Information processing in neural and gene regulatory networks

Speaker: Gašper Tkačik
Department:
IST Austria
Subject:
Information processing in neural and gene regulatory networks
Location: A1.100 TU Delft
Date: 22-03-2017

Author: Kristian Blom

On the 22nd of March I visited a seminar given by Gašper Tkačik, a theoretical physicist who is interested in using statistical physics and information theory to explain phenomena related to the cell. The most fundamental principle that underlies all the research that dr. Tkačik conducts is that information processing networks have evolved or adapted to maximize the information transmitted from their inputs to the outputs, given the biophysical noise and resource constraints.

Dr. Tkačik showed us multiple examples of his research during his talk. For now I’d like to focus on the most interesting one (from my point of view), which is about reading the positional code in early development. It is commonly known that a morphogen gradient in early development generates different cell types in distinct spatial orders. This is called the French flag model. Despite decades of biological study, a quantitative answer to how much appositional information there is in an expression pattern remained unanswered. Therefore Dr. Tkačik to look at the French flag model from an information theory point of view and asked the following question: How much information is there in spatial patterns of gene expression? Using the gap genes in the Drosophila embryo he measured the amount of information in bits. I will now discuss shortly how one can measure the information contained in gap genes.

Figure 1: Normalized dorsal profiles of fluorescence intensity, which we identify as Hb expression level g, from 24 embryos selected in a 38- to 48-min time interval after the beginning of nuclear cycle 14. Considering all points with g = 0.1, 0.5, or 0.9 (Left) , yields conditional distributions with probability densities P(x|g) (Right). Note that these distributions are much more sharply concentrated than the uniform distribution P(x) shown in light gray. Image adapted from: Dubuis, J.O.; Tkačik, G.; Wieschaus, E.F.; Gregor, T; Bialek, W. PNAS, 2013, 110 (41), pp 16301-16308

We start by looking at the early stages of Drosphila development. At this stage most cells are similar in morphology, so we do not have any information about the position of cell when we neglect gene expression information. Mathematically we can say that the position of the cell is drawn from a distribution of possibilities P(x). If we know take into account the gene expression levels, our uncertainty in position is reduced.  Looking specifically at the expression levels of the hunchback gap (Hb) gene (figure 1), one can see that a certain expression level (g) is not a unique indicator for the position of the cell along the posterior/anterior axis.  Instead there is a range of positions that have the value g. Let P(x|g) be the conditional probability that a cell with expression level g is located at position x.

We define the entropy  of our two probability distributions as:

The information gain due to an observation of the hg expression level at on cell is now given by

From this point I will leave the mathematical expressions as it is, but I challenge you to get a firm understanding of why the final expression represents the information gain. After a small adaption to the final formula, Dr. Tkačik  used that result to make a ‘’direct’’ measurement of the amount of information carried in the gap genes. Using this method he found that individual genes carry almost two bits of information. In the extension of this result he also found that four gap genes carry enough information to define a cell’s location within an error bar of ~1% along the anterior/posterior axis of the embryo. How cool is that!

Although the talk went a bit fast, the content was really good. During the talk I was reminded of the lectures we had during evolutionary & developmental biology (evodevo), since it was this course where I got familiar with the gap genes in drosophila development. Therefore I decided to inform one of the evodevo teachers with the content of this talk, because it might be of good use in the future for them. Although it sounds a bit cliché, afterwards I was again (it happens on a regular basis) astonished by the fact that nanobiology is a really strong field of science. What Dr. Tkačik did fits very well into our program because he used mathematics, especially information theory, to understand why those gap genes function the way they do. For me it was really a wakeup call to keep questioning myself: Why? If one keeps asking this again and again, I think at some point you will find yourself in the fields of mathematics and physics where the answer will be waiting for you to be found.

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