13th International Conference on Membrane Computing - MTA Sztaki

A case-study on the influence of noise to log-gain principles for flux dynamic
discovery
2 Motivation
Because of the prevalence of noise and the fact that it is considered a nuisance,
it is important that the models we design be equipped to tolerate a degree of
noise relative to the amount commonly encountered in their relative elds of
study. Biological data is often said to be quite noisy, and usually has a signal-tonoise
ratio (SNR)which is considered to be quite low; due to the nature of the
calculation, the lower the SNR, the greater the percentage of noise present in the
data. As such, observing some amount of noise in biological data is considered
to be inevitable. Randomness in constantly occurring biochemical processes will
by it's very nature always be aecting other processes, and these interactions
will be detected; this is biological noise. It is extremely unlikely that we will
ever be able to completely remove these inuences from the biological data we
collect, and we must be prepared to deal with the reality that the conclusions
and inferences we make based on noisy data may be quite wrong if the models
and tools we use to make these conclusions and inferences are ill-equipped to
deal with an appropriate degree of noise. For instance, if we assume that a model
that cannot correctly handle noise is correct in all cases, then we may be led to
believe that our model is correct when it is in fact wrong. This could potentially
have dire consequences depending on the model and circumstances. Therefore,
we can plainly see that the study of the eects of noise on our models and other
tools is of great importance, and that all care should be taken when designing
models designed to work with typically noisy data.
3 Experimental Setup
Our experimental setup consists of a few basic steps followed by a comparison
of results generated. [23] First, we assume some substances and associated ux
functions and initial values. Using the various tools in MetaPlab we compute
the time series data for these substances. This time series data acts as a sort
of pseudo-experimental data set, as it is currently not feasible to gather time
series data from biological sources. To better represent what would be collected
from biological sources Gaussian noise is applied to this time series data. The
next step is to apply log-gain principles to our noisy time series data to test
the log-gain procedure. To apply these principles to our data we will once again
be making use of MetaPlab. The application of log-gain principles to our noisy
time series will result in a set of ux functions. These ux functions can then
be compared to the ux functions we assumed and error between the two sets
can be quantied. Furthermore, we then use these new ux functions to show
the noiseless time series that would have resulted in their creation via log-gain
principles. By comparing these time series to the ones actually used we can see
a representation of the error inherent in the process.
The table below shows the initial concentrations and molar weights for three
arbitrary substances: A, B, and C. Using this data we could use log-gain theory
to compute the ux-dynamics of each of these substances. However, for the
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