Mathematical Foundations of Information and Decisions in Dynamic Cell Signalling

Because DNA is a linear string of the base pairs A, T, C and G, the nature of information stored in the genome is well-described by classical information theory. However, this information is translated by molecular interactions into dynamical processes in the cell and it is these processes that determine the end-states of the cell such as its final cell type or whether it will kill itself or decide to divide. These processes are modelled mathematically by stochastic dynamical systems. They respond to signals generated both inside and outside the cell and can use the dynamical interactions to pass information in these signals to processing units, such as networks of genes, to be used for cellular decision-making. However, while the notion of information content is clear when one is talking about strings formed from a finite alphabet as in DNA or RNA, there is currently no clear conceptual framework once the genomic information has been passed into the dynamic processes.

A key aim of this project is to develop such a conceptual framework in the context of dynamic signalling systems by providing the mathematical foundations. A key idea behind our approach which is novel is the integration of cellular decision-making with information transmission. In this approach the value of the information in the signalling system is defined by how well it can be used to make the "correct" decisions. Rather than asking how much information is being transmitted, we ask whether the amount and quality of the information is adequate for reliable decision-making either at the single cell level or at the level of populations of cells. Decision-making will be viewed in a context similar to hypothesis testing and discrimination analysis. The basic idea will be that the cell is using the information provided by the signalling system to test multiple hypotheses or discriminate between multiple choices each of which determines a particular cellular outcome.

To do this we study the way that the probability distribution of gene responses changes as the input signal changes. Cells receive many signals informing them about the external environment and their internal state. These signals are communicated by signalling systems made up of interacting proteins into the nucleus of the cell typically by raising the level of a transcription factor (TF) in the nucleus. These transcription factors regulate genes. In this way the input signal S causes a response R by the genes. However, the process is highly stochastic and therefore the response R has a distribution P(R|S) and we are very interested in how this changes as S changes.

Gene networks can be designed so that the response R encodes a decision. For example, R might be the level of a gene that causes the cell to divide or kill itself. We will determine the principles behind such decision making and will understand the general principles governing it. In particular we will develop tools to understand its effectiveness.

To do this we will need to analyse detailed models of signalling systems. We have developed new approaches to this and will be further developing these in the project. These models indicate that the dependence of P(R|S) has a surprising dependence on S when S is multi-dimensional - the response moves in a much lower-dimensional space than the input S which implies that such systems will find complex decision making difficult. We will investigate whether this is behind the commonly observed modifications of the TFs that regulate genes because we hypothesise that while tightly coupled oscillating systems allow more complex decisions than equilibrium systems, the multiplexing is severely limited because of the above low-dimensionality. It can grow greatly when these modification states are included in the model because the ability of the TF to be modified or bound by other proteins that can be dynamically regulated allows the TF to change its function dynamically.

(i) Mathematicians interested in analysis and modelling of biological and biomedical systems. The ability to model information flows and decision-making will open up new areas for interaction with biologists. This impact will be felt in the short term (0-5 years).

(ii) Mathematicians and engineers interested in decision-making in noisy environments. While the project orientation is biological and medical, the problems and methodology proposed are likely to be of much broader interest. For example, next-generation cars will have to respond to noisy signals and base decisions on this and the methodology developed here is likely to be useful in such situations. This will be developed through our EPSRC funded MathSys CTD which has JLR as a partner. This impact will be felt in the first 2-5 years.

(iii) Biologists and biomedics who can start to design experiments to directly test cellular decision-making in complex systems. These issues are of great relevance to them but they currently lack to conceptual framework within which to design experiments and formulate deep questions about the decision-making aspects of their systems. The results should enable a more global treatment of inflammation and related diseases by enabling a more coherent integration of the signalling systems involved. While the treatment here directly concerns inflammation it can be applied to other areas where the signals are used to move cells into different states. For example, the can be applied to development and regenerative medicine where signals drive cells from one equilibrium to another or to cancer where the signalling has broken down and where one needs the conceptual framework to discuss this in a more global fashion. Some impact will be from day one (as I am already talking to them) but significantly in the first 2-5 years.

(iv) Health service. The use of new-technology and sensor data to stratify patients according to risk and/or to predict adverse events needs tools for forecasting and these will have to analyse noisy signals similar in principle to those discussed here. The methods developed in this project are likely to impact on such work, in particular that concerned with developing methods for appropriately integrating diverse probabilistic systems, with online updating of information bases including inferential methodologies. This will be developed through established contacts in the health service with who we have established collaborations e.g. clinicians such as Professor Francis Levi and Professor Nick James, hospitals such as University Hospital Birmingham and University Hospitals Coventry & Warwickshire, and international organisations such as INSERM (with which we are one of the Laboratoires Européens et Internationaux Associés) and the International Association for Research in Cancer (IARC) in Lyon. This research will make a significant contribution to this field in the medium term (3-10 years).