1. A Model of the Evolution of Cell Signaling Networks Chrisantha Fernando School of Computer Science Birmingham University.

2. Preliminary Questions. How did protein networks evolve? What constraints existed, and what was the selective pressure? Are there evolutionary motifs? (multiple weak to few strong) Can domain shuffling allow ‘function shuffling’? (reusability, incremental evolution, protein neural network robot control) How do they deal with thermal noise? How do they best use conformational change?

3. My train of thoughts. First consider evolving a CSN to solve a very simple task. A step function.

4. There are lots of ways to produce a step function so it should be easy!

7. No conformational change. No allostery Single binding site

8. A chemical buffer

9. Multiple binding sites. No conformational changes. Adding functionality to our mesoscopic protein models.

11. Introducing reconfigurable molecules.

14. Now I got stuck because I wanted to produce a mechanical metaphor for an allosteric system, but could not easily do so. Allostery can easily obtain an approximation to the step function if the Hill coefficient can be made high enough. Allosteric Mechanisms of Signal Transduction Jean-Pierre Changeux and Stuart J. Edelstein Science, Vol 308, Issue 5727, 1424-1428, 3 June 2005 How can we use artificial evolution in simulation to evolve protein networks capable of all the above mechanisms, including allostery?

15. Artificial Evolution of Protein Structure. The model genome must encode protein features at some level of description. –It could encode shape, charge etc… –Is it necessary to model folding? –Even using a toy folding model, how do we infer function from shape? –Molecular dynamics simulations too slow. –We don’t know how to map sequence to protein function in any case.

16. Genome elements encode protein binding site domains. For any protein pair or protein complex pair, we need to define a method of allocating reaction rates for the forward and backward reactions, as a function of binding sites. A + B AB How therefore to design the structure- function map for binding sites? For the moment we ignore allostery.

17. What properties of binding sites are encoded? What about no explicit notion of shape, just a direct representation of some notion of ‘binding strength’!

18. Let each protein store a list of the binding sites it has. P 1 : a,v,n,f. P 2 : a,x. To calculate total ‘binding strength’, add all pairwise entries in the previous matrix, for non-occupied sites. i.e. aa + ax + va + vx + na + nx + fa + fx, if all sites are free. But what does this ‘binding strength’ mean?

19. Lets go back and look at the toy molecules. So far we have only had one value representing each binding site. But what about when it is difficult to reach that binding site, even though it is strong? Therefore we need some value to represent the ease of reaching the binding site.

20. What about two platonic matrices? One for probability of binding between two binding sites. One for probability of two binding sites interacting during a random collision. To calculate the total probability of association we multiply the two matrices pair- wise, and sum the resulting products, for all free pairs. Alternatively we could just encode in the genome the product P(binding) = P(getting to site) x P(binding at site).

21. Ultimately, 2 matrices are required, one for association and one for dissociation. P(association) = Sum all free sites [ P(getting to site) x P(binding at site)] P(dissociation) = Sum all bound sites [ P(breaking bond) x P(getting away from molecule)

22. In Summary. The GA Encoding so far consists of: –Association matrix [N x N] N = no of binding site types. –Dissociation matrix [N x N]. –Vector of Protein objects: Initial number (we assume no transcription regulation for now. No proteins synthesized or destroyed). Binding sites on protein, e.g. a,a,a,b. *,0,1 binding templates, P(c1-> c2) and P(c2->c1) 2 C 2 cooperativity coefficient matrices (assoc, dissoc)

23. Genetic Operators. In proteins mutation has complex effects on shape, and function. In our model (for now) we assume that mutation acts –on the platonic association and dissociation matrices. –on the initial numbers of proteins –on the binding sites on the proteins to Duplicate binding sites, either with the same letter, or given another letter, i.e. with the capacity for divergence. Erase binding sites. Insert an already existing binding site.

24. Computational Capacity What computations is such a network capable of evolving solutions for? So far the proteins are extremely limited because there is no cooperativity. How should we model cooperativity?

25. Effect of Conformation Change. What does a change in protein configuration do? It changes the P(association) and P(dissociation) of binding sites in a potentially highly structured manner. A change in conformation can be described as two matrices of coefficients [N x N] stored in each protein and applied to the association and dissociation matrices. These matrices could be initialized with 1s, but have the capacity to mutate.

26. Cause of Conformation Change. A conformation change depends on the state of the protein, in particular what is bound to it. Let each protein have a maximum of 2 conformations. Let each protein possess initially two binary vector templates representing the binding state that corresponds to a transition probability from C 1 -> C 2 and from C 2 -> C 1 Initialize the template at null, and P= 0. Allow mutation to create new templates, and to alter them, and the associatied probabilities of transition.

27. Allostery. With the inclusion of cooperativity, it is possible for allostery to evolve. Nonreversible (or very stable) conformational changes can also evolve. e.g. phosphorylation like behaviors, e.g. A + B 1 -> AB 1 -> AB 2 -> A + B 2 Intrinsic protein dynamics may result in rapid conformational changes without anything bound! These could then be unchanged when something IS bound. This requires that the templates contain a ‘don’t care’ element *, as well as 0 and 1.

28. Relevant Results. Recent Nature paper shows that enzymes have lots of intrinsic conformational change dynamics. It is found that more highly expressed proteins are slower to evolve. The protein-protein interaction network is being explored in many organisms. What is the effect of mutations on this network?

29. To Do. Write the GA with the encoding just described. See if it can be used to evolve things like –Bistable switches. –Oscillators. –Perfect adaptation. –Step functions. –Flux regulatory systems. –Robot controllers. –Speech recognition, real time computing tasks, etc…

30. Questions. Does anyone think this encoding is un-biological? Of-course it is, but how, and precisely what biases will this introduce? What will be the conclusions we can draw about BIOLOGY, even if solutions are evolved to the problems mentioned? How should the probability of different types of mutation be distributed,e.g. should binding site shuffling be more frequent than binding site P(assoc) P(dissoc) mutation? Will the system be superior to traditional techniques for evolving neural networks to solve complex control tasks, e.g. CTRNNs?