| Abstract |
Information processing is ubiquitous in biological systems and essential for many biological processes, ranging from performing regular tasks to reacting to perturbations. Many of these processes are decisive for the survival of the system. Studying information processing can provide a better understanding for various properties of biological processes, such as their robustness, their proximity to optimality or the underlying network architecture. On the cellular level, one way to transfer information is via chemical reactions. In this context, the idea is that a chemical species triggers a chain of reactions which results in a final output species. To this end, biological information can be defined via the abundance of a chemical species. As these chemical species occur in copy numbers, the change of their abundance is discrete and moreover, highly dynamic. This means that in this kind of systems, information is carried by the dynamic time-trajectories or paths of chemical species. From a mathematical point of view, information theory provides a powerful framework to quantify information in various contexts. However, the high dimensionality and nonlinearities of the networks of chemical reactions make it challenging to apply existing quantities directly to biochemical systems. There are several approaches available for deriving variants of information theoretical quantities to make them more applicable to biochemical processes. One of these quantities is the mutual information, which quantifies the information transferred between two variables. In biochemical networks, the mutual information between two paths has traditionally been calculated using continuous approaches such as Gaussian approximations. However, these approaches do not capture the discreteness of chemical reactions. Other approaches for discrete systems are defined only for special cases. Thus, a general approach for discrete systems is still missing. Building on previous, in this thesis we derive a general method for calculating the mutual information between Continuous-Time Markov Chains. This will allow for a quantification of information transfer between discrete paths of the components of a biochemical network. We further develop different methods for calculating the so-called path mutual information that vary in computational speed and scope. Moreover, we compare the resulting equation to a commonly used method based on Gaussian theory and find fundamental differences between them. Together with the group of Pieter Rein ten Wolde at the AMOLF in Amsterdam, who developed that method, we explored the origin of the discrepancies between the discrete path mutual information and the results obtained by using Gaussian theory. We find that the major difference lies in the way, individual reaction events are treated in the two cases. Based on that, we develop a deeper understanding of the information content of paths and the consequences of different path compositions. Furthermore, we develop a new method for calculating path mutual information based on Gaussian theory that aligns with the path description of the discrete case, which we present in the beginning of this thesis. With that, we obtain an easy and efficient way of calculating mutual information in biochemical networks. Lastly, we apply our in the end presented method to two biological examples which does not only highlight the benefits of the developed method, it also leads to additional insights into these systems. In the first example, we characterise the features of information transfer in intercellular communication for two different communication strategies. In the second example, we analyse how much information a single cell can gain about its environment and how cells can maximise this information. In conclusion, in this thesis we derive and analyse methods for calculating the path mutual information in biochemical networks and present how they can be used to study biological systems. We obtain a deeper understanding of information transfer in these networks and at the same time, mathematical insights into the differences between the presented methods. These insights provide a better understanding of a different notion of paths and its consequences when it comes to calculating information. |