BIOMAT 2015

The following sections are included:

• Preface
• Editorial Board of the BIOMAT Consortium
• Contents

Leishmaniasis is a widespread neglected tropical disease caused by Leishmania protozoan parasites that are transmitted to mammalian hosts through bites of infected female sandfly vectors. The human and sandfly hosts provide a harsh ecological niche for Leishmania parasites to survive and proliferate. Due to its adaptation to the host environment, Leishmania parasites optimize their metabolism to utilize the available inadequate resources for maximum growth and energy generation. This adaptation is developed through a long-standing evolutionary relationship of the parasite phenotype with the host. Understanding the role of metabolic function on evolution of enzymes requires a systems-wide perspective. In our study, we attempt to bridge the molecular evolution of the genotype with the phenotype thereby understanding the influence of metabolic network structure and its function on enzyme evolution in the Leishmania parasite. To explore this phenomenon, using an available reconstruction of Leishmania major metabolism, we attempt to understand the relationship of in-silico predicted flux profiles of the L. major metabolic network and its topological properties with the evolutionary rates of metabolic enzymes. Our results suggest that the central, highly connected metabolic enzymes evolve at a faster rate as compared to less connected enzymes. On the contrary, enzymes bearing a higher flux under a minimal environment with rich carbon sources presented by the host, experience higher evolutionary constraints. Performing a genome-wide flux coupling analysis, we also explain the trend of evolutionary rate within enzymes belonging to flux-coupled pathways. Also, we explain the relationship of codon usage with network flux to understand the influence of the genome on metabolic function. Our study highlights the importance of systems-based approaches to understand the role of enzymatic evolution in L. major thereby leading to an adaptive description of metabolic function.

Influenza causes many deaths and affects millions of individuals worldwide every year. Immunity against influenza can be acquired through natural infection or vaccination. Immunity, however, will wane over time as immune system cells die and the ciruclating influenza strains evolve. We have developed a model to study the effects of waning immunity over two years of infection and vaccination history. Results show that natural infection in the previous year and immunization in the current year provide the best protection against seasonal influenza, depending on the transmissibility of the circulating strain. Using our results, targets for reduction in influenza incidence can be determined. These results are relevant to public health, allowing updates of vaccination coverage targets are the relative fitness between the current circulating strain to the vaccine and previous year's circulating strain change.

We study how the distribution of infectious periods influences the dynamics of epidemics on networks. In our recently developed framework, we use pairwise models for network epidemics with non-Markovian recovery times. It is shown for typical families of distributions (such as gamma, uniform and lognormal) that higher variance in the recovery times generates lower reproduction numbers and different epidemic curves within each distribution family. We also show that knowing the expected value and the variance of the recovery times is not sufficient to determine the key characteristics of the epidemics such as initial growth rate, peak size, peak time and final epidemic size. For accurate predictions, more detailed information on the distribution of the infectious period is required, thus carefully estimating this distribution in the case of real epidemics has paramount public health importance.

The discovery of glycoconjugate vaccines has had a significant impact on reducing the health burden of several infectious diseases, including Haemophilus influenzae serotype b. However, the use of such vaccines against a single or several serotypes of some pathogens has been a concern for serotype replacement. Previous studies have demonstrated this replacement phenomenon with limited evidence. However, the possible mechanisms of serotype replacement in the context of vaccination are not well understood. Here, we propose a modelling framework, which integrates the two scales of in-host and between-host infection dynamics to investigate the pathogen-host characteristics that are essential for serotype replacement. We integrate a stochastic model of pathogen dynamics in-host with an agent-based model of disease transmission between-hosts, which provides a novel approach for our investigation. We apply this multi-scale modelling framework to better understand the factors involved in serotype replacement of as a result of vaccination.

We present an overview of the current status of the European collaborative project PAEON. The challenge of PAEON is to provide specialists in reproductive medicine with a computerised model of the menstrual cycle under normal and various pathological conditions, which will allow them to get further insight in fertility dynamics. This model also enables the simulation of treatment protocols, which were used within in vitro fertilization. By the definition of virtual patients through biologically admissible parametrizations our approach allows not only the evaluation of a given treatment strategy in silico, but also the design and optimization of such protocols. Once a protocol is formalized in the virtual hospital, the success can be controlled by a treatment execution monitor, which works then as a clinical decision support system. All these tools will be combined in a virtual hospital environment, enabling the access to the PAEON services through the web.

Networks are known to effectively represent the architecture of many complex biological systems. We propose a new network metric, edge proximity, 𝔓_e, which identifies proteins with essential cellular functions in protein-protein interaction networks. It pinpoints regulatory neural connections and important portions of the neural and brain networks, respectively. Energy flow interactions identified by 𝔓_e form the backbone of long food web chains. We briefly discuss the potential that networks possess in diagnostics and how this can be utilised to build suitable biomedical devices. We introduce the technique of differential networks (DN). DN lend us valuable information about the light-dark transition observed in an entire class of light-sensitive proteins having wide applications in synthetic protein designing, especially with regard to optogenetics. It provides a suitable alternative and simultaneously introduces a framework to guide extensive mutagenesis studies.

To counteract the antagonistic relationship between milk yield and fertility in dairy cow, a deeper understanding of the underlying biological mechanisms is required. For this purpose, we study physiological networks related to reproduction and metabolism of dairy cows. We interactively develop dynamic, mechanistic models by fitting the models to experimental data and mechanistic knowledge.

We have already developed models for potassium balance and hormonal regulation of fertility in the dairy cow, which will briefly be reviewed here. The main focus of this article is on a currently developed glucose-insulin model. This model links the bovine hormonal cycle and the potassium balance to glucose and thus to energy metabolism. The models can be applied in scientific research, education, experimental planning, drug development and production on farms.

Graph theory provides mathematical insight into many areas of contemporary biology such as genomics, metabolonomics, ecology, evolution, biochemistry, etc. because it provides a highly visual and easily comprehensible representation of patterns, processes, and products for testing causal hypotheses. Thus, there is an enormous need for graph theoretic visualization tools that make it easy for biologists to enter data, interact with existing data bases, and generate a variety of different layouts of graphs. BioGrapher is a versatile Excel front-end for the Graphviz graphical visualization library and software package that we have contributed to the Biological Excel Simulations and Tools for Exploratory, Experiential Mathematics (ESTEEM) collection, available online at www.bioquest.org/ESTEEM. While a number of excellent stand-alone applications that incorporate Graphviz for different platforms and operating systems are available, BioGrapher is unique in that, in keeping with the best practices standards of the ESTEEM suite of which it is a part, it uses the standard and ubiquitous Excel environment as the front-end and graphical user interface. It implements the visualization of graphs (nodes and edges) that are specified as standard adjacency matrices using the Excel spreadsheet paradigm of rows and columns, with connections between nodes represented by a non-zero (non-empty) cell value for the appropriate row and column. A complete Visual Basic for Applications (VBA) Excel interface has been programmed and implemented as an additional custom menu bar menu, with enough functionality for the user to invoke many graphical drawing and manipulation routines. Herein we present details of the Excel app (available for both MacOS X and MS Windows 7/8) and its applications in problem solving in mathematical biology. Specifically, we present details for food webs as canonical examples of biological networks that may display the properties and features associated with small world networks. An algorithmic approach using graph theory, BioGrapher, and the complementary JavaBENZER app for generation of interval graphs is demonstrated.

In developmental biology, molecular genetic components have been considered as key in regulating the developmental mechanisms of plants and animals. Stem cells divide at a different rate depending on their position in the tissue, and eventually differentiate to form a recognisable anatomic entity. How this process happen if stem cells are identical sharing the same composition, DNA, genes and genetic networks? We propose that cells collect positional information on their environment by sensing mechanical and chemical fields. We propose a dynamical model to describe the early development of stem cells in a tissue. We choose the root meristem of Arabidopsis thaliana to explore the emergence of cellular patterns through a cooperative dynamics, as this system is well studied at the molecular, genetic and cellular levels and presents the key features of multicellular stem-cell niches. We successfully predict the variations of cell life cycle seen in the actual root meristem. Our model could be applied to other systems of interest, as the emergence of colorectal cancer. We also give a brief description of the dynamics of stem cells in the colonic crypts.

Water fluidity is modified, in a nontrivial manner, by the presence of bacteria above a threshold number density. Under such threshold conditions swimming bacterial suspensions impose a coordinated water movement on a length scale of the order (10–100) micrometers compared with a bacterial size of the order of 3 micrometers. This observation leads to fundamental questions concerning the cell-to-cell communication presently known as quorum sensing. The aim of this paper is to study the quorum state using non-local hydrodynamics. We emphasize that densely packed bacteria may be viewed as ‘bacterial fluid’ or ‘living fluid’ similar to that of dense granular systems. The behaviour of the fluid of granular mass is quite different from that of typical fluids. This granularity imposes a second source of fluctuations because grains cannot be treated as points at any length scale. This type of fluctuation is known as non-local noise in contrast to local noise in usual hydrodynamic flow. The non-local hydrodynamical framework is applied here to consider the effect of non-local noise. In this framework of nonlocal hydrodynamics viscosity is generated by self-induced noise. This viscosity leads the actively moving bacteria into the meta-stable states required to support quorum, given the non-local nature of stresses mediated by autoinducers. The shear stress created non-locally within this framework depending on the non-local noise of granularity and the viscosity associated to the this noise can be tested experimentally. The existence of this kind non-chemical self-induced process may be present not only in cell-to-cell bacteria communication but also in eukaryotic cell-to-cell interactions.

Proteins exhibit intriguing diversity in their three dimensional conformations that enables them to perform different functions. Detailed understanding of protein conformational landscape is imperative for application in structure based inhibitor design. In this study, protein structures have been analyzed for the pattern of convex hulls based on C_α atom coordinates. A convex hull is a polygon whose vertices are a subset of a given set of points such that all the points are enveloped within the polygon. Iterative calculations of convex hull for proteins have provided interesting insights into their conformational features. A detailed and comprehensive analysis of convex hull pattern for non-redundant dataset of proteins revealed that the number of layers per protein ranged from 5 to 20 with an average of 8 layers. Statistical analysis shows that there exist 70% correlation between number of convex hull layers and radius of gyration of a protein. Correlation between radius of gyration and number of convex hull layers for different structural classes of proteins has also been performed. These results provide a novel approach for convex hull based interpretation/ comparison of proteins structures.

Biological systems are complex, large and quasi-deterministic. Study and analysis of such large systems by holistic approaches are difficult in most cases due to lack of various resources. But if the system can be reduced to an abstract level without compromising the essential data, it can be handled and still significant results can be inferred from it. Boolean Networks provide one way of such abstract level analysis for dynamic biological systems. State transition matrices derived from dynamic behavior of these systems allow application of standard inference methods to discover dependencies among the elements present in such a system. Signal transduction pathways (by which cells detect, convert, and internally transmit information) can be modeled by ideas taken from such predictive methods. Wnt signal transduction pathway is an appropriate candidate for such kind of modeling due to its crucial presence in multiple types of cancers. Here we present a methodology pipeline for detecting i) stable system states, ii) robustness, and iii) stability of a whole system using Boolean logic based thumb rules. A unique thumb rule is designed for each biological interaction found in signal transduction pathways. A predicted system state is deemed as stable when it can be predicted without any clash of thumb rules. Robustness of a stable system state is measured by the number of permissible state transitions it can tolerate without loosing its stability. Stability of a whole system is studied by creating a state transition diagram, where stable system states are nodes and the transitions among them are edges. The methodology pipeline is tested on a 5-node (4 interactions) hypothetical network, a 14-node (15 interactions) example network and the human Wnt signal transduction pathway (59 nodes and 68 interactions). In the hypothetical network only two stable system states are found against the predicted 2⁵ states. In the example network, system states 1 and 17 are found to be maximally robust. State transition diagram of the example network revealed it to be a bistable system with two distinct phases each containing one of the maximum robust system states. The human Wnt signal transduction pathway is found to exist in 8 distinct phases that can be supported by existing works.

The expertise of senior biologists has been used to identify and classify Protein Domains. In despite of usual discordances among biological research groups, a good overlap of conclusions has been obtained on the task of assembling Protein Domains into families. A subsequent classification obtained from assembling families into “Clans” is tested on the present work with ANOVA Statistical Techniques. The available results do not seem to reject the “Clan” classification but some suggestions for deleting families and the possible partition of “Clans' are proposed from the present statistical analysis.

We seek a better understanding of this evolution over influenza seasons. In a previous work, we studied the evolution (antigenic drift) of the highly variable influenza A H3N2 by focusing on the hemagglutinin (HA) viral glycoprotein. In this update, we include also the neuraminidase (NA) glycoprotein, another protein that contributes to the antigenic drift of influenza. Our method is based on a dimension reduction technique combined with a fully automatic Hamming distance statistical clustering method for categorical data (Zhang et al. JASA, 2006). The new NA results are compared with the previous HA results to provide a more complete picture of flu virus evolution.

Millions of people get infected every year by viral pathogens. Newly emergent diseases such as Ebola, Swine-flu, HIV/AIDS, etc. are spreading worldwide at an alarming rate. We introduced a delayed mathematical model with immune response and therapeutic drug treatment to understand the dynamics of pathogenimmune interaction. Here, we are considering the innate immune response and the two major component of the acquired immune response, namely, cytotoxic T lymphocytes (CTLs) and humoral immunity. This model also incorporates the absorption of pathogens i.e. loss of pathogens and its related mechanisms. Further, an optimal control model is formulated with two optimal controls i.e. maximization of uninfected cells count and minimization of cost of treatments. This is done by using the Pontryagins' Maximum Principle. Existence of non-negative equilibria is established and their stability behavior is studied using theory of ordinary differential equations. Further, numerical simulations are carried out to exemplify the qualitative results.

In this paper, we investigate a mathematical model depicting the dynamics between immune effector cells, healthy tissue cells or host cells and the tumor cells by using a system of nonlinear ordinary differential equations (ODEs). We characterize the dynamics of the ODE system by locating biologically meaningful equilibrium points and determine local stability analysis. We perform the Hopf-bifurcation analysis when the proliferation rate α of healthy tissue cells crosses the threshold value α_cr. Numerical simulations are carried out to illustrate the dynamical behavior of the model system for different values of α including the regular and irregular periodic oscillations, which indicates the long-term dynamics of tumor relapse.

In this paper a mathematical model, at the cellular level, related to the onset and evolution of cancer cells contrasted by the immune system, is derived by tools of kinetic theory of active particles, for short KTAP's approach. The dynamics refers to an early stage of the competition, where cancer is viewed as sequence of phenotype mutations, which generate cells with the ability of suppressing the innate programmed death ability-apopthosis- on one side and on the other with the ability to escape recognition by immune cells. The subsequent dynamics of selection and competition for survivance determines the growth or depletion of tumor cells. The originated model introduced in Ref. 13, which has been further developed in Ref. 20 to include interactions with the outer environment, which can also be subject to mutation and selection. More specifically, we develop an analytic study of the well-posdenes of the initial value problem, and we will investigate numerically how our model depict some interesting behaviors of the immune response, where some biological interpretations are discussed.

Under what circumstances is a higher death rate for males an acceptable trait? When, if ever, is a higher death rate for males an advantageous trait? These questions represent the null hypothesis for a variety of auxiliary reasons that have been proposed for the persistence from generation to generation of dichromatism and other forms of sexual dimorphism that appear to disadvantage the male.

Assume that two breeding species are in competition for the same resources. The only difference between the two species is that the death rate of the male of one species is higher than the death rate of the female of his species, which in turn is equal to the death rate of the competing species. Assume that the mating system of these species is efficient. That is, a relatively small number of males can impregnate females at a relatively high rate. We develop models demonstrating that the mathematics of mating (without sexual selection), birth, death, and competition are enough to guarantee a range of evolutionary patterns favoring sexual dimorphism that increases male death rates, without recourse to extra mechanisms or assumptions.

We present two models for a farm breeding that is assumed to be infected by just one lentivirus genotype. In the asymptomatic case the disease can be eradicated, while for the more widely spread genotype even the hygienic measures taken by the farmer may be insufficient to contain the epidemics.

A conservation model is proposed and analyzed for an age structured forestry biomass exploited by Industrialization. The age structured forestry biomass and Industrialization is considered as dynamic variable. Industries can only harvest the semi-mature and mature trees. Variable taxation works as the control instrument for the excess utilization of forestry biomass by industries. The dynamic behavior of the system is established using the theory of differential equation. Numerical simulation is carried out to support the analytical results. Sensitivity analysis of the parameters is also carried out for all feasible equilibrium points using a normalized forward sensitivity index. A detailed analysis of the proposed model leads to understand how the taxation works toward the conservation of the forestry resource.

Having attracted much attention in the past few years, predator-prey system provides a good mathematical model to present the association among predators and preys. The novel concept of this paper is that the prey predator model is developed in fuzzy environment by considering the imprecise nature of the biological parameters. This paper explores stability analysis of this competition model with fuzzy initial conditions. Here we have used fuzzy generalized differentiable approach. We derived the model formulation of our stated model and discussed about Equilibrium points and their feasibility. The fuzzy solution and stability concepts are developed by prior numerical simulations.

Traditionally chemotherapy, radiotherapy, and surgery have been the primary therapeutic interventions used to treat cancers. Over the last decade, High Intensity Focused Ultrasound (HIFU) has emerged as a potentially powerful additional primary therapeutic modality for certain cancers. In addition to avoiding side effects associated, for example, with chemotherapy and radiotherapy, it also presents a non-invasive alternative to surgery which still has the potential to completely eradicate solid tumours. In this paper, we briefly present a possible classical set-up to administer HIFU and discuss the mathematical modeling of HIFU in the context of bone sarcomas. Finally, we briefly discuss several possible alternative applications of HIFU ranging from clot lysis to a potential method for relaxing the Blood Brain Barrier in order to permit the delivery of chemotherapeutic agents (in the context of brain tumours). These lead to many interesting questions that should be amenable to mathematical modeling.

We present systematic numerical studies of electrical-wave propagation in two-dimensional (2D) and three-dimensional (3D) mathematical models, for human, ventricular tissue with myocyte cells that are attached (a) regularly and (b) randomly to distributed fibroblasts. In both these cases we show that there is a parameter regime in which single rotating spiral- and scroll-wave states (RS) retain their integrity and do not evolve to a state ST that displays spatiotemporal chaos and turbulence. However, in another range of parameters, we observe a transition from ST to RS states in both 2D or 3D domains and for both cases (a) and (b). Our studies show that the ST-RS transition and rotation period of a spiral or scroll wave in the RS state depends on (i) the coupling strength between myocytes and fibroblasts and (ii) the number of fibroblasts attached to myocytes. We conclude that myocyte-fibroblast coupling strength and the number of fibroblasts are more important for the ST-RS transition than the precise way in which fibroblasts are distributed over myocyte tissue.

Oxidative stress (OS) is a central causal locus through which hyperglycemia leads to post-diabetic complications. Using a mechanistically derived minimal mathematical model, we showed that steady state OS and glycemic state (GS) in newly diagnosed type 2 diabetics can be fitted well using a Goldbeter-Koshland function (GK) [Kulkarni R et al., PLoS ONE 9(6): e100897, 2014]. In clinical usage, however, it would be attractive to use a simpler model to describe changes in OS as GS is controlled. Here we use a logistic sigmoidal function (LS) and compare the two models. Both the models capture a quantal dose-response relationship between plasma glutathione (an oxidative stress marker) and glucose for each diabetic individual (n=48, for both the models). Individual diabetic curves show variation in response to the glycemic treatment which can be captured in terms of parameters of the model, namely, GSH_max: maximal glutathione level attained by diabetic patient, υ: glucose concentration when plasma glutathione is half maximal and k: slope of the curve. Parameter distributions of υ and GSH_max predicted by both the models are comparable, but distributions of k show considerable variation. Further, the measures of model selection, namely, mean sum of squared errors and Akaike's information criterion (AIC) suggest that LS model fits better compared to the GK model. Overall, our analysis shows that the LS model is a simple and statistically better alternative to the GK model to establish a quantitative relationship between OS and GS. We hope that OS threshold predictions by the LS model would help in the clinical investigations of hyperglycemia mediated OS responses.

The following sections is included:

• Index