Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

Global Stability of Reversible Enzymatic Metabolic Chains

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. We give some conclusions concerning the dynamical behavior of coupled genetic/metabolic systems.     

Bio-array images processing and genetic networks modelling

The new tools available for gene expression studies are essentially the bio-array methods using a large variety of physical detectors (isotopes, fluorescent markers, ultrasounds...). Here we present first rapidly an image-processing method independent of the detector type, dealing with the noise and with the peaks overlapping, the peaks revealing the detector activity (isotopic in the presented example), correlated with the gene expression. After this primary step of bio-array image processing, we can extract information about causal influence (activation or inhibition) a gene can exert on other genes, leading to clusters of genes co-expression in which we extract an interaction matrix M and an associated interaction graph G explaining the genetic regulatory dynamics correlated to the studied tissue function. We give two examples of such interaction matrices and graphs (the flowering genetic regulatory network of Arabidopsis thaliana and the lytic/lysogenic operon of the phage Mu) and after some theoretical rigorous results recently obtained concerning the asymptotic states generated by the genetic networks having a given interaction matrix and reciprocally concerning the minimal (in the sense of having a minimal number of non-zero coefficients) matrices having given stationary stable states.     

Analyse formelle de circuits de régulation génétique: le contrôle de l'immunité chez les bactériophages lambdoïdes

This paper is an attempt to describe and analyze in formal terms a genetic circuit which is rather complex and reasonably well disentangled: the control of immunity in lambdoid bacteriophages. Known models are expressed as logic equations, which relate the stade of activity of genes to variables of three kinds: genetic variables which describe the genotype of the organism, environmental variables like temperature and memorization variables. The value of each memorization variable (presence or absence of a gene product) is related to the value of the corresponding function (operation or not of the gene) by two characteristic time delays, an «establishment delay and a «decay delay.From the equations, one can derive matrices which facilitate comparison between models by showing which stable states are predicted by each model. Implications of current models, which had apparently remained cryptic, have been realized and experimentally tested.From the matrices, one can derive graphs which show the pathways (sequences of states) consistent with each model. These graphs are frequently branched and in these cases one has to analyze which conditions determine that one pathway rather than another one, is followed.     

Some natural viability systems for a multiallelic locus: a theoretical study

The maintenance of genetic polymorphism under various natural structured viability regimes vs. general unrestricted fitness assignments are compared. The selection models considered include a generalized dominance fitness system, a generalized viability model based on allelic activity values, viability matrices based on multilocus activity levels, viability matrices defined by partitioned "resource" or "substrate" variables, and circulant-type viability matrices. A number of examples that support these formulations are discussed. Detailed results on the nature of the genotype frequency equilibrium configurations for the specified viability models are presented. An increased likelihood for a globally stable equilibrium is predicted for the more structured viability models.     

Linking saturation,stability and sustainability in food webs with observed equilibrium structure

Stability of a dynamic equilibrium in a predator-prey system depends both on the type of functional response and on the point of equilibrium on the response curve. Saturation effects from Holling type II responses are known to destabilise prey populations, while a type III (sigmoid) response curve has been shown to provide stability at lower levels of saturation. These effects have also been shown in multi-trophic model systems. However, stability analyses of observed equilibria in real complex ecosystems have as yet not assumed non-linear functional responses. Here, we evaluate the implications of saturation in observed balanced material-flow structures, for system stability and sustainability. We first make the effects of the non-linear functional responses on the interaction strengths in a food web transparent by expressing the elements of Jacobian ‘community’ matrices for type II and III systems as simple functions of their linear (type I) counterparts. We then determine the stability of the systems and distinguish two critical saturation levels: (1) a level where the system is just as stable as a type I system and (2) a level above which the system cannot be stable unless it is subsidised, separating a stable materially sustainable regime from an unsustainable one. We explain the stabilising and destabilising effects in terms of the feedbacks in the systems. The results shed light on the robustness of observed patterns of interaction strengths in complex food webs and suggest the implausibility of saturation playing a significant role in the equilibrium dynamics of sustainable ecosystems.     

ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION

Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian‐MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson–Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses.     

Duration time of a one-dimensional random walk as a function of the energies of the intermediate states: application for dissociation and relaxation processes in DNA hybrids.

Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.     

Reconstruction of DNA sequences using genetic algorithms and cellular automata: Towards mutation prediction?

Change of DNA sequence that fuels evolution is, to a certain extent, a deterministic process because mutagenesis does not occur in an absolutely random manner. So far, it has not been possible to decipher the rules that govern DNA sequence evolution due to the extreme complexity of the entire process. In our attempt to approach this issue we focus solely on the mechanisms of mutagenesis and deliberately disregard the role of natural selection. Hence, in this analysis, evolution refers to the accumulation of genetic alterations that originate from mutations and are transmitted through generations without being subjected to natural selection. We have developed a software tool that allows modelling of a DNA sequence as a one-dimensional cellular automaton (CA) with four states per cell which correspond to the four DNA bases, i.e. A, C, T and G. The four states are represented by numbers of the quaternary number system. Moreover, we have developed genetic algorithms (GAs) in order to determine the rules of CA evolution that simulate the DNA evolution process. Linear evolution rules were considered and square matrices were used to represent them. If DNA sequences of different evolution steps are available, our approach allows the determination of the underlying evolution rule(s). Conversely, once the evolution rules are deciphered, our tool may reconstruct the DNA sequence in any previous evolution step for which the exact sequence information was unknown. The developed tool may be used to test various parameters that could influence evolution. We describe a paradigm relying on the assumption that mutagenesis is governed by a near-neighbour-dependent mechanism. Based on the satisfactory performance of our system in the deliberately simplified example, we propose that our approach could offer a starting point for future attempts to understand the mechanisms that govern evolution. The developed software is open-source and has a user-friendly graphical input interface.     

Equilibrium structure and stability in a frequency-dependent,two-population diploid model

We investigate the equilibrium structure for an evolutionary genetic model in discrete time involving two monoecious populations subject to intraspecific and interspecific random pairwise interactions. A characterization for local stability of an equilibrium is found, related to the proximity of this equilibrium with evolutionarily stable strategies (ESS). This extends to a multi-population framework a principle initially proposed for single populations, which states that the mean population strategy at a locally stable equilibrium is as close as possible to an ESS.     

Investigating monogenic and complex diseases with pluripotent stem cells

Human genetic studies have revealed the molecular basis of countless monogenic diseases but have been less successful in associating phenotype to genotype in complex multigenic conditions. Pluripotent stem cells (PSCs), which can differentiate into any cell type, offer promise for defining the functional effects of genetic variation. Here, we recount the advantages and practical limitations of coupling PSCs to genome-wide analyses to probe complex genetics and discuss the ability to investigate epigenetic contributions to disease states. We also describe new ways of using mice and mouse embryonic stem cells (ESCs) in tandem with human stem cells to further define genotype-phenotype relationships.     

Dual selection of a genetic switch by a single selection marker

Forward engineering of synthetic genetic circuits in living cells is expected to deliver various applications in biotechnology and medicine and to provide valuable insights into the design principles of natural gene networks. However, lack of biochemical data and complexity of biological environment complicate rational design of such circuits based on quantitative simulation. Previously, we have shown that directed evolution can complement our weakness in designing genetic circuits by screening or selecting functional circuits from a large pool of nonfunctional ones. Here we describe a dual selection strategy that allows selection of both ON and OFF states of genetic circuits using tetA as a single selection marker. We also describe a successful demonstration of a genetic switch selection from a 2000-fold excess background of nonfunctional switches in three rounds of iterative selection. The dual selection system is more robust than the previously reported selection system employing three genes, with no observed false positive mutants during the simulated selections.     

遗传负荷理论的一种普适框架

遗传负荷表示种群由于遗传变异能力的存在而在平均适宜度上的损失,定量讨论各种遗传负荷,对研究现实发生水平上的物种进化具有重要意义,以往的遗传负荷理论从种群平衡出发,探讨现实发生水平上的物种进化,可是,进化是种群平衡的位移;这便构成了理论与现实之间的矛盾,为拓展以往的遗传负荷理论,给出了一个描述各种遗传负荷的普适理论框架,利用这个理论框架既能探讨平衡种群的遗传负荷,又能模写非平衡种群的遗传负荷及其变化,从而克服了以往的遗传负荷理论不能描述非平衡种群和不时与生物进化现实相悖的不足之处,为研究物种的进化提供了一种可靠的模拟方法。     

A modified Ising model of Barabási–Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

     

Genetic code,hamming distance and stochastic matrices

In this paper we use the Gray code representation of the genetic code C = 00, U = 10, G = 11 and A = 01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are doubly stochastic and symmetric. We determine the frequency distributions of the Hamming distances, building blocks of the matrices, decomposition and iterations of matrices. We present an explicit decomposition formula for the genetic code-based matrix in terms of permutation matrices, which provides a hypercube representation of the genetic code. It is also observed that there is a Hamiltonian cycle in a genetic code-based hypercube.     

Lethal mutagenesis and evolutionary epidemiology

The lethal mutagenesis hypothesis states that within-host populations of pathogens can be driven to extinction when the load of deleterious mutations is artificially increased with a mutagen, and becomes too high for the population to be maintained. Although chemical mutagens have been shown to lead to important reductions in viral titres for a wide variety of RNA viruses, the theoretical underpinnings of this process are still not clearly established. A few recent models sought to describe lethal mutagenesis but they often relied on restrictive assumptions. We extend this earlier work in two novel directions. First, we derive the dynamics of the genetic load in a multivariate Gaussian fitness landscape akin to classical quantitative genetics models. This fitness landscape yields a continuous distribution of mutation effects on fitness, ranging from deleterious to beneficial (i.e. compensatory) mutations. We also include an additional class of lethal mutations. Second, we couple this evolutionary model with an epidemiological model accounting for the within-host dynamics of the pathogen. We derive the epidemiological and evolutionary equilibrium of the system. At this equilibrium, the density of the pathogen is expected to decrease linearly with the genomic mutation rate U. We also provide a simple expression for the critical mutation rate leading to extinction. Stochastic simulations show that these predictions are accurate for a broad range of parameter values. As they depend on a small set of measurable epidemiological and evolutionary parameters, we used available information on several viruses to make quantitative and testable predictions on critical mutation rates. In the light of this model, we discuss the feasibility of lethal mutagenesis as an efficient therapeutic strategy.     

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2ⁿ possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.     

Using Correlation Proximity Graphs to Study Phenotypic Integration

Characterizing and comparing the covariance or correlation structure of phenotypic traits lies at the heart of studies concerned with multivariate evolution. I describe an approach that represents the geometric structure of a correlation matrix as a type of proximity graph called a Correlation Proximity graph. Correlation Proximity graphs provide a compact representation of the geometric relationships inherent in correlation matrices, and these graphs have simple and intuitive properties. I demonstrate how this framework can be used to study patterns of phenotypic integration by employing this approach to compare phenotypic and additive genetic correlation matrices within and between species. I also outline a graph-based method for testing whether an inferred correlation proximity graph is one of a number of possible models that are consistent with a “soft” biological hypothesis.     

The Arabidopsis thaliana flower organ specification gene regulatory network determines a robust differentiation process

The Arabidopsis thaliana flower organ specification gene regulatory network (FOS-GRN) has been modeled previously as a discrete dynamical system, recovering as steady states configurations that match the genetic profiles described in primordial cells of inflorescence, sepals, petals, stamens and carpels during early flower development. In this study, we first update the FOS-GRN by adding interactions and modifying some rules according to new experimental data. A discrete model of this updated version of the network has a dynamical behavior identical to previous versions, under both wild type and mutant conditions, thus confirming its robustness. Then, we develop a continuous version of the FOS-GRN using a new methodology that builds upon previous proposals. The fixed point attractors of the discrete system are all observed in the continuous model, but the latter also contains new steady states that might correspond to genetic activation states present briefly during the early phases of flower development. We show that both the discrete and the continuous models recover the observed stable gene configurations observed in the inflorescence meristem, as well as the primordial cells of sepals, petals, stamens and carpels. Additionally, both models are subjected to perturbations in order to establish the nature of additional signals that may suffice to determine the experimentally observed order of appearance of floral organs. Our results thus describe a possible mechanism by which the network canalizes molecular signals and/or noise, thus conferring robustness to the differentiation process.