Modeling of Actual Eukaryotic Control Gene Subnetworks Based on the Method of Generalized Threshold Models

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thalianaflower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogasterearly ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.     

On parametric stability of gene networks controlling ontogenetic processes

The problem of evaluating the parametric stability of three models of pro- and eukaryotic gene networks controlling ontogenetic processes has been defined and solved. Experimental plans of testing gene networks for parametric stability based on the method of generalized threshold models were developed and realized as a software application. We examined the "sensitivity" of the functioning modes to random variations of the parameters in the three model systems: the system of developmental control of phage lambda, the subsystem of morphogenetic control of Arabidopsis thaliana flower, and the gene subnetwork controlling early ontogeny in Drosophila melanogaster. The parametric stability was quantitatively assessed for these models.     

A new method for the analysis of the dynamics of the molecular genetic control systems. I. Description of the method of generalized threshold models.

In the molecular system of coding polymers and metabolites a control subsystem has been singled out that forms controlling variables showing the action of regulatory molecules and a controlled subsystem where, depending on the values of controlling variables controlled variables are formed, i.e. concentrations of DNA, m-RNA, proteins and metabolites. Relationships have been obtained which enable controlling variables to be found. Equations showing the dynamics of molecular genetic control systems' components have been obtained. A method of generalized threshold models that enables kinetic curves to be obtained by pure mathematical means for macromolecular components (DNA, RNA, proteins) of molecular genetic control systems of varying complexity is suggested.     

On Parametric Stability of Gene Networks Controlling Ontogenetic Processes

The problem of evaluation of parametric stability of three models of pro- and eukaryotic gene networks controlling ontogenetic processes has been defined and solved. Experimental schemes of testing gene networks for parametric stability based on the method of generalized threshold models were developed and realized as a software application. We studied the sensitivity of the functioning modes to random variations of the parameters in three model systems: phage development control system, Arabidopsis thaliana flower morphogenesis control subsystem, and gene subnetwork controlling early ontogeny of Drosophila melanogaster. The parametric stability was quantitatively assessed for these models.     

GeneNet database: description and modeling of gene networks

Almost all cellular processes in an organism are controlled by gene networks. Here we report on the analysis of gene networks functioning using two associated methods - data accumulation in GeneNet system and generalized chemical kinetic method for mathematical simulation of gene network functional dynamics. The technology of the usage of these methods is shown on the example of the gene network of macrophage activation.     

Gene and epigene networks: Two levels in organizing the hereditary system

Intracellular governing gene networks consisting of genes and regulatory bonds among them are considered as the first level in organizing the hereditary system. We give examples of both prokaryotic gene network that controls the development of the λ-phage and eukaryotic gene network that controls the early Drosophila ontogenesis. Using the method of generalized threshold models kinetic curves are shown for some gene products of these networks. Gene networks that govern ontogenetic processes can be envisioned as epigene networks, the networks of the subsequent level in organizing the hereditary systems. Based on the mathematical model our computer experiments show that even the simplest hypothetical two-epigene network is capable of ensuring divergent determination, conservation of determinate states and reproduction of the initial “zygotic” functional state. In addition, the experimental results are given on construction an artificial epigene.     

Molecular mechanics modeling of azobenzene-based photoswitches

We present an extension of the generalized amber force field to allow the modeling of azobenzenes by means of classical molecular mechanics. TD-DFT calculations were employed to derive different interaction models for 4-hydroxy-4'-methyl-azobenzene, including the ground (S(0)) and S(1) excited state. For both states, partial charges and the -N = N- torsion potentials were characterized. On this basis, we pave the way to large-scale model simulations involving azobenzene molecular switches. Using the example of an isolated molecule, the mechanics of cyclic switching processes are demonstrated by classical molecular dynamics simulations.     

Parametric stability evaluation in computer experiments on the mathematical model of Drosophila control gene subnetwork

Using the method of generalized threshold models, the problem is formulated and solved to evaluate the parametric stability of the model of a gene subnetwork controlling the early ontogenesis of the fruit fly Drosophila melanogaster. Computer experiments have been performed to test the parametric stability of the model. Quantitative evaluations have been obtained for parametric stability of the Drosophila gene subnetwork in nuclei along the embryo's anterior-posterior axis. The results of computer experiments have been compared with the previous research data on "sensitivity" of functioning regimes to random changes of the parameters in the models of prokaryotic and eukaryotic systems, namely the system controlling the lambda-phage development and the subsystem controlling the flower morphogenesis of Arabidopsis thaliana. The obtained results confirm high parametric stability of gene networks that control the development of organisms.     

Ecological theory of mutualism: Robust patterns of stability and thresholds in two‐species population models

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two‐species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.     

Analysis of protein distribution in budding yeast

Flow cytometry is a fast and sensitive method that allows monitoring of different cellular parameters on large samples of a population. Protein distributons give relevant information on growth dynamics, since they are related to the age distribution and depend on the law of growth of the population and the law of protein accumulation during the cell cycle. We analyzed protein distributions to evaluate alternative growth models for the budding yeast Saccharomyces cerevisiae and to monitor the changes in population dynamics that result from environmental modifications; such an analysis could potentially give parameters useful in the control of biotechnological processes. Theoretical protein distributions (taking into account the unequal division of yeast cells and the exponential law of protein accumulation during a cell cycle) quantitatively fit experimental distributions, once appropriate variability sources are introduced. Best fits are obtained when the protein threshold required for bud emergence increases at each new generation of parent cells.     

The utility of behavioral models and modules in molecular analyses of social behavior

It is extremely difficult to trace the causal pathway relating gene products or molecular pathways to the expression of behavior. This is especially true for social behavior, which being dependent on interactions and communication between individuals is even further removed from molecular-level events. In this review, we discuss how behavioral models can aid molecular analyses of social behavior. Various models of behavior exist, each of which suggest strategies to dissect complex behavior into simpler behavioral 'modules.' The resulting modules are easier to relate to neural processes and thus suggest hypotheses for neural and molecular function. Here we discuss how three different models of behavior have facilitated understanding the molecular bases of aspects of social behavior. We discuss the response threshold model and two different approaches to modeling motivation, the state space model and models of reinforcement and reward processing. The examples we have chosen illustrate how models can generate testable hypotheses for neural and molecular function and also how molecular analyses probe the validity of a model of behavior. We do not champion one model over another; rather, our examples illustrate how modeling and molecular analyses can be synergistic in exploring the molecular bases of social behavior.     

Quantitative character dynamics: Gametic model

A gametic model of quantitative character dynamics is introduced that fills the gap between the two existing models: genic and zygotic/phenotypic. In this model, a gamete is treated as the elementary unit of evolution, all biological processes at the levels below gametic remain unspecified, and a gamete is characterized by its effect on the quantitative character rather than by the genotype. The hereditary and developmental processes are accounted for in a generalized form by gametogenetic and developmental functions defined for a pair of gametic effects representing an individual. A parameterization of these functions is suggested that imposes constraints on the heredity of quantitative characters similar to the constraints imposed by traditional genic models. It is shown that this parameterization can be derived for some polygenic additive models. General expressions for the dynamics of the mean and variance of additive quantitative characters are obtained, and the dynamics under random mating for sex-independent, sex-controlled, and sex-linked characters are considered. Comparisons with the dynamics predicted by genic models are made.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

Perspectives in stochastic models of human reproduction: A review and analysis

The purpose of this paper is to review, to analyze, and to take steps toward synthesizing, two research areas in stochastic models of population dynamics. The first of these areas consists of stochastic models of human reproduction associated with the late Mindel C. Sheps and the second area is a class of stochastic models of population growth called generalized age-dependent branching processes, a class of models that shows promise of throwing more light on the classical mathematical demography of Lotka. The substantive material of the paper is arranged in eight sections ranging in content from a comparison of classical mathematical demography with generalized age-dependent branching processes, to suggestions for restructuring models of the Sheps school in quest of greater realism. The paper ends with a section on numerical examples illustrating applications in family planning evaluation and an appendix suggesting ways in which algebraic concepts are useful in short cutting computations.     

Application of Quasi-Steady-State Methods to Nonlinear Models of Intracellular Transport by Molecular Motors

Molecular motors such as kinesin and dynein are responsible for transporting material along microtubule networks in cells. In many contexts, motor dynamics can be modelled by a system of reaction–advection–diffusion partial differential equations (PDEs). Recently, quasi-steady-state (QSS) methods have been applied to models with linear reactions to approximate the behaviour of the full PDE system. Here, we extend this QSS reduction methodology to certain nonlinear reaction models. The QSS method relies on the assumption that the nonlinear binding and unbinding interactions of the cellular motors occur on a faster timescale than the spatial diffusion and advection processes. The full system dynamics are shown to be well approximated by the dynamics on the slow manifold. The slow manifold is parametrized by a single scalar quantity that satisfies a scalar nonlinear PDE, called the QSS PDE. We apply the QSS method to several specific nonlinear models for the binding and unbinding of molecular motors, and we use the resulting approximations to draw conclusions regarding the parameter dependence of the spatial distribution of motors for these models.