Quantum processes in evolution of regulation of living systems (mathematical modeling)

We have developed an imitation model of the appearance of regulation of physiological functions of protocell at initial stages of evolution of living system. It is based on suggestion of the appearance of signal function in spontaneously formed products of partial hydrolysis of the protocell polypeptides, based on which there appear the regulatory molecules—quanta of regulation. For construction of the model, the mathematical apparatus of final automats and of genetic algorithm is used. The model has demonstrated the positive role of involvement of regulatory peptides in the system of regulation of protocell functions to provide its viability under the changing envelopment conditions.     

A mathematical model of periodic processes in membranes (with application to cell cycle regulation)

A mathematical model of the regulation of the cell cycle by the plasma membrane is suggested. The model is based on the hypothesis that structural transitions of the cell membrane play an important role in the regulation of cell division. Conditions of transition from the proliferating state to the resting state and back are investigated. Possible qualitative differences between models of the cell cycle of a normal and a tumour cell are pointed out.     

Biomathematical aspects of numerical evaluation and mathematical modelling of non-monotonous exponential measuring processes

Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched. By means of 2 real examples of measured data, it will be demonstrated how the results of the model-free evaluation may serve for internal regression to estimate starting parameter values for an iterative fitting of a BATEMAN function to measured data courses. Furthermore, it is shown that the model-free approach of data evaluation may give substantial hints for the mathematical model building process and for model verification.     

The feasibility of utilizing a mathematical model in studying nonlinear transport processes in living systems

On the basis of proportionality between flow and its conjugated force a mathematical model for volume, current and osmotic flows was designed and a method for the experimental measurement of flows, the transbarrier (trans-segmental) potential and the rate of flow was devised. The results obtained experimentally as well as using the mathematical model indicate that the plant root is differentiated not only according to localization, but also according to the conductivity, permeability and selectivity of these tissues.     

A mathematical framework for modelling cambial surface evolution using a level set method

Background and Aims

During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale.

Methods

The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes.

Key Results

The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself.

Conclusions

Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure.     

Adaptive processes drive ecomorphological convergent evolution in antwrens (Thamnophilidae)

Phylogenetic niche conservatism (PNC) and convergence are contrasting evolutionary patterns that describe phenotypic similarity across independent lineages. Assessing whether and how adaptive processes give origin to these patterns represent a fundamental step toward understanding phenotypic evolution. Phylogenetic model‐based approaches offer the opportunity not only to distinguish between PNC and convergence, but also to determine the extent that adaptive processes explain phenotypic similarity. The Myrmotherula complex in the Neotropical family Thamnophilidae is a polyphyletic group of sexually dimorphic small insectivorous forest birds that are relatively homogeneous in size and shape. Here, we integrate a comprehensive species‐level molecular phylogeny of the Myrmotherula complex with morphometric and ecological data within a comparative framework to test whether phenotypic similarity is described by a pattern of PNC or convergence, and to identify evolutionary mechanisms underlying body size and shape evolution. We show that antwrens in the Myrmotherula complex represent distantly related clades that exhibit adaptive convergent evolution in body size and divergent evolution in body shape. Phenotypic similarity in the group is primarily driven by their tendency to converge toward smaller body sizes. Differences in body size and shape across lineages are associated to ecological and behavioral factors.     

Systems biology and the mathematical modelling of antibody-directed enzyme prodrug therapy (ADEPT)

Antibody-directed enzyme prodrug therapy (ADEPT) can generate highly localised concentrations of cytotoxic agents directly in a tumour, thereby reducing the collateral toxicity associated with normal tissue exposure. ADEPT is a two-component approach. First, a non-toxic antibody-enzyme fusion protein is localised in the tumour matrix by binding a specific antigen expressed only on the surface of a cancer cell. Once the fusion protein is bound, an inert small molecule prodrug is administered which is the substrate for the enzyme bound to the tumour surface. When the prodrug comes into contact with the bound enzyme, an active cytotoxic agent is generated. A multiple length-scale model of ADEPT therapy in solid tumours is presented. A four-compartment pharmacokinetic (PK) model is formulated where the tumour is comprised of interstitial and cell-surface subcompartments. The macroscopic PK model which describes the biodistribution of antibody-enzyme conjugate, prodrug and active drug at the largest length scale is coupled to a reaction-diffusion tumour model. The models are qualitatively validated against current literature and experimental understanding. The relationship between tumour localisation and the affinity of the antibody-enzyme conjugate for its surface antigen is explored by simulation. The influence of pharmacokinetic and biophysical parameters such as renal elimination rate and permeability of the tumour vasculature upon tumour uptake and retention of the fusion protein are also explored. Lastly, a technique for establishing an optimal prodrug dosing schedule is formulated and initial simulation results are presented.     

Nonuniform processes of chromosome evolution in sedges (Carex: Cyperaceae)

Holocentric chromosomes-chromosomes that lack localized centromeres-occur in numerous unrelated clades of insects, flatworms, and angiosperms. Chromosome number changes in such organisms often result from fission and fusion events rather than polyploidy. In this study, I test the hypothesis that chromosome number evolves according to a uniform process in Carex section Ovales (Cyperaceae), the largest New World section of an angiosperm genus renowned for its chromosomal variability and species richness. I evaluate alternative models of chromosome evolution that allow for shifts in both stochastic and deterministic evolutionary processes and that quantify the rate of evolution and heritability/phylogenetic dependence of chromosome number. Estimates of Ornstein-Uhlenbeck model parameters and tree-scaling parameters in a generalized least squares framework demonstrate that (1) chromosome numbers evolve rapidly toward clade-specific stationary distributions that cannot be explained by constant variance (Brownian motion) evolutionary models, (2) chromosome evolution in the section is rapid and exhibits little phylogenetic inertia, and (3) explaining the phylogenetic pattern of chromosome numbers in the section entails inferring a shift in evolutionary dynamics at the root of a derived clade. The finding that chromosome evolution is not a uniform process in sedges provides a novel example of karyotypic orthoselection in an organism with holocentric chromosomes.     

On the mathematical modelling of pain

In this review a case is presented for the use of mathematical modelling in the study of pain. The philosophy of mathematical modelling is outlined and a recommendation is made for the use of modern nonlinear techniques and computational neuroscience in the modelling of pain. Classic and more recent examples of modelling in neurobiology in general and pain in particular, at three different levels—molecular, cellular and neural networks—are described and evaluated. Directions for further progress are indicated, particularly in plasticity and in modelling brain mechanisms. Major advantages of mathematical modelling are that it can handle extremely complex theories and it is non-invasive, and so is particularly valuable in the investigation of chronic pain. Special issue dedicated to Dr. Herman Bachelard     

Patterns and processes in the evolution of the eukaryotic endomembrane system

Abstract

The eukaryotic endomembrane system (ES) is served by hundreds of dedicated proteins. Experimental characterization of the ES-associated molecular machinery in several model eukaryotes complemented by a recent progress in phylogenomics and comparative genomics have revealed a conserved complex core of the machinery that appears to have been established before the last eukaryotic common ancestor (LECA). At the same time, modern eukaryotes exhibit a huge variation in the ES resulting from a multitude of evolutionary processes operating along the ever-branching paths from the LECA to its descendants. The most important source of evolutionary novelty in the ES functioning has undoubtedly been gene duplication followed by divergence of the gene copies, responsible not only for the pre-LECA establishment of many multi-paralog families of proteins in the very core of the ES-associated machinery, but also for post-LECA lineage-specific elaborations via family expansions and the origin of novel components. Extreme sequence divergence has obscured actual homologous relationships between potentially many components of the machinery, even between orthologous proteins, as illustrated by the yeast Vps51 subunit of the vesicle tethering complex GARP hypothesized here to be a highly modified ortholog of a conserved eukaryotic family typified by the zebrafish Fat-free (Ffr) protein. A dynamic evolution of many ES-associated proteins, especially those centred around RAB and ARF GTPases, seems to take place at the level of their domain architectures. Finally, reductive evolution and recurrent gene loss are emerging as pervasive factors shaping the ES in all phylogenetic lineages.     

Patterns and processes in the evolution of the eukaryotic endomembrane system

The eukaryotic endomembrane system (ES) is served by hundreds of dedicated proteins. Experimental characterization of the ES-associated molecular machinery in several model eukaryotes complemented by a recent progress in phylogenomics and comparative genomics have revealed a conserved complex core of the machinery that appears to have been established before the last eukaryotic common ancestor (LECA). At the same time, modern eukaryotes exhibit a huge variation in the ES resulting from a multitude of evolutionary processes operating along the ever-branching paths from the LECA to its descendants. The most important source of evolutionary novelty in the ES functioning has undoubtedly been gene duplication followed by divergence of the gene copies, responsible not only for the pre-LECA establishment of many multi-paralog families of proteins in the very core of the ES-associated machinery, but also for post-LECA lineage-specific elaborations via family expansions and the origin of novel components. Extreme sequence divergence has obscured actual homologous relationships between potentially many components of the machinery, even between orthologous proteins, as illustrated by the yeast Vps51 subunit of the vesicle tethering complex GARP hypothesized here to be a highly modified ortholog of a conserved eukaryotic family typified by the zebrafish Fat-free (Ffr) protein. A dynamic evolution of many ES-associated proteins, especially those centred around RAB and ARF GTPases, seems to take place at the level of their domain architectures. Finally, reductive evolution and recurrent gene loss are emerging as pervasive factors shaping the ES in all phylogenetic lineages.     

A mathematical model of the regulation system of the secretion of glucocorticoids

We propose a mathematical model for the regulation system of the secretion of glucocorticoids and determined the coefficients in the system of ordinary differential equations. Some results are calculated which agree with the experimental results.     

The case for mathematical modelling of schistosomiasis

Large problems, such as the large-scale transmission of parasitic disease, are complex and difficult to predict. Understanding them, in order to make cost-efficient choices about possible control interventions, requires knowledge from a very wide range of specialists. Modelling the system can help to do this, but must not ignore the specific requirements of administrators and executives who have to work with high-level decisions about disease control. To many, the modelling approach seems arcane and divorced from reality, unable to answer the decision-makers. But techniques are improving, and in this article, Norman Bailey puts the case for the mathematical modelling of schistosomiasis.     

How mathematical modelling elucidates signalling in Bacillus subtilis

Appropriate stimulus perception, signal processing and transduction ensure optimal adaptation of bacteria to environmental challenges. In the Gram‐positive model bacterium Bacillus subtilis signalling networks and molecular interactions therein are well‐studied, making this species a suitable candidate for the application of mathematical modelling. Here, we review systems biology approaches, focusing on chemotaxis, sporulation, σ^B‐dependent general stress response and competence. Processes like chemotaxis and Z‐ring assembly depend critically on the subcellular localization of proteins. Environmental response strategies, including sporulation and competence, are characterized by phenotypic heterogeneity in isogenic cultures. The examples of mathematical modelling also include investigations that have demonstrated how operon structure and signalling dynamics are intricately interwoven to establish optimal responses. Our review illustrates that these interdisciplinary approaches offer new insights into the response of B. subtilis to environmental challenges. These case studies reveal modelling as a tool to increase the understanding of complex systems, to help formulating hypotheses and to guide the design of more directed experiments that test predictions.     

Development of energetics in evolution of the living world (Stages,Digits, Postulates)

This work deals with the current stage of study of energy exchange between living organ-isms and the environment. In the epoch of molecular biology, study of energy exchange might have seemed a study of old, well known concepts. However, the retrospective insight into the energy exchange of quite a few organisms allows obtaining new data about development of energetics of the living world, approaches to interesting comparisons, opens the earlier unknown quantitative relations in energetics of living organisms, provides a possibility of analyzing causes of very high values of energy consumption by living organisms, causes of different sensitivity of living organisms to deficit of energy, etc. Based on all these data, there have been noted 12 principal moments or postulates in development of energetics of the living world from the most ancient to the present time.     

Hierarchical modelling of acclimatory processes

The term acclimation has been used with several connotations in the field of acclimatory physiology. An attempt has been made, in this paper, to define precisely the term “acclimation” for effective modelling of acclimatory processes. Acclimation is defined with respect to a specific variable, as cumulative experience gained by the organism when subjected to a step change in the environment. Experimental observations on a large number of variables in animals exposed to sustained stress, show that after initial deviation from the basal value (defined as “growth”), the variables tend to return to basal levels (defined as “decay”). This forms the basis for modelling biological responses in terms of their growth and decay.Hierarchical systems theory as presented by Mesarovic, Macko & Takahara (1970) facilitates modelling of complex and partially characterized systems. This theory, in conjunction with “growth-decay” analysis of biological variables, is used to model temperature regulating system in animals exposed to cold. This approach appears to be applicable at all levels of biological organization. Regulation of hormonal activity which forms a part of the temperature regulating system, and the relationship of the latter with the “energy” system of the animal of which it forms a part, are also effectively modelled by this approach. It is believed that this systematic approach would eliminate much of the current circular thinking in the area of acclimatory physiology.