Synthesizing and tuning chemical reaction networks with specified behaviours

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimise the reaction rates of each CRN using a combination of stochastic search techniques applied to the chemical master equation, simultaneously improving the of correct behaviour and ruling out spurious solutions. In addition, we use techniques from continuous time Markov chain theory to study the expected termination time for each CRN. We illustrate our approach by identifying CRNs for majority decision-making and division computation, which includes the identification of both known and unknown networks.Comment: 17 pages, 6 figures, appeared the proceedings of the 21st conference on DNA Computing and Molecular Programming, 201

The noisy edge of traveling waves

Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling waves remain elusive because they are often dominated by rare fluctuations in the wave tip, which have defied any rigorous analysis so far. Here, we show that by adjusting nonlinear model details, noisy traveling waves can be solved exactly. The moment equations of these tuned models are closed and have a simple analytical structure resembling the deterministic approximation supplemented by a nonlocal cutoff term. The peculiar form of the cutoff shapes the noisy edge of traveling waves and is critical for the correct prediction of the wave speed and its fluctuations. Our approach is illustrated and benchmarked using the example of fitness waves arising in simple models of microbial evolution, which are highly sensitive to number fluctuations. We demonstrate explicitly how these models can be tuned to account for finite population sizes and determine how quickly populations adapt as a function of population size and mutation rates. More generally, our method is shown to apply to a broad class of models, in which number fluctuations are generated by branching processes. Because of this versatility, the method of model tuning may serve as a promising route toward unraveling universal properties of complex discrete particle systems.Comment: For supplementary material and published open access article, see http://www.pnas.org/content/108/5/1783.abstract?sid=693e63f3-fd1a-407a-983e-c521efc6c8c5 See also Commentary Article by D. S. Fisher, http://www.pnas.org/content/108/7/2633.extrac

Field theory for a reaction-diffusion model of quasispecies dynamics

RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a second-order phase transition, which has been dubbed the ``error catastrophe.'' Here we explore this phenomenon using a field theory approximation to the spatially extended Swetina-Schuster quasispecies model [J. Swetina and P. Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape. In analogy with standard absorbing-state phase transitions, we develop a reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model. The field theory representation of the reaction-diffusion system is constructed. The proposed field theory belongs to the same universality class than a conserved reaction-diffusion model previously proposed [F. van Wijland {\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we obtain the full set of exponents that characterize the critical behavior at the error threshold. Our results present the error catastrophe from a new point of view and suggest that spatial degrees of freedom can modify several mean field predictions previously considered, leading to the definition of characteristic exponents that could be experimentally measurable.Comment: 13 page

The three different phases in the dynamics of chemical reaction networks and their relationship to cancer

We investigate the catalytic reactions model used in cell modeling. The reaction kinetic is defined through the energies of different species of molecules following random independent distribution. The related statistical physics model has three phases and these three phases emerged in the dynamics: fast dynamics phase, slow dynamic phase and ultra-slow dynamic phase. The phenomenon we found is a rather general, does not depend on the details of the model. We assume as a hypothesis that the transition between these phases (glassiness degrees) is related to cancer. The imbalance in the rate of processes between key aspects of the cell (gene regulation, protein-protein interaction, metabolical networks) creates a change in the fine tuning between these key aspects, affects the logics of the cell and initiates cancer. It is probable that cancer is a change of phase resulting from increased and deregulated metabolic reactions.Comment: 5 pages, 2 figures, EPL, in pres

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure -- network modularity (the propensity for edges to be cluster into dense groups that are sparsely connected between each other). To reach this goal, we design a model of reaction-systems where network modularity can be controlled and measure how well the reduction to simple graphs capture the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate-product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction-systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreate correlations between degree and mass of the molecules.Comment: to appear in J. Roy. Soc. Intefac

Toward Cultural Oncology: The Evolutionary Information Dynamics of Cancer

'Racial' disparities among cancers, particularly of the breast and prostate, are something of a mystery. For the US, in the face of slavery and its sequelae, centuries of interbreeding have greatly leavened genetic differences between 'Blacks' and 'whites', but marked contrasts in disease prevalence and progression persist. 'Adjustment' for socioeconomic status and lifestyle, while statistically accounting for much of the variance in breast cancer, only begs the question of ultimate causality. Here we propose a more basic biological explanation that extends the theory of immune cognition to include elaborate tumor control mechanisms constituting the principal selection pressure acting on pathologically mutating cell clones. The interplay between them occurs in the context of an embedding, highly structured, system of culturally specific psychosocial stress which we find is able to literally write an image of itself onto disease progression. The dynamics are analogous to punctuated equilibrium in simple evolutionary proces

Lost in translation: Toward a formal model of multilevel, multiscale medicine

For a broad spectrum of low level cognitive regulatory and other biological phenomena, isolation from signal crosstalk between them requires more metabolic free energy than permitting correlation. This allows an evolutionary exaptation leading to dynamic global broadcasts of interacting physiological processes at multiple scales. The argument is similar to the well-studied exaptation of noise to trigger stochastic resonance amplification in physiological subsystems. Not only is the living state characterized by cognition at every scale and level of organization, but by multiple, shifting, tunable, cooperative larger scale broadcasts that link selected subsets of functional modules to address problems. This multilevel dynamical viewpoint has implications for initiatives in translational medicine that have followed the implosive collapse of pharmaceutical industry 'magic bullet' research. In short, failure to respond to the inherently multilevel, multiscale nature of human pathophysiology will doom translational medicine to a similar implosion