poor visibility of neurites at the bottom of the grooves. Diffraction at the edges of the groove walls diminishes optical resolution with increasing structure depth. This dilemma is elegantly solved by processing two resist layers on top of each other. A single thin layer for guiding neurites while not impairing visibility and two layers in areas surrounding the somata to provide enough force to keep them in place. The process is adapted from the single layer process, but slightly more complex. Its first steps, including the post exposure bake, are identical to those described above, but are then followed by: spin-on of second resist layer, softbake, bead removal, second exposure, post exposure bake, development and hardbake. As the first resist layer remains photosensitive in areas not illuminated in the first exposure, care must be taken that the second mask also protects them during the second exposure, otherwise the first pattern is overwritten by the second. This constraint limits the three-dimensional features that are accessible with the procedure, e.g. bridges and covered conduits cannot be made, as they require an exposed layer on top of unexposed areas, see [44] for a technique to build these structures. Fig. 2.8B depicts such a two layer device, again note the vertical walls and the perfectly aligned second layer. 2.4 Theory part I: Neurons, synapses and cables Understanding the behavior of an entire neuronal network at the basic level requires profound knowledge about its building blocks, namely neuronal somata, neurites and synapses; a theory describing these building blocks is presented in this section. All neurons used throughout the study only form electrical synapses, which also transmit negative, hyperpolarizing signals; in contrast to chemical synapses. Because of this behavior the voltage-independent synaptic conductances can be determined with a passive model. The model implies that all parameters, such as synapse and membrane conductance, do not depend on the transmembrane voltage. These conditions can be experimentally realized best, when neurons are hyperpolarized. Based on these assumptions, subsection 2.4.1 and 2.4.2 present equivalent circuits and related equations for a single soma, a soma with neurites and small networks. More complex neuronal behavior, such as the generation of action potentials, can only be described with an active model including voltage-dependent conductances, as outlined in 2.4.3. 2.4.1 Passive model and cable theory The isolated soma is the elementary unit of all neural networks. In a passive model its equivalent circuit is represented by a single, isopotential compartment with a capacitance Cs in parallel to an ohmic conductance Gs and a battery V0, see fig.2.9A. Cs and Gs are properties of the soma membrane (index s), the resting potential V0 is generated by different ionic concentrations between intra and extracellular space; for more details refer to subsection 2.4.3. A current Iinj injected into the cell via an electrode charges its capacitance and leaves through the membrane conductance. The dynamics of the somatic membrane voltage, Vs, of this circuit is described by the following differential equation: 18 dVs Iinj = Cs dt + Gs(Vs − V0) (2.1)
2.4. THEORY PART I: NEURONS, SYNAPSES AND CABLES Figure 2.9: A: Equivalent circuit of a neuronal soma with passive membrane. B: Passive model of a neuron with neurites. Soma and neurites can have different membrane conductance and capacitance, but the same cytoplasmic resistance r. Its solution for a current step from Iinj,0 to Iinj,∞ applied at time zero is given by: Vs(t) = V∞ + Iinj,0 − Iinj,∞ t − e τs (2.2) Gs This monoexponential voltage transient decays with the time constant τs = Cs/Gs governed by the cell membrane. V∞ = V0 + Iinj,∞/Gs is the steady state voltage after the current step. The realistic description of an individual neuron as part of a network must include neurites, along which electrical signals are exchanged. In contrast to somata, long, thin neurites can usually not be considered isopotential because changes of the somatic membrane potential decrease as they propagate from the cell body to the tip of the neurite. This is due to electrical currents leaving via the neuritic membrane and charging the membrane capacitance, as well as to the voltage drop caused by the finite conductance of the cytoplasmic solution inside the neurite. W. Rall [85] derived a differential equation for the potential distribution in a passive neuron with neurites under the following set of assumptions: neurites are cylindrical, uniform electrical properties over the entire surface of the neuron, constant extracellular potential, isopotential soma, intracellular potential and currents are continuous throughout the entire neuron, axial ohmic resistance inside the neurite is proportional to its cross-sectional area; the equivalent circuit for a patch of membrane consists of an ohmic resistance in parallel to a capacitance with a constant electromotive force in series to the resistance. Problems with fitting voltage and current transients calculated from the Rall model to experimental data led to a more general version, the ‘somatic shunt cable model’ [25]. The postulate of uniform electrical properties is abandoned, the soma can have different membrane capacitance and conductance than the neurites. These generalizations are the basis for the equivalent circuit depicted in fig. 2.9B. The somatic conductance Gs and capacitance Cs are the product of the soma-specific quantities and the somatic membrane area, with ds denoting the diameter of the cell body. Gs = gsπd 2 s and Cs = csπd 2 s (2.3) For practical reasons the respective neurite parameters are defined as quantities per unit length and are calculated from the specific values c and g according to: Gj = gπdj and Cj = cπdj and Rj = 4r πd 2 j Rj is the axial ohmic resistance of neurite j and r is the specific resistance of the cytoplasm inside. Note that while different neurites can have diverse diameters dj, resulting in different values of Rj, their specific electrical properties g, c and r are identical for all. (2.4) 19
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characterizing the dynamics of the
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3.5. THEORY PART III: NEURON-SILICO
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3.6. NEURON-SILICON INTERFACE: EXPE
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demonstrated by the examples in fig
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Chapter 4 Defined networks on chips
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4.2. RESULTS Figure 4.2: A: Microgr
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4.2. RESULTS 2 postsynaptic action
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4.2. RESULTS Since neuron 1 could a
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4.2. RESULTS Figure 4.5: A: Transis
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4.3. FINAL DISCUSSION Data in diagr
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4.3. FINAL DISCUSSION Some very har
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Chapter 5 Conclusion and outlook Th
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Appendix A Cell culture protocols a
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ethanol and 30% water during UV-ste
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For two-layer structures, steps 3 t
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The flatband voltage VF B and elect
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Appendix D Abbreviations ABS : anti
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Bibliography [1] R. W. Aldrich, P.
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BIBLIOGRAPHY [32] P. Fromherz. Neur
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BIBLIOGRAPHY [69] C. D. McCaig, A.
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BIBLIOGRAPHY [105] N. I. Syed, A. G
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Ich danke PROF. DR. P. FROMHERZ fü
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Topologically Defined Neuronal Networks Controlled by Silicon Chips

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