Artificial Evolution of Cell Signaling Networks

Our previous model of the evolution of cell signaling networks failed due to various reasons. 1. Slow simulation, 2. No cyclic intra-complex bonds permitted. 3. Overly complex rule specification resulting in hilly fitness landscape. We are begining to try to solve these problems using Vincent Danos' Kappa, a process language like BioNetGen, where rules can be specified, simulations run, and outputs recorded. This allows easy integration into an evolutionary algorithm to optimize rule sets to carry out desired tasks. Click here for more details.

Could Bacterial Gene Regulatory Motifs be Adaptations for Evolvability?

We're testing the hypothesis that where a structural gene appears in the GRN may have something to do with how much phenotypic plasticity it shows. See here for more details.

The Role of Self-Loops in E. coli Gene Transcription Networks.

Uri Alon's work reveals that the E coli GTN is large feedforward with only self-loops. Not a single two node loop was found. What are the computational capabilities of FF networks with self-loops? What are the biological functions of self loops? I consider these issues here.

Liquid State Machine Properties of Cell Signaling Networks.

Click here to find out about some new experiments with cell signaling networks to see if they are capable of perceptual discriminations between temporal sequences of chemical inputs.

Robustness and Evolvability of Cell Signaling Networks.

What is the minimal level of enzymatic control that a cell must have in order to allow unlimited heredity? One approach to the problem is to first define the fundamental control problem faced by the cell. This involves integrating research from bottom-up approaches, i.e. production of protocells, and top-down approaches, i.e. pearing down of bacteria to identify a `minimal gene set'. Artificial evolution models may then be made of postulated fundamental cellular operations, in order to investigate the control mechanisms that are required.

References: Constructing a Model for Use in Analysis of Cell Signaling Network Evolution.

J. Adler and W. Tso. Decision Making in Bacteria: Chemotactic Response of E. Coli to Conflicting Stimuli. Science (1974) Download pdf

U. Alon and M.G. Surrette and N. Batkai and S Leibler. Robustness in bacterial chemotaxis. Nature (1999) 397:168- Download pdf.

R. Barak and M. Eisenbach. Chemotactic-like response of E.Coli cells lacking the known chemotaxis mechinery but containing overexpressed CheY. Molecular Microbiology (1999) 31(4): 1125-1137. Download pdf. [Even without the proteins of the chemotaxis pathway, poor quality chemotaxis is still observed by an alternative mechanism. Could this be due to cross-talk?]

N. Barkai and S. Leibler. Robustness in simple biochemical networks. Nature (1997) 387:913-917 Download pdf. Download review. [Analysis of a method of achieving perfect adaptation with robustness to changes in network kinetics. The receptor complex has two states E and Em. Em is more likely to be active when bound to ligand. The rate of conversion of Em to E is related positively to the activity. Therefore, if the activity is higher than desirable, more Em is converted to E, and vice versa. This feedback based on the deviation of activity from desired activity allows perfect adaptation. Ignores the downstream phosphorylation cascade. This is an integral feedback system. Download a list of chemotaxis simulations. ]

S.A. Benner and A.D. Ellington The Last Ribo-organism Nature (1987) 329:295-296. Download pdf. [An argument for the existence of a highly evolved ribo-metabolism, before the onset of translation.]

S.A. Benner et al Natural Selection, Protein Engineering, and the Last Riboorganism: Rational Model Building in Biochemistry. Cold Spring Harbour Symposia on Quantitative Biology (1987) 53-63 Download pdf. [ 1. Ask what are selected and non-selected behaviours in proteins . Proposes the functions of a complex riboorganism.]

S.A. Benner and A.D. Ellington Return of the last riboorganism. Nature (1988) 332:688-689 Download pdf. [Further discussion about what we can imply from introns about primitive RNA functions (in conclusion, little).]

J.J.E. Bijlsma and E.A. Groisman. Making informed decisions; regulatory interactions between two-component systems. Trends in Microbiology. (2003). 11: 359- Download pdf.

L. Bintu et al. Transcriptional regulation by the numbers: models. Curr Opinion. in Genetics and Development. 2005, 15:116-124. Download pdf.

L. Bintu et al Transcrptional regulation by the numbers: applications Current Opinion in Genetics and Development, 2005, 15:125-135. Download pdf. [A good review of the dynamics of cis-regulation of RNAP transcription. Variation in such dynamics should be included in the evolutionary model that we design of CSNs. E.g. coorperativity in transcriptional activation and repression, why it is required, sensitivity (gain), dissociation constants, cooperative coactivation, synergistic coactivation, simple repression, repression by DNA looping, cooperative repression, ]

R. Blossey and L. Cardelli and A. Phillips. A Compositional approach to the stochastic dynamics of gene networks. Download pdf. [Introduction to Process Calculi e.g. Pi-Calculus, a stochastic concurrent programmign language, that might be useful in modeling CSNs. The Gillespie algorithm is used to run the pi-calculus specification of the network. The pi-calculus seems nothing more than one convenient (but not necessarily biological) way of describing a CSN or a GRN. Also see Guet et al(2002) Science, 296:1466-1470. Thatti et al PNAS 98:8614-7153. (2001). Paulsson, J. Berg and Ehrenberg (2000) PNAS, 97:7148-7153. for analysis of stochastic effects in control.]

D. Bray. Protein molecules as computational elements in living cells. Nature (1995) 376:307- Download pdf. [An excellent review of proteins as computational units, with useful reference.]

D. Bray Signaling Complexes: Biophysical Constraints on Intracellular Communication. Annu. Rev. Biophysics. Biomol. Struct. (1998) 27:59-75. Download pdf. [Constraints considered are 1. Molecular Crowding. 2. Rates of diffusion. E.g. many collisions are required for the transduction of a signal by PDGF, but the receptor complex is already assembled in the Tar complex. E.g. multienzyme complexes are formed by protein receptors etc.. assembling together on scaffold proteins, thus allowing complex transfer functions. The complex may be like a 'swarm' rather than tightly bound all the time (e.g. PDGF). Complexes may have less noise, act more rapidly 3. Energy cost of information. The cell will benefit from minimizing the number of proteins that must be synthesized, e.g. few IC signaling complexes for lots of PDGF surface receptors. 4. Interfearence minimization. Distinct CSN modules must be prevented from unnecessary interfearence. Localizing functions to regions, e.g. membrane rafts, cytosol, etc... may aid evolvability of cell signaling, because a mutation will tend not to place a protein into a completely different environment (compartment) very often, but change its function in a minor way, whilst it remains in interaction with its fellows. Bray puts forward a neural analogy, complexes are like cortical regions, and diffusion is the communication between cortical regions. Such constraints could be included into an in silico model of CSN evolution, such as that of Francois, download pdf.]

D. Bray and S. Lay Computer Simulated Evolution of a Network of Cell-Signaling Molecules. Biophysical Journal (1994) 66:972-977. Download jpgs (1), (2), (3). [Uses a simulated evolution approach to explain the existence of high-affinity forms and low-affinity forms of cell-surface receptors. The task was i) to produce a square wave pulse of phosphorylated protein that matched the concentration of applied ligand, ii) to produce a maximal response at an optimal ligand concentration. The GA optimized 7 kinetic parameters of a fixed topology CSN. The CSN was modeled using numerically integrated ODEs. Sigmoidal and differential responses could not be obtained with this topology. There was no noise. Is the solution a good stratergy given stochastic noise? Is the task representative of the normal biological function of CSNs with such topologies? How would the solution differ if topology were allowed to evolve too? See Francois and Hakim's paper, Download pdf.] It is possible to replicate this experiment using our model, and in addition to include more complex genetic operators and scope for variation.

D. Bray and S. Lay Computer-based analysis of the binding steps in protein complex formation. PNAS (1997) 94:13493-13498. Download pdf. Considers the prozone reaction mechanism whereby Protein A and B if present in optimal concentrations form a stoichiometric lattice, but if either is present in excess, small soluble complexes are formed instead. OLIGO-D is similar to our program, except it assumes that once two proteins associate by a binding site pair, that all other possible intra-complex bonds are formed between the two proteins in the same complex (presumably where there are several possible intra-complex bond arrangements, it must decide bnetween them. ). This tends to limit aggregates expanding through combinatorial explosions. There is no intra-complex bonding allowed in our simulation so far, and therefore, prevention of aggregates of increasing size can only be achieved by binding site specificity increase. It will be interesting to see whether including intra-complex aggregation (cyclic protein graphs) will aid the evolution of protein network functionality.

D. Bray and Steven. Lay. A computer program for the analysis of protein complex formation. CABIOS (1997) 13: 439-444. Download Pdf.

D. Bray. Bacterial chemotaxis and the question of gain. PNAS (2002) 99:7-9. Download pdf.

D. Bray and T. Duke. Conformational Spread: The Propagation of allosteric states in large multiprotein complexes. (2004) Annu. Rev. Biophys. Biomol. Struct. 33:53-73. individual subunits have a certain probability of being active or inactive depending on (a) whether they are bound to a ligand and (b) the conformational states of their two neighbors. This is a restricted case of our model. Examples 1) "In 1998 this quantitative discrepancy between theory and experiment [w.r.t. gain of aspartate receptor protein] led to the suggestion that crosstalk between receptors in the cluster might result in “front end” amplification (7). 2) Ca2+ channels in cardiac muscle. 3). CheY binding to C ring of bacteria (++ sensitive). 3) Conformational changes of flagella proteins mediate flagella waves. Patterns can be generated in protein lattices. "If each subunit in the ring is assumed to make rapid stochastic transitions between its two conformations and the chain is at
thermodynamic equilibrium, then the probability of occurrence of a particular configuration will be determined by its free energy according to the usual Boltzmann formulation. In the case where interactions between adjacent subunits are negligible, the subunits flip conformation largely independently and there is little correlation of states along the chain. But suppose that there is a significant interaction between neighbors and, moreover, that when two adjacent subunits have the same conformation, their combined energy is lower than when they have different conformations. This coupling causes the conformation of each subunit to influence that of its neighbor, and so on down the chain—the basic mechanism of conformational spread." [Such interactions can be easily described in our model.] Download pdf.

A. Burgard et al. Biotechnol. Prog. (2001) 17:791-797. [Minimal number of metabolic reactions in E.Coli supplied with rich nutrients is 122.]

L. Cardelli. Abstract Machines of Systems Biology. (2005). Download pdf. [Thoughts on a pi-calculus description of cell processes.]

J.M. Carlson and J. Doyle. Complexity and Robustness. PNAS. (2002), 99(suppl 1): 2538-2545. Download pdf.

M.E. Csete and J.C. Doyle. Reverse Engineering of Biological Complexity. Science (2002) 295:1664- Download pdf. [An important article applying Engineering Control Theory principles to biology. Highly evolved feedback based control systems display all sorts of characturistic patterns of robustness and failure. These are seen in biology as they are seen in Engineering also. Often catastrophic failure occurs when variation arises in a feature that the system was not evolved with. Various tasks are suggested for FB systems. ]

M. Castellanos and D.B Wilson and M.L. Shuler. A modular minimal cell model: Purine and pyrimidine transport and metabolism. PNAS (2004) 101(17):6681-6686. Download pdf. [ Describes the Cornell E. Coli model, a metabolic model of E.Coli that uses experimentally determined kinetic values. It gives references to papers that have used the model, e.g.M. Domach et al. Biotechnol. Bioeng. (2000) 67:827-840. Download pdf. M. Shuler and S. Leung and C. Dick Ann. N.Y . Acad. Sci (1979) 326:35-56. M. Shuler and M. Domach ACS Symp. Series. (1983) 207: 92-133. J. Shu and M. Shuler. Biotechnol. Bioeng. (1991) 37:708-715. L. Laffend and M. Shuler. Biotechnol. Bioeng (1994) 43: 388-398, 399-410. M. Shuler J. Biotechnol (1999) 71: 225-228. Download pdf. S. Browning and M. Shuler Biotechnol. Bioeng. 76: 187-192. [Examines the effect of changes in rate constant ratios in a "course-grained" model of metabolism.] A more detailed model of nucleotide reactions is added to the course grained model. A review by Shuler. Download pdf.]

R.L. Charlebois and W.F. Doolittle. Computing prokaryotic gene ubiquity: Rescuing the core from extinction. Genome Research (2004) 14:2469-2477. Download pdf.

C. Chassagnole et al. Biotechnol. Bioeng. (2002) 79:50-53. [Proposals of how to model the dynamics of central metabolism.]

M. Chaves and R. Albert and E.D. Sontag. Robustness and Fragility of Boolean models for genetic regulatory networks. J. Theor. Biol. (2005) 235:431-449. Download pdf.

M. Domach et al. Biotechnol. Bioeng. (2000) 67:827-840. Download pdf. [A minimal cell model of an E.Coli, consisting of i. Division of chemical reactions into modules. ii. Pseudochemical reactions representing stoichiometic relationships in the cell. iii. Kinetic relationships that reflect the general dependencies between major metabolic pathways. iv. Metabolic control signals that depend on the concentration of chemical components. v. Obtaining kinetic and stoichiometric information from real cells growing exponentially.

J.S. Edwards, R.U. Ibarra and B.O. Palsson. In Silico predictions of E. Coli metabolic capabilities are consistant with experimental data. Nature Biotechnology (2001) 19:125-130. Download pdf. [Flux Balance Analysis confirms that E. Coli metabolism is efficient. ]

D. Fell Understanding the Control of Metabolism. [An excellent review of Metabolic Control Theory.]

P. Fernandez and R.V. Sole. The Role of Computation in Complex Regulatory Networks (2003) Download pdf.

P. Francois and V. Hakim. Design of genetic networks with specified functions by evolution in Silico. PNAS (2004) 101(2):580-585. Download pdf. [Artificial evolution used to evolve the topology and the kinetics of bistable switches and oscillating circuits in simulated gene regulatory networks. The variational primitives are the genes and their proteins. Proteins can promote or repress genes. Post-translational events can occur, i.e. proteins can join to make a single complex, or can modify another protein (simulating phosphorylation). The mutation operator has 5 options, randomly drawn (with bias). 1. Change the degredation rate of a protein. 2. Change the kinetic constant of a reaction. 3. Create a new gene and its corresponding protein, and the degredation pathway for that protein with random kinetics. 4. Create a new protein-gene interaction. This involves creating 3 new reactions. Protein + Gene <-> Complex, and the complex's effect on protein production.5. Post-translational reaction. i. If involving one protein (phosphorylation), new protein in chain created, with its own degredation rate. If a protein complex is chosen, a partial degredation can occur. ii. If involving two proteins, a. Dimerization, b. Catalytic degredation. c. Partial catalytic degredation, if one of the protein entities is a complex.Tasks: 1) - Bistable Switch: We wish the network to have two stable states differing in [A]/[B] ratio. System started at one desired stable state. Scored for state 1. Pulse of B added at time T, at conc required of B in the desired state 2. Scored until time = 2T, for state 2. Score = Integral of ([A] - [A]*)^2 + ([B] - [B]*)^2, where[B]* is the desired concentration at state *. T = 100min. Networks were evolved without noise, but the kinetics were used to implement stochastic models. Some designs were more robust to noise and parameter variation than others. 2) - Oscillating Networks. Selection for network capable of fitting a square wave with top and bottom concentrations [A1] and [A2], over 10 periods. Oscillation did not start in response to a signal, but at initiation. Are the same constaints that apply to translational and post-translational control in biological systems present in the model? Why would control be post-translational rather than translational, or transcriptional? See Bray's article on biophysical constraints, Download pdf. The model does not answer these questions becuase it appears not to embody the relavent biophysical constraints. I.e. phosphorylation occurs without an enzyme being involved, so that phos-dephos coupling cannot be produced. How common are degredations in real systems? Promotion and repression have limited dynamics. Genetic operators act on global network properties and not on protein structure, therefore there is no capacity for structured effects on network evolution. New genes are introduced with random interactions between its protein and other existing proteins. There is no duplication and divergence of genes.]

T. Genoud and J. Metraux. Crosstalk in plant cell signaling: Structure and function of the genetic network. Trends in Plant Science. (1999) 4(12), 503-507. Download pdf.

P. Green and E. Koonin. Genomes and Evolution. Glimpses of an emerging synthesis. Current Opinion in Genetics and Development. (1999) 9:621-623. Download pdf.

R. Gil et al. Extreme genome reduction in Buchnera spp.: Toward the minimal genome needed for symbiotic life. PNAS (2002) 99(7): 4454-4458. Download pdf.

J.P. Gogarten and W.F. Doolittle and J.G Lawrance. Prokaryotic Evolution in Light of Gene Transfer. Mol. Biol. Evol. (2002) 19(12):2226-2238. Download pdf.

M. Goilian. Robust Control in Bacterial Regulatory Circuits. Current Opinion in Microbiology. (2004). 7:198-202. Download pdf. [An excellent review of robustness in cell regulation. Suggests plenty of useful example tasks to try in evolutionary experiments. Discusses robust circuit motifs. E.g. E.g. EnvZ/OmpR in E.Coli, Glutamine synthetase ultrasensitivity robust to change in conc. of regulatory proteins. Feedforward control e.g sigma factor in heat-shock. Discrete control (e.g. lactose and arabinose-inducible genes), Continuous control (e.g. Tn10 tetracycline resistance and porin osmoregulation). Robust oscillators , e.g. circadian oscillations in cyanobacteria, see Circadian programing in cyanobacteria, Semin Cell Dev Biol 2001, 12:271-278. See Atkinson et al Cell 2003 113:597-607 for a designed oscillator. Barkai and Leibler Circadian clocks limited by noise Nature 2000, 403:267-268. Vilar et al Mechanisms of noise-resistance in genetic oscillators. PNAS 2002 99:5988-5992. Also read de Visser et al Perspective: evolution and detection of genetic robustness. Evolution Int J. Org Evolutin 2003, 57:1959-1972. ]

C. Guet and M.B. Elowitz and W. Hsing and S. Leibler. Science (2002) 296:1466-1470. [Combinatorial synthesis of small network topologies of transcroption encoding genes.]

I. Harvey Homeostasis and Rein Control: From Daisyworld to Active Perception Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems, ALIFE'9, Pollack, J., Bedau, M,. Husbands, P., Ikegami, T., and Watson, R.A. (eds), pp. 309-314. MIT Press, Cambridge MA. Download pdf. [A model of integral rein control. Could such mechanisms be operating in the cell?]

K.J. Hellingwerf and P.W. Postma and J. Tommassen and H.V. Westerhoff. Signal Transduction in bacteria: phospho-neural network(s) in E.Coli. FEMS Microbiology Reviews (1995) 309-321. Download pdf. [Proposes a neural network consisting of cross-talking elements between the 30 or so 2-component systems of E.Coli, but does not say what tasks such a neural network should solve! Why would cross-talk be useful in E.Coli?]

N. Ishii et al Toward large-scale modeling of the microbial cell for computer simulation. Journal of Biotechnology (2004) 113: 281-294. Download pdf.

M. Itaya. FEBS Letters (1995) 362: 257-260. Download pdf [B. Subtilis gene disruption to find the minimal viable genome derivable from this species. ]

H. Kitano. Biological Robustness. Nature Reviews. (2004). 5:826- Download pdf. [Robustness contributes to evolvability.]

K. Kobayashi. Essential Bacillus subtilis genes. PNAS (2003) 100(8): 4678-4683. Download pdf. [Analysis of essential genes in B. Subtilis.]

J.H. Koeslag and P.T. Saunders and E. Terblanche. A reappraisal of the blood glucose homeostat which comprehensively explains the type 2 diabetes mellitus-syndrome X complex. J. Physiol (2003). 549:333-346. Download pdf.

E.V. Koonin. Comparative genomics, minimal gene-sets and the last universal common ancestor. Nature Reviews Microbiology (2003) 1:127-136. Download pdf.

E.V. Koonin and A.R. Mushegian and K.E. Rudd. Curr Biol (1996), 6:404-416. Download pdf [Functional analysis of a minimal genome.]

D.A. Kraut and K.S. Carrol and D. Herschlag. Challenges in Enzyhme Mechanism and Energetics. Annu. Rev. Biochem. 2003. 72: 517-571. Download pdf.

D.A. Lauffenburger. Cell signaling pathways as control modules: Complexity for simplicity? PNAS (2000) 97(10) 5031-5033 Download pdf. [A review of papers exploring the dynamics of the chemotaxis pathway of E. Coli, containing useful references. A control theory analogy of a water tank is used. The tank has influx and outflux, its core is simple, but a complex control system may be needed to ensure it does not overflow. Similarly, basic cell dynamics may be simple, but much of CSN complexity may be for safety and efficiency.]

S. Light and P. Kraulis. Network analysis of metabolic enzyme evolution in E. Coli. BMC Bioinformatics. (2004) 5:15 Download pdf.

B.A. Melloi And Y Tu. Perfect and near-perfect adaptation in a model of bacterial chemotaxis. Biophysical Journal (2003) 84:2943-2956. Download pdf. [A model of chemotaxis with 4 methylation sites.]

S.S. Morrison and C.W. Mullineaux and M.K. Ashby. The Influence of acetyl phosphate on DspA signalling in the Cyanobacterium Synechocystis sp. PCC6803. BMC Microbiology 2005, 5:47- Download pdf. [Demonstrates how a response regulator protein is phosphorylated both by the sensor kinase and by the global signal of acetyl phosphate. Does not really address why this might be adaptive. What factors cause an increase in acetyl phosphate?]

C.J. Morton-Frith and T.S. Shimizu and D. Bray. A Free-energy-based Stochastic SImulation of the Tar Receptor Complex. J. mol. Biol. (1999) 286:1059-1074. [Another model of chemotaxis, with details of the equations and rates used. ] Download pdf.

A.R. Mushegian. The minimal genome concept. Current Opinion in Genetics and Development (1999) 9:709-714. Download pdf.

A.R. Mushegian and E.V. Koonin. A minimal gene set for cellular life derived by comparison of complete bacterial genomes. PNAS (1996) 93, 10268-10273. Download pdf. [Trying to think about the minimal cell. The authors found that M. Genitalium and H. Influenze shared 240 orthologous genes, but these catalyzed incomplete pathways, so non-orthologous gene displacements were hypothesised, resulting in 256 genes "necessary and sufficient to sustain the existence of a modern cell-type". But what is the definition of a minimal self-sufficient gene set? What is the justification for the 'orthology' criteria used; just because a pair of scissors may have arisen from the same design, does not mean they are used to cut the same materials. Similarly, two proteins related by vertical descent and even if identical, do not necessarily have to carry out the same function, in two different organisms. The `minimal genome' produced a quite complex set of proteins capable of translation, DNA replication, recombination and repair, transcription, anaerobic metabolism consisting of glycolysis and substrate phosphorylation, protein export, membrane ATPase, nucleotide lipid and metabolism, and other transport proteins e.g. for amino acids. There was no amino acid biosynthesis. What kind of cell signaling is observed in this hypothetical minimal organism, and what is its function? It appears that M. Genitalium lacks `virtually all known regulatory genes' (Koonin et al 1996).

The authors suggest an algorithm for further reduction of the minimal gene set,

1. Eliminate pathways requiring complex cofactors.

2. Eliminate the remaining regulatory genes.

3. Replace highly conserved families with a multifunctional 'founder'.

4. Apply the `parsimony principle'. A primitive cell's components should be ubiquitously found in all cells today.

5. Addition of photo-autotrophic or chemoautotrophic systems (This awaits full sequencing of autotrophic organisms).]

E.G. Nesbit and N.H. Sleep The habitat and nature of early life. Nature (2001) 409:1083-1091. Download pdf. [Review of a hyperthermophilic LUCA.]

S. Paterson and C. Fraser. Genome Biol. (2001) 2:1-8. The Complexity of Simplicity Download pdf. [Review of minimal genome project.]

D. Penny and A. Poole The nature of the last universal common ancestor. Current Opinion in Genetics and Development (1999) 9:672-677. Download pdf.

T, Pfeiffer and O.S. Soyer and S. Boenhoeffer. The Evolution of Connectivity in Metabolic Networks. Plos Biology (2005) 3(7): 1269-1275 Download pdf.

S.R. Proulx and D.E.L Promislow and P.C. Phillips. Network thinking in ecology and evolution. Trends in Ecology and Evolution. (2005) 20(6): 345-354. Download pdf. [Some very interesting hypothesis about network connectivity and cross talk, that could be tested, see Refernces]

C.V. Rao and J.R. Kirby and A.P. Arkin. Design and Diversity in Bacterial Chemotaxis: A Comparative Study in E.Coli and B. Subtilis. PloS Biology (2004) 2(2):0239- Download pdf. [Comparison of topology of chemotaxis network in two organisms, suggesting a conserved evolutionary mechanism. Simulations performed using matlab. Matlab m-files available at http://genomicslbl.gov/~chris/chemotaxis Note that when producing our evolutionary model, it is necessary that the system could in theory evolve all the known mechanisms by which chemotaxis is observed in practice.]

H.M. Sauro and B.N. Kholodenko Quantitative analysis of signaling networks. Progress in Biophysics and Molecular Biology (2004) 86:5-43. Download pdf.

H.M. Sauro The Computational Versatility of Proetomic Signaling Networks. Current Proteomics (2004) 1:67-81. Download pdf.

M. Schwehm. Parallel Stochastic Simulation of Whole-Cell Models [Discussion of implementation of whole cell stochastic models.] Download pdf.

T.S. Shimizu. The Spatial Organization of Cell Signalling Pathways. PhD Thesis. Darwin College, Cambridge. (2002). Linked site. [An excellent introduction to stochastic modeling of the chemotaxis system of E.Coli. ]

T.W. Simpson and B.D. Follstad and G. Stephanopoulos. Anaysis of pathways structure of metabolic networks. Journal of Biotechnology (1999) 71:207-223. Download pdf.

J.M. Skerket and M.S. Prasol and B.S. Perchuk and E.G. Biondi and M.T. Laub. Two-component signal transduction pathways regulating growth and cell cycle progression in a bacterium: A System-Level Analysis. PLoS Biology. 3(10): 1770-. Download pdf. [Further support for the claim that cross-talk in vivo is rare, and may not be an adaptation. In vitro demonstrations of cross-talk are likely to be artifacts.]

P.A. Spiro and J.S. Parkinson and H.G. Othmer. A Model of excitation and adaptation in bacterial chemotaxis. PNAS (1997) 94:7263-7268. Download pdf. [Contains a full set of reaction equations and rates. Analysis of response to step and ramp stimuli.]

E.J. Stewert et al. Aging and Death in an Organism that reproduces by morphologically symmetric division. PloS Biology 3(2):e45. Download pdf.

R.L Tatusov and A.R. Mushegian et al. Curr Biol (1996), 6:279-291. Download pdf. [Functional analysis of a minimal genome.]

M. Tomita. Trands Biotechnol. (2001) 19:205-210. [Whole cell models of metabolism.]

M. Tomita et al. Bioinformatics. (1999) 15:72-84. [Whole cell models of metabolism. E Cell.] Download pdf.

D.T. Verhamme, J.C. Arents, P.W. Postma, W. Crielaard, K.J. Hellingwerf. Investigation of in vivo cross-talk between key two-component systems in E.Coli. Microbiology (2002) 148:69-78. Download pdf. [Cross talk is "the (modulation of) transfer of phosphoryl groups from a sensory kinase to a 'non-cognate' response regulator." No significant cross-talk was observed in wild-type cells between 4 2-component systems of sensor kinases and response regulators.]

B.E. Wright and M.H. Butler and K.R. Albe. Systems Analysis of the Tricarboxylic Acid Cycle in Dictyostelium Discoideum. 1. The basis for model construction. The Journal of Biological Chemistry (1992), 267 (5):3101-3105. Download pdf.

T.M. Yi. Y. Huang, M.I. Simon, J. Doyle. Robust perfect adaptation in bacterial chemotaxis through integral feedback control. PNAS (2000) 97(9): 4649-4653. Download pdf. [Analysis of integral control mechanisms in bacterial chemotaxis.]

L. You. Toward Computational Systems Biology. Cell Biochemistry and Biophysics. (2004) 40:1-19. Download pdf. [A review of some methods in computational systems biology.]

A review by J. Whitfield in Nature about LUCA, the last common universal ancestor, and Woese's idea of a gene pool. Download pdf.

 

Research In Progress. (2005- )

 

 

Tasks to Evolve a Cell Signaling Network To Solve.

 

Task 1: Evolve a CSN capable of perfect adaptation of a variable, or interdependent variables, subject to perturbations.

 

Possible Solutions

1. Integral feedback control. (see Barkai and Leibler)

2. Daisyworld mechanism with bidirectional rein control, with no error signal required, (see Harvey, and Peter Saunders papers).

Are there other methods? How do the above methods differ? How do the evolved solutions differ given particular patterns of mutational noise, e.g. if there is lots of variation in kinetic rates of enzymes, or stochastic low enzyme numbers, etc... For the same task, but a very different noise pattern, would the networks be very different?

Task 2: Evolve a CSN capable of acting as a bistable switch.

See: D. Bray 1995, Refs 14 [SHACTER ET AL J. NIOL. CHEM 259:12252-12259 (1984)] & 15 [STADTMAN CHOCK PNAS 74:2761-2765, (1977)]. 13 [ARKIN ROSS J. BIOPHYS 67:560-578 (1994)] (Arkin and Ross. Fuzzy logic in control of glycolysis.)

Task 3: Evolve a CSN capable of signal amplification.

See: D. Bray 1995. Ref 22. [CHONK AND STADTMAN. PNAS 74:2766-2770. (1977)] Coupled cycles acting as amplifiers. Computation by cyclic reactions. Ref 23. [OKAMOTO ET AL BIOL. CYBERN 58:295-299(1988)] (Neuron model using proteins). Ref 24: [HJELMFELT SCHNEIDER ROSS SCIENCE 260:335-337, (1993)] Turing machine with proteins.

Task 4: Evolve a CSN for one task, then evolve the resulting CSNs to do another task different and simultaneous task. Is cross-talk a feature of evolved solutions?

See Kitano's paper on robustness and evolvability. Download pdf.

Questions: 1. What is required for re-use, and incremental evolution, i.e. the capacity to utilize previous solutions to solve novel tasks without having to re-evolve the whole thing from scratch?

Task 5: Evolve a CSN capable of osmotic regulation or quorum sensing.

E.g. Download pdf on quorum sensing and cross-talk.

Task 6: Evolve a CSN capable of various metabolic control tasks.

 

Task 7: Evolve a range of CSN designs for bacterial chemotaxis, and understand why different solutions were evolved under different conditions.

Several simulations of bacterial chemotaxis exist (see here). Why is this system used and not another system also capable of perfect adaptation? Why is absolutely perfect adaptation necessary? What mechanisms were evolved before systems capable of perfect adaptation evolved? Are there any factors that prevent perfect adaptation in extant systems?

An outstanding problem was that the sensitivity AND wide-dynamic range of E.Coli chemotaxis was not understood, based on protein concentrations and measured rate-constants.

1. BCT.

2. Simple deterministic model with one methylation site. (Bray et al )

3. Deterministic model with 4 methylation sites. (Mello and Tu )

4. Stochastic model with explicit representation of all kinetics. (Morton-Firth et al ) StochSim stuff.

Levels of description of cell processes.

Consider a toy model consisting of only three kinds of protein. Let each protein be produced by a gene. We assume that a system capable of transcription and translation exists, e.g. polymerase proteins, tRNAs, ribosomes etc... We assume that these base level processes have been stably selected, and that they are no longer subject to selection. I.e. these three proteins may have some functions that are no longer variable, and some properties that are variable. We also provide the system with a high-energy substance equivalent to ATP, that can be used to phosphorylate proteins, in order to change their state, reactivities and specificities. We require that the three proteins be able to evolve a very wide range of interactions, e.g. catalysis of a reaction between another protein and ATP or protein-phosphate e.g. phosphoylation or dephosphorylation of the reactant protein, inhibition and activation of catalysts to produce various commonly observed reaction rate curves, allosteric interactions between proteins producing commonly observed reaction profiles. e.g. if the fixed function of one of the proteins is a polymerase, then we require that the system can evolve a wide range of repression and promotion dynamics, of the sort observed in real systems. First we describe the specification of the system without gene duplication and divergence, or horizontal gene transfer. This simple system is assumed to be capable of only within-gene mutations. Later we will introduce operators that alter the number of genes and proteins.

Let one protein (Pol) be assumed to contain a domain capable of polymerase function, and let the other two proteins be labelled A and B. Alternatively we could have imagined that one of the proteins had a doman capable of activating bacterial flagella. As a first approximation, such a domain is assumed to be fixed and not subject to evolution. The genetic representation of a protein is as follows,

PROTEIN:

1. Non-evolvable Domain Function: E.g. polymerase, flagella activator, membrane protein, cytosolic protein, etc... Fixed (described by some transfer function).

2. Binding properties to other proteins, and other copies of itself. This is determined by a Km, of binding, and a forward and backward rate of binding. There are an infinite number of possible forward and backward rates of binding consistent with a given value of Km. These are a function of the activation energy of intermediates. The Km is determined by the difference in free energy between the products and the reactants. The rates are determined by various conformational properties of the protein. Some method is required therefore to systematically determine the free energy of a given protein that would result due to association of two proteins, and preferably also the kinetics of the reaction. Production of such a method is non-trivial, and it seems that evolution would have been active in production of a mapping between gene sequence and protein function, that would have produced protein particles that responded in interesting ways to mutation, such that the protein network change that resulted from mutation differed in interesting non-random thermodynamic and kinetic patterns.

One approach would be to specify protein shape and force in a physical simulation of some sort, and then to allow the Km and kinetics to emerge from the physical laws of interaction within the simulated world. Another possibility is to give an intermediate level of discription of the Km and kinetics between particles, randomly generating a free energy for each new particle that forms, and allowing mutation to alter the Km and rates of interactions between particles. However, this approach fails to allow the evolution of structural properties of proteins, that allow later evolution by shuffling of protein modules which allows the transfer of thermodynamic and kinetic modules, evolved elsewhere, for use in new problems. Therefore at the very least, our model must contain some notion of protein shape that determines interactivity between proteins. One possibility here is to utilize a non-uniform cellular automata model of protein-protein interaction. Alternatively protein modules could be defined explicitly. A module is defined by its Km and rates of binding and unbinding from other modules. However, whenever two modules are bound, either covalently at protein synthesis, or transiently during non-covalent protein interactions, there is some evolved behaviour that changes the Km and kinetic profile of the contacting modules.

There have been several approaches to defining the details of interactions between artificial molecules. Often these use some sort of labeling, and then determine rates arbitrarily, however, these do not take into account the thermodynamics of interactions. The consideration of a simple simulated physical model of a protein would at least ground our thinking in the physical world. The cell signaling network is fundementally a chemical system, and therefore it is negligent to attribute kinetic circuitries which could not be sustained were energy a state function.

How the network of protein-protein interactions changes as a function of mutation, and other genetic operators, will be crucial in biasing an evolutionary trajectory. Therefore it is necessary to be cognicent of the biases introduced into an artificial evolutionary system in this regard. Some simple examples are useful to demonstrate this fact. [Produce a set of algorithms that results in the generation of interaction graphs between 'proteins'. Try to understand how mutation has different effects on the graph, depending on the algorithm used. Produce a set of algorithms that simply considers three proteins, and the interactions between them. Produce a language to describe these interactions, that allows a wide range of interactions to be specified.]

Questions arising. 1. Do phosphorylated proteins have greater reactivity than non-phosphorylated proteins? 2. What is the network structure of protein-protein interactions (See Maslov)? How does this structure change with mutation?

 

References on Modeling Protein-Protein Interactions (Kinetics and Thermodynamics).

Schreiber G.. Kinetic studies of protein-protein interactions. Curr Opin Struct Biol. 2002 Feb;12(1):41-7.

S. Maslov. K. Snippen. Specificity and stability in topology of protein networks. Download pdf. (2) [Highly connected nodes do not interact very much, just like hubs in airlines. Why is this? H: To minimize interference? ]

Modeling Protien interactions. ppt.

http://www.weizmann.ac.il/mcb/UriAlon/groupWelcome.html

 

Task: Write an algorithm that allows extremely structured and varied network topologies of binding and unbinding proteins to be evolved, by mutation operators applied only to properties of the protein nodes. Ignore the description of biologically plausible dynamics of interactions between proteins for now. In fact ignore the idea that any chemical modifications occur. We are interested purely in evolving a system of particles capable of interesting topologies, thermodynamics and kinetics of non-modifying associations. Much like a set of fixed shapes that could be made from lego, where breakage and formation of bricks is only allowed at the original surfaces. One possibility is to consider each protein as a binary string, and to determine association probability as a function of overlap due to a randomly chosen alignment (or fixed alignment) between the two strings.

 

Task: Superimpose upon the above algorithm another algorithm that is able to generate an interesting and varied range of reaction dynamics again as functions of protein node properties.

The key principle of dynamic network construction using the protein metaphor is that genetic operators act purely on the node properties, exploiting an underlying chemistry that determines how topological interactions will be formed, given node properties. The underlying chemistry itself, may be subject to higher-order evolution.

Notes on Work In Progress (Nov, 2005).

Preliminary notes. Initial thoughts on modeling CSN evolution (Oct, 2005).

Notes on a mesoscopic CSN model. Crazy idea about making a CSN using bits of plastic and magnets.

An ppt of an informal talk given at the new computational biology group at Birmingham University (November 2005) on the evolution of cell signaling networks. . Download ppt.

A ppt. of an informal talk given at the systems biology group at Birmingham University (17th November 2005) on the evolution of metabolism. Download ppt.

 

 

29th November 2005: Preliminary protein dynamics model completed (no conformational changes as yet).

A simulation has been written that models 'protein' interactions. The system is initialized with a list of proteins A,B,C.... each consisting of a list of binding sites, a,b,c,d,... All proteins start with N binding sites (3 for now). Binding site interactions are determined by two matrices, an association matrix and a dissociation matrix. The free energy of an association between two protein complexes is the sum of all possible pairwise association free energies between the free binding sites on each complex. The free energy of a dissociation is the sum of all dissociation free energies of bound binding site pairs on a complex. For the moment, we ignore conformational changes. This is expected to severely limit the computational capacity of the system.

Task 1. Obtain a fixed number of 'a' binding sites (500). The fitness of a population of size 10, is shown over several 'sexual' events carrried out using a microbial GA. Vector mutation is applied to association and dissociation matrices. There is a small probability of a protein type gaining and loosing binding sites. Fitness = -(([a] - [a]*)^2)^0.5, i.e Fitness = 0 if [a] is equal to [a]* for the whole trial. It is not known how the network is solving the problem.

 

Task 2. After 0.03 'seconds' a bolus of 'a' is introduced. We intend this to act as a switch, shifting the system into a new attractor, from ([a] = 10, [b] = 300) to ([a] = 300, [b] = 10). The simulation does not last for a fixed time period, but for 200 events. A fitness score is determined per event. The bolus however is injected at an absolute time of 0.03 seconds. It is not expected that a chemical system without conformational change will be able to solve this problem. The fitness profile of the population is shown below.

 

18th January: Evolution of a stochastic CSN, implemented with 2 branch neighbourhood dependent conformational changes (conformational and binding allostery).

Details of the model in progress can be downloaded from here, or found in the 1st 3 month progress report of the Birmingham group at the ESIGNET wiki.