BIOMAT 2006

Preface.

Editorial Board of the BIOMAT Consortium.

Contents.

Within the last decade, our modeling attempts in stem cell biology have considerably evolved. Starting from the cellular level, our models now comprise a broad spectrum of phenomena on different scales, ranging from the molecular to the tissue level. Such a scale-bridging description of biological processes does exactly match the intentions of the newly emerging field of systems biology with its central objective to understand biological complexity from molecular scales to ecosystems by a joint application of experimental and theoretical techniques. This work is an attempt to illustrate our systems biological perspective on tissue stem cell organization. Herein, I will describe the general principles of a new concept that understands stem cell organization as a dynamic, self-organizing process rather than as a pre-defined sequence of discrete developmental steps, as classically proposed.

The suitability of these principles to explain a broad variety of experimental results is illustrated for hematopoietic stem cells (HSC). For this system, the general stem cell concept has been translated into a stochastic model that comprises the processes of stem cell self-renewal and differentiation as well as lineage specification on the cellular level. Starting from this model, I will describe one possible way to extend the description towards the intra-cellular level. To do so, we considered a simple transcription factor network as the underlying mechanism controlling lineage specification decisions of HSC and analyzed its dynamical properties applying a system of ordinary differential equations. Finally, a clinical application of the proposed single-cell based model of HSC will shortly be outlined. This application again extends the description level of the model, now also incorporating systemic effects of therapeutic interventions. Based on the assumption that chronic myeloid leukemia can be modeled by a clonal competition process of normal and malignant cells, we analyzed the potential dynamic treatment effects of the tyrosine kinase inhibitor imatinib. Our results suggest a selective activity of imatinib on proliferating cells which implies the hypothesis that the therapeutic efficiency might benefit from a combination of imatinib with drugs promoting the cell cycle activation of primitive stem cells.

We consider a system of two coupled identical cells. The dynamics of the chemical substances in the individual cells are the same, and the coupling is proportional to the differences in the concentrations of its chemical constituents. Without coupling, the cells have a unique and identical stable steady state — the quiescent state. We show that the coupled system of cells can have a new collective stable steady state, not present if the cells were uncoupled. We obtain the conditions for the emergence of this collective steady state. When the collective stable steady state exists, the concentrations of the (two) morphogens assume different values inside the cells, introducing a symmetry breaking in the chemical characterization of the cells. This is a hypothetical mechanism of developmental differentiation in systems with a small number of identical cells.

We present a class of models aiming to describe generic protocells hypotheses, improving a model introduced elsewhere¹³. These models, inspired by the "Los Alamos bug" hypothesis, are composed by two coupled subsystems: a self-replicating molecule- SRM- and a lipid container. The latter grows thanks to the replication of the former, which in turn can produce copies of itself thanks to the very existence of the lipid container, as it is assumed that SRMs are preferentially found in the lipid phase. Nevertheless, due to abstraction level of our models, they can be applied to a wider set of detailed protocell hypotheses. It can thus be shown that, under fairly general assumptions of generic non-linear growth law for the container and replication for the SRM, the two growth rates synchronize, so that the lipid container doubles its size when the quantity of self-replicating molecules has also doubled — thus giving rise to exponential growth of the population of protocells. Such synchronization had been postulated a priori in previous models of protocells, while it is here an emergent property. Our technique, combining a continuous-time formalism, for the growth between two successive protocell divisions, and a discrete map, relating the quantity of self-replicating molecules in successive generations, allows one to derive several properties in an analytical way.

In this paper we study the stability under diffusion of the lymit cycle solution to the Schnakenberg system. It is shown that diffusive instabilites for this periodic spatially homogeneous solution may lead to pattern formation. We explore conditions for such instabilities.

Human immunodeficiency virus (HIV) is the cause of the most severe pandemic that the world has ever seen. In 2005, there were 40 million people living with this infection and 2.8 million people died, the vast majority in the 15-49 age group. Altogether, acquired immunodeficiency syndrome (AIDS), a condition that follows from HIV infection and leaves the host unable to fight infectious challenges, has resulted in over 25 million deaths worldwide. Unfortunately, the spread of this disease continues at a fast pace, and the best hope for any successful intervention is the development of a vaccine against this virus. However, studies and trials of HIV vaccines in animal models suggest that it is difficult to induce complete protection from infection ('sterilizing immunity'), and it may only be possible to reduce viral load and to slow or prevent disease progression following infection. What would be the effect of such vaccine on the spread of the epidemic? We have developed an age-structured epidemiological model of the effects of a disease modifying HIV vaccine that incorporates intra host dynamics of infection (transmission rate and host mortality that depend on viral load), the possible evolution and transmission of vaccine escape mutant virus, a finite duration of vaccine protection, and possible changes in sexual behavior. Using this model we investigate the long-term outcome of a disease modifying vaccine and utilize uncertainty analysis to quantify the effects of our lack of precise knowledge of various parameters.

This work deals with some results of the analysis of molecular-genetic mechanisms of interconnected activity between hepatocytes and hepatitis B virus (HBV) based on mathematical modeling. The functional-differential equations of functioning regulatory mechanisms (regulatorika) of molecular-genetic systems of cells in multicellular organisms are used as equations class for the quantitative analysis of activity regularities of "hepatocytes-HBV" genetic system. Results obtained during qualitative studies show that there are different scenarioes for fulfilling the infectious process on cellular level at HBV, including symbiotical coexistence between hepatocyte and virus, also periodical excitement of the virus infection.

Mathematical models are a useful tool to help understand patterns of global spread of infectious diseases and to help prepare for these risks and develop and implement appropriate control strategies. Examples are presented of how two modeling approaches, a population-based ODE model and an individual-based computer model, are used to study the geographic spread of the 1918-19 influenza epidemic in central Canada. The basic structure and major results of each of the models is presented and the insights derived from each approach are compared. Results from both models show that movement between communities serves to introduce epidemic diseases into the communities, but that within-community social factors have a stronger influence on disease severity. However, results of the two models are sometimes significantly different. Discussion of these differences highlights the advantages of using multiple approaches to address similar questions.

Tuberculosis is a leading cause of infectious mortality. Although anti-biotic treatment is available and there is vaccine, tuberculosis levels are rising in many areas of the world. The recent emergence of drug-resistant of TB is alarming, as are the potential effects of HIV on TB epidemics. Mathematical models have been used to study tuberculosis in the past and have influenced policy; there is renewed opportunity for mathematical models to contribute today. Here we review and compare the mathematical models of tuberculosis dynamics in the literature. We present two models of our own: a spatial stochastic individual-based model and a set of delay differential equations encapsulating the same biological assumptions. We compare two different assumptions about partial immunity and explore the effect of preventative treatments. We argue that seemingly subtle differences in model assumptions can have significant effects on biological conclusions.

San Francisco (SF) has the highest rate of TB in the US. Although in recent years the incidence of TB has been declining in the general population, it appears relatively constant in the homeless population. In this paper, we present a spatio-temporal outbreak detection technique applied to the time series and geospatial data obtained from extensive contact and laboratory investigation on TB cases in the SF homeless population. We examine the sensitivity of this algorithm to spatial resolution using zip codes and census tracts, and demonstrate the effectiveness of it by identifying outbreaks that are localized in time and space but otherwise cannot be detected using temporal detection alone.

Tuberculosis still remains as a serious public health problem. Thinking about more efficient interventions for its combat and control WHO advocates that DOTS (Directly Observed Short-time Treatment Strategy) can improve cure rates and case detection. In this context, mathematical modeling can be used to evaluate the behavior of tuberculosis under DOTS, supplying informations to optimal action strategies. The model presented in this work, describes the dynamic of 4 individuals groups: susceptibles, never before infected; latently-infected or cured of TB under chemotherapy; infectious individuals with pulmonary TB and sputum smear positive; and noninfectious with pulmonary TB but sputum-smear negative or extra-pulmonary TB. Individuals, who complete treatment successfull, are cured of tuberculosis but remain infected and individuals, who do not complete treatment, continue with the illness (infectious or noninfectious). The model, as considered here allows us to evaluate the effect of improve cure rates and case detection. The Effective Reproductive Rate was found for this model and used as epidemiological measure of severity of an epidemics. If , an epidemics occurs and if , it is eradicated. The time-dependent uncertainty analysis is presented using the Monte Carlo Method.

The International Union of Physiological Sciences (IUPS) has undertaken a project called the Physiome Project with the goal of developing a comprehensive framework for modeling the human body using computational techniques which incorporate the biochemistry, biophysics and anatomy of cells, tissues and organs. The project aims to establish a web-accessible physiological databases dealing with model-related data which includes bibliographic information, at the cell, tissue, organ and organ system levels. The databases are intended to provide a quantitative description of physiological dynamics and functional behavior of the intact organism. The long-range objective is to understand and describe the human organism, its physiology and to use this understanding to improve human health. In this survey, we will give an overview of the Physiome Project and an analysis of the collection of mathematical and computational models aimed at detection, prevention and treatment of physiological disorders such as aneurysms. In conclusion, we will show the connection between the aneurysm database and the Physiome Project.

In this work we propose an application of the optimal control theory to the planning of tumor treatments. The tumor growth is represented by a system of three differential equations that considers the dynamics and interactions of three types of cells: normal, immune and tumoral. The problem of the tumor treatment was formulated in terms of the optimal control theory as the state regulator problem, aiming the reduction of the tumor cells population. The linear feedback regulator, that stabilized the nonlinear system with tumor around the globally stable tumor-free equilibrium point, was found. The numerical simulations show that the proposed optimal strategies can be accomplished by existing methods of cancer treatment, including radiotherapy.

Imaging modalities such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) produce sequences of planar parallel cross-sectional images taken at regular or irregular intervals of 3D objects (brain, coronary arteries, etc). In order to reconstruct a 3D object which has been imaged using MRI or CT there is a need for a fast, accurate and robust algorithm. Reconstruction usually starts with an appropriate segmentation algorithm that detects the trace of the 3D object boundary on each 2D image. Segmentation can be either manual, semi-automatic or ideally automatic. After segmentation, one needs to "glue" together the contours in order to reconstruct the 3D object. Both the segmentation technique and the method used to glue individual contours affect the quality of the reconstructed object. In this paper we introduce a novel initialization that speeds up a semi-automatic segmentation technique recently developed by Chan and Vese (IEE Trans. Im. Proc., vol. 10, No. 2, February 2001, pp 266-277). We implement Vese and Chan (Int. J. Comp. Vis. vol 50, N0. 2, 2002, pp 271-293) multi-phase segmentation using relaxed Gauss-Seidel method. As a result we obtain an algorithm faster than the one proposed by Vese and Chan . We employ the heat kernel to piece together 2D parallel contours in order to obtain 3D reconstruction. This approach is preferred because of the slowness of 3D segmentation using level sets. In case of large volumes we indicate how to use fast Gauss transform to achieve fast reconstruction. Numerical experiments are provided to support our methodology.

Described is a mathematical model that evaluates the distribution of cellular adenosine nucleotides (ATP/ADP) to test the hypothesis that local changes in the concentrations of these molecules can modulate cell function without a significant change in global cytosolic concentrations. The model incorporates knowledge of cell structure to predict the spatial concentration profiles of ATP, ADP and inorganic phosphate. The steady state was perturbed by increasing the activity of membrane bound ion transporters including the Na-K ATPase on the cell periphery or the V-type H⁺ ATPase which serves to acidify intracellular compartments including endosomes/lysosomes. Both of these transporters utilize ATP and produce ADP and P_i in the process. Both models are run over a range of cytosolic diffusivities, including local low diffusivity near the pump sites. Results suggest that local changes in the concentration of ADP (not ATP) during activation of ion transport, in particular at near membrane sites, may serve to modulate ion transport, and thereby cell behavior.

An abstract representation, similar to a Periodic Table, was used to generate a large number of idealised protein folds. Each of these was taken as a framework onto which a variety of predicted secondary structures were mapped and the resulting models constructed at a more detailed level. The best of these were refined and rescored. On a set of five proteins, the correct fold was scored highly in each with the top models having a low root-mean-square deviation from the known structure.

Some considerations about the modelling of the structure of biological macro-molecules are studied in the present work. It is emphasized the usefulness of the concept of Steiner trees and some derived parameters like the Steiner Ratio and chirality functions for characterizing the potential energy minimization process of these structures.

One main characteristic of proteins is their ability to bind other molecules with high binding affinity and specificity, enabling them to realize their function. The structural and functional diversity of proteins, however, is much smaller than the enormous combinatorial diversity of amino acid sequences. One reason for this loss of complexity is that some naturally occurring amino acids have very similar physico-chemical properties. This paper discusses an empirical method to determine groups of amino acids similar with respect to their binding properties. It is founded on binding affinity data for 68 peptide-antibodies pairs, including measurements of binding strength for all peptides with a single amino acid substitution. The frequency with which a substitution of an amino acid by another preserves the original high binding affinity is determined, resulting in a similarity measure which is used to define a substitution matrix and group amino acids with similar binding properties. Each group can be represented by an amino acid, thus defining a reduced alphabet of maximally dissimilar amino acids. Restraining investigation of peptide sequences to this reduced alphabet can diminish the combinatorial diversity in such a way that it renders experimental assessment of binding affinity landscapes for maximally dissimilar substitutions possible. The same applies when restraining substitutions to amino acids within similarity groups. Our results suggest that a reduced set of amino acids can coarsely cover sequence space and thus be used to find antibody epitopes rapidly and economically.

The Protein Structure Prediction (PSP) problem aims at determining protein tertiary structure from its amino acids sequence. PSP is a computationally open problem. Several methodologies have been investigated to solve it. Two main strategies have been employed to work with PSP: homology and ab initio prediction. This paper presents a Multi-Objective Evolutionary Algorithm (MOEA) to PSP problem using an Ab initio approach. The proposed MOEA uses dihedral angles and main angles of the lateral chains to model a protein structure. This article investigates advantages of multi-objective evolutionary approach and discusses about methods and other approaches to the PSP problem.

We have shown that the problem of existence of a mitochondrial Eve can be understood as an application of the Galton–Watson branching process and presents interesting analogies with critical phenomena in Statistical Mechanics. We shall review some of these results here. In order to consider mutations in the Galton–Watson framework, we shall derive a general formula for the number of generations between successive branching events in a pruned genealogic tree. We show that in the supercritical regime of the Galton–Watson model, this number of generations is a random variable with geometric distribution. In the critical regime, population in the Galton–Watson model is of constant size in the average. Serva worked on genealogic distances in a model of haploid constant population and discovered that genealogic distances between individuals fluctuated wildly both in time and in the realization of the model. Also, such fluctuations seem not to disappear when the population size tends to infinity. This phenomenon was termed lack of self-averaging in the genealogic distances. Although in our model, population is not strictly constant, we argue that the lack of self-averaging in the genealogic distance between individuals may be viewed as a consequence of being exactly at or near a critical point.

An important trend in the study of insect societies has taken place in the last 30 years. Traditional theories of social organization such as adaptive demography and worker castes have been revised in the light of new evidence of the dynamic nature of regulatory processes underlying social behaviour. However, this new trend is still markedly reductionist in its methods. This paper advocates a unifying approach to the study of insect sociality, illustrated by an agent-based computational model allowing detailed investigations of the dynamics of insect social behaviour. The model incorporates key components of social organization and their underlying mechanisms, both at the individual and colony levels. The model was applied to field studies of behavioural plasticity in red harvester ants, in order to evaluate its performance when applied to a concrete problem in insect sociobiology. Simulation experiments reproduced several aspects of harvester ant social organization and produced insights into the dynamics of collective responses to changing ecological conditions. The results suggest that temporal patterns of colony resource allocation may be more complex than currently believed. We found a non-linear relationship between ecological stress and the colony's response strategy, revealing a significant event in the temporal dynamics of the system behaviour: the collapse of the relative priorities of communal tasks. We present a testable hypothesis about the hierarchy of task priorities in harvester ants, as well as suggestions for an experimental procedure for testing the hypothesis. The paper concludes with a discussion of the prospects and pitfalls of computational approaches to the study of insect societies.

Marine life cycles commonly include a planktonic larvae phase that is transported by ocean currents. In this work, to assess the relationship between the physical processes that disperse larvae and the intensity of species interaction in the benthic habitat, we use a two dimensional stage-structured finite element model that introduces an interspecific competition for space among adults of the barnacles Balanus glandula (dominant species) and Chthamalus (Chthamalus dalli and Chthamalus fissus - subordinate species) which inhabit the rocky intertidal zone of North American Pacific coast. The main objective of this work is to characterize the effect of some idealized current patterns combined with hierarchical competition for space among adults on their relative abundances. A four stage-structured representation of the species life cycle is used. Numerical simulations showed that coastal flows may affect the adult distribution and the population interaction strength of the dominant on the subordinate species, that decreases as the velocity speed of the flow field increases. This behavior yields different population distribution patterns at the coast depending on the current pattern.

In this article we study bio-economics of renewable resources which define processes with impulsive dynamical behavior. The biomass is modelled by an ordinary differential equation, but in a sequence of punctual times the biomass jumps by harvest. We consider that the catches are dependent of an effort parameter, the size of the biomass and the time. We suppose that the waiting time for the next harvest instant is a function of the amount captured. We establish the introductory elements for a theory of this new type of impulsive differential equations. It is shown in an example that under logistic growth and impulsive harvest it is always possible to fix a function of the length of closed seasons that determines a sustainable regulation.

In this work, a bidimensional continuous-time differential equations system is analyzed which is derived from a Leslie type predator-prey model by considering a nonmonotonic functional response (or Holling type IV or Monod Haldane). This functional response is employed to explain a class of prey antipredator strategies and we study how it influences in bifurcation and stability behavior of model. System obtained can have one, two or three equilibrium point at interior of the first quadrant, but here we describe the dynamics of the particular cases when system has one or two equilibrium points. Making a time rescaling we obtain a polynomial differential equations system topologically equivalent to original one and we prove that for certain subset of parameters, the model exhibits biestability phenomenon, since there exists an stable limit cycle surrounding two singularities of vector field one of these stable. We prove that there are conditions on the parameter values for which the unique equilibrium point at the first quadrant is stable and surrounded by two limit cycles, the innermost unstable and the outhermost stable. Also we show the existence of separatrix curves on the phase plane that divide the behavior of the trajectories, which have different ω–limit sets, and we have that solutions are highly sensitives to initial conditions. However, the populations always coexist since the singularity (0, 0) is a nonhyperbolic saddle point.

INDEX.