In Silico Evolution of Biochemical Log-Response.

Numerous biological systems are known to harbor a form of logarithmic behavior, from Weber's law to bacterial chemotaxis. Such a log-response allows for sensitivity to small relative variations of biochemical inputs over a large range of concentration values. Here we use a genetic algorithm to evolve biochemical networks displaying a logarithmic response. A quasi-perfect log-response implemented by the same core network evolves in a convergent way across our different in silico replications. The best network is able to fit a logarithm over 4 orders of magnitude with an accuracy of the order of 1%. At the heart of this network, we show that a logarithmic approximation may be implemented with one single nonlinear interaction, that can be interpreted either as multisite phosphorylations or as a ligand induced multimerization. We provide an analytical explanation for the effect and exhibit constraints on parameters. Biological log-response might thus be easier to implement than usually assumed.

φ-evo: A program to evolve phenotypic models of biological networks.

Molecular networks are at the core of most cellular decisions, but are often difficult to comprehend. Reverse engineering of network architecture from their functions has proved fruitful to classify and predict the structure and function of molecular networks, suggesting new experimental tests and biological predictions. We present φ-evo, an open-source program to evolve in silico phenotypic networks performing a given biological function. We include implementations for evolution of biochemical adaptation, adaptive sorting for immune recognition, metazoan development (somitogenesis, hox patterning), as well as Pareto evolution. We detail the program architecture based on C, Python 3, and a Jupyter interface for project configuration and network analysis. We illustrate the predictive power of φ-evo by first recovering the asymmetrical structure of the lac operon regulation from an objective function with symmetrical constraints. Second, we use the problem of hox-like embryonic patterning to show how a single effective fitness can emerge from multi-objective (Pareto) evolution. φ-evo provides an efficient approach and user-friendly interface for the phenotypic prediction of networks and the numerical study of evolution itself.

Phenotypic spandrel: absolute discrimination and ligand antagonism.

We consider the general problem of sensitive and specific discrimination between biochemical species. An important instance is immune discrimination between self and not-self, where it is also observed experimentally that ligands just below the discrimination threshold negatively impact response, a phenomenon called antagonism. We characterize mathematically the generic properties of such discrimination, first relating it to biochemical adaptation. Then, based on basic biochemical rules, we establish that, surprisingly, antagonism is a generic consequence of any strictly specific discrimination made independently from ligand concentration. Thus antagonism constitutes a 'phenotypic spandrel': a phenotype existing as a necessary by-product of another phenotype. We exhibit a simple analytic model of discrimination displaying antagonism, where antagonism strength is linear in distance from the detection threshold. This contrasts with traditional proofreading based models where antagonism vanishes far from threshold and thus displays an inverted hierarchy of antagonism compared to simpler models. The phenotypic spandrel studied here is expected to structure many decision pathways such as immune detection mediated by TCRs and FCϵRIs, as well as endocrine signalling/disruption.

Evolution of sparsity and modularity in a model of protein allostery.

The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary constraints may take is important to interpret the information in protein sequences. To study this problem, we introduce a simple but physical model of protein evolution where selection targets allostery, the functional coupling of distal sites on protein surfaces. This model shows how the geometrical organization of couplings between amino acids within a protein structure can depend crucially on its evolutionary history. In particular, two scenarios are found to generate a spatial concentration of functional constraints: high mutation rates and fluctuating selective pressures. This second scenario offers a plausible explanation for the high tolerance of natural proteins to mutations and for the spatial organization of their least tolerant amino acids, as revealed by sequence analysis and mutagenesis experiments. It also implies a faculty to adapt to new selective pressures that is consistent with observations. The model illustrates how several independent functional modules may emerge within the same protein structure, depending on the nature of past environmental fluctuations. Our model thus relates the evolutionary history of proteins to the geometry of their functional constraints, with implications for decoding and engineering protein sequences.