Modeling ganglioside headgroups by conformational analysis and molecular dynamics

The conformations and dynamics of gangliosides GM1, GM2, 6-GM2 and GM4 have been studied by computational means, and the results compared to NMR data. Unconstrained conformational searches were run using the AMBER* force field augmented by MNDO derived parameters for the Neu5Ac anomeric torsion, the GB/SA water solvation model, and the MC/EM alogorithm; extended (10–12[emsp4 ]ns) dynamic simulations in GB/SA water were performed with the MC/SD protocol, and the stored structures were minimized. The overall mobility of the Neu5Ac2,3Gal linkage and the position of its minimum energy conformation have been shown to depend mainly on the presence or the absence of a GalNAc residue at the adjacent position. The best quantitative agreement with the available NOE data was achieved after minimization of the structures stored during the MC/SD dynamic runs. The latter protocol appears to reproduce satisfactorily the available experimental data, and can be used with confidence to build three-dimensional models of ganglioside headgroups.     

Modeling and analysis of prion dynamics in the presence of a chaperone

Prions are infectious agents and are polymers called PrP(Sc)-Prion protein scrapies, of a normal protein, a monomer called PrP(c)-Prion protein cellular. These PrP(Sc)s cause TSEs-transmissible spongiform encephalopathies such as bovine spongiform encephalopathy (BSE) in cattle, scrapies in sheep, Kuru and Creutzfeld-Jacob diseases in humans. Cellular molecular chaperones, which are ubiquitous, stress-induced proteins, and newly found chemical and pharmacological chaperones have been found to be effective in preventing misfolding of different disease-causing proteins, essentially reducing the severity of several neurodegenerative disorders and many other protein-misfolding diseases. In this work, we propose a model for the replication of prions by nucleated polymerization in the presence of a chaperone. According to this model, the biological processes of coagulation, splitting and the inhibitory effects of the chaperone can be described by a coupled system consisting of ordinary differential equations and a partial differential equation. The model is converted into a system of ordinary differential equations and the equilibrium points are computed and their stability is studied. We give a numerical simulation of the model and we find that a disease free state can be achieved in the presence of a chaperone. The duration of the disease free state is found to increase with the amount of chaperone and this amount of chaperone can be computed from the model.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.     

Modeling tight junction dynamics and oscillations

Tight junction (TJ) permeability responds to changes of extracellular Ca(2+) concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na(+). The early events of TJ dynamics were evaluated by the fast Ca(2+) switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca(2+)(bl)) and closing by returning Ca(2+)(bl) to normal values. Oscillations of TJ permeability were observed when Ca(2+)(bl) is removed in the presence of apical calcium (Ca(2+)(ap)) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca(2+) binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca(2+) binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca(2+) binding sites and delivers a signal that regulates the TJ barrier. Ca(2+) moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca(2+) diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca(2+) and attainment of a new steady-state, (c) the escape phase which follows the halt of TJ opening induced by apical Ca(2+), (d) the oscillations of TJ permeability, and (e) the effect of Ca(2+)(ap) concentration on the frequency of oscillations.     

Modeling the dynamics of choice

A simple linear-operator model both describes and predicts the dynamics of choice that may underlie the matching relation. We measured inter-food choice within components of a schedule that presented seven different pairs of concurrent variable-interval schedules for 12 food deliveries each with no signals indicating which pair was in force. This measure of local choice was accurately described and predicted as obtained reinforcer sequences shifted it to favor one alternative or the other. The effect of a changeover delay was reflected in one parameter, the asymptote, whereas the effect of a difference in overall rate of food delivery was reflected in the other parameter, rate of approach to the asymptote. The model takes choice as a primary dependent variable, not derived by comparison between alternatives—an approach that agrees with the molar view of behaviour.     

Modeling and dynamics of an ecological-economic model

In this paper, an eco-economic model with harvesting on biological population is established, which takes the form of a differential-algebra system. The impact of the economic profit from harvesting upon the dynamics of the model is studied. By using a suitable parameterization for the differential-algebra system, we derive an equivalent parameterized system which gives the stability results for the positive equilibrium point of our model. Moreover, based on the parameterized system as well as the approaches of normal form and formal series, the conditions on the Hopf bifurcation and the stability of center are obtained. Several numerical simulations for demonstrating the theoretical results are also presented. Lastly, according to the dynamical analysis, we provide a threshold value for the economic profit, which can maintain the sustainable development of our eco-economic system.     

Modeling truncated hemoglobin vibrational dynamics

We present a study on the near equilibrium dynamics of two small proteins in the family of truncated hemoglobins, developed under the framework of a Gaussian network approach. Effective beta carbon atoms are taken into account besides Calphas for all residues but glycines in the coarse-graining procedure, without leading to an increase in the degrees of freedom (beta Gaussian Model). Normalized covariance matrix and deformation along slowest modes with collective character are analyzed, pointing out anticorrelations between functionally relevant sites for the proteins under study. In particular, we underline the functional motions of an extended tunnel-cavity system running inside the protein matrix, which provide a pathway for small ligands binding with the iron in the heme group. We give a rough estimate of the order of magnitude of the relaxation times of the slowest two overdamped modes and compare results with previous studies on globins.     

Modeling HIV quasispecies evolutionary dynamics

Background

During the HIV infection several quasispecies of the virus arise, which are able to use different coreceptors, in particular the CCR5 and CXCR4 coreceptors (R5 and X4 phenotypes, respectively). The switch in coreceptor usage has been correlated with a faster progression of the disease to the AIDS phase. As several pharmaceutical companies are starting large phase III trials for R5 and X4 drugs, models are needed to predict the co-evolutionary and competitive dynamics of virus strains.

Results

We present a model of HIV early infection which describes the dynamics of R5 quasispecies and a model of HIV late infection which describes the R5 to X4 switch. We report the following findings: after superinfection (multiple infections at different times) or coinfection (simultaneous infection by different strains), quasispecies dynamics has time scales of several months and becomes even slower at low number of CD4+ T cells. Phylogenetic inference of chemokine receptors suggests that viral mutational pathway may generate a large variety of R5 variants able to interact with chemokine receptors different from CXCR4. The decrease of CD4+ T cells, during AIDS late stage, can be described taking into account the X4-related Tumor Necrosis Factor dynamics.

Conclusion

The results of this study bridge the gap between the within-patient and the inter-patients (i.e. world-wide) evolutionary processes during HIV infection and may represent a framework relevant for modeling vaccination and therapy.

     

Modeling analysis of the lymphocytopoiesis dynamics in chronically irradiated residents of Techa riverside villages

A biologically motivated dynamical model of the lymphocytopoietic system in irradiated humans is applied here to analyze the data obtained under hematological examinations of residents of Techa riverside villages. Those people were exposed to chronic irradiation with varying dose rates, due to the radioactive contamination of the river basin by the Mayak Production Association. Modeling studies revealed the relationship between the dynamics of the lymphocytopoietic system in the examined individuals and the variation of dose rate over the considered period of time. It is found that the developed model is capable of reproducing the decreased level of blood lymphocyte concentration observed during the period of maximum radiation exposure, the recovery processes in the system observed during the period of decreasing dose rate, as well as the enhanced mitotic activity of bone marrow precursor cells in this hematopoietic lineage observed during the entire period under consideration. Mechanisms of these effects of chronic irradiation on the human lymphocytopoietic system are elucidated based on the applied model. The results obtained demonstrate the efficiency of the developed model in the analysis, investigation, and prediction of effects of chronic irradiation with varying dose rate on the human lymphocytopoietic system. In particular, the developed model can be used for predicting any radiation injury of this vital system in people exposed to chronic irradiation due to environmental radiological events, such as anthropogenic radiation accidents or radiological terroristic attacks.     

Genomic Object Net: I. A platform for modelling and simulating biopathways

Genomic Object Net (GON) 1.0 is a software package for creating models and simulations of biopathways. Its core architecture employs the notion of a hybrid functional Petri net with extension (HFPNe). HFPNe can seamlessly handle discrete and continuous objects and events while keeping the model components themselves simple. With the feature and graphical model editor, biopathways can be modelled intuitively and simulated on GON. The subsequent output of the simulation results can be evaluated in customised views on GON Visualizer by writing an XML file. Additionally, GON provides a tool to transform biopathway models in KEGG and BioCyc to the GON XML files for modelling and simulation. The tool avoids a lot of tedious work by users, enabling them to focus on the biological model.     

Modeling epidemics dynamics on heterogenous networks

The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.     

Modeling the T-cell dynamics and pathogenesis of HTLV-I infection

Human T-cell lymphotropic virus type I (HTLV-I) infection in humans causes a chronic infection of CD4⁺ T cells, and is associated with various disease outcomes, among them with the development of adult T-cell leukemia (ATL). The T-cell dynamics after HTLV-I infection can be described in a mathematical model with coupled differential equations. The infection process is modeled assuming cell-to-cell infection of CD4⁺ T cells. The model allows for CD4⁺ T cell subsets of susceptible, latently infected and actively infected cells as well as for leukemia cells. Latently infected T cells may harbor the virus for several years until they become activated and able to infect susceptible T cells. Uncontrolled proliferation of CD4⁺ T cells with monoclonal DNA-integration of HTLV-I results in the development of ATL. The model describes basic features that characterize HTLV-I infection; the chronic infection of CD4⁺ T cells, the increasing number of abnormal cells and the possible progression to ATL.     

Modeling of particle dynamics in a thruster

Numerical solutions to the equations describing the process of ion acceleration in a Hall current plasma accelerator (thruster) are studied. The system itself represents a three-component plasma: neutral atoms, free electrons, and singly-ionized atoms. The ions in the acceleration tract move without collisions, i.e., the length of the free path of ions is larger than that of the acceleration tract, while electrons move in a diffusion mode across the magnetic field. It is shown that in case the Poisson equation for an electric field is used the set of dynamic equations does not have an acoustic peculiarity that appears when solving a quasineutral set when the velocity of the ion flow and the ion-acoustic velocity coincide.     

Modeling transmission dynamics of stage-specific malaria vaccines

Population effects of malaria vaccination programs will depend on a complex interaction of the stage specificity of the vaccine, its duration of effectiveness, whether it is responsive to natural boosting, the strategy implemented, the proportion vaccinated and the pre-existing endemic conditions. In this article, Elizabeth Halloran and Claudio Struchiner review models of malaria transmission that incorporate aspects of immunity relevant to studying the effects of stage-specific malaria vaccination programs. They discuss the difference in the assumptions and applicability of the models and compare their predictions. Experience with malaria has demonstrated the difficulty in eliminating transmission, so emphasis needs to be on the new host-parasite balance that will be induced by the vaccination program. Although Halloran and Struchiner advise caution in interpreting the results of such models, they conclude that quantitative and theoretical analysis will be important in planning and evaluating interventions with malaria vaccines.     

Modeling dissolved and free phase gas dynamics under decompression

Dissolved and free gases do not behave the same way in tissue under pressure, and their interaction is complex. Differences are highlighted, particularly with respect to time scales, gradients and transport. Impacts of free phases on diving are described, contrasting increased off-gassing pressures, slower ascent rates, safety stops and reduced repetitive exposures as consistent practical measures within Haldane models (limited supersaturation) which can be played off against buildup of dissolved gas. Simple computations illustrate the points.     

Modeling Daphnia population dynamics and demography under natural conditions

Various approaches to modeling the population dynamics and demography of Daphnia have been published. These methods range from the simple egg-ratio method, to mathematically complex models based on partial differential equations and numerically complex individual-based Daphnia population models. The usefulness of these models in unraveling the population dynamics and demography of Daphnia under natural conditions is discussed. Next to this, an extended version of an existing individual-based Daphnia model is documented (Cladosim) and its application to a typical field data set collected in 1995 in Lake Volkerak is shown. To answer the question which factor was limiting Daphnia numbers during the course of the season food level and temperature in the model were varied and results were compared with those obtained for the observed food level and temperature. These analysis showed that in April temperature was limiting while during May–July and September–October food was limiting. In August neither temperature nor food was limiting. Analysis with a set of size-selective mortality scenarios showed that on average the Daphnia population in Lake Volkerak experienced a mild positive size-selective mortality during the year that was analyzed. Birth rates derived with the detailed individual-based model were compared with those derived with the much simpler egg-ratio method. For the conditions as observed in Lake Volkerak in 1995, both methods gave very comparable results, despite sampling intervals of up to four weeks. The same holds under the environmental scenarios. Using the size-selective mortality scenarios it could be shown, however, that under strong mortality of the smaller daphnids, the egg-ratio method severely underestimates the birth rate. The vices and virtues of the new model and potential extensions are discussed.     

Modeling brain dynamics using computational neurogenetic approach

The paper introduces a novel computational approach to brain dynamics modeling that integrates dynamic gene–protein regulatory networks with a neural network model. Interaction of genes and proteins in neurons affects the dynamics of the whole neural network. Through tuning the gene–protein interaction network and the initial gene/protein expression values, different states of the neural network dynamics can be achieved. A generic computational neurogenetic model is introduced that implements this approach. It is illustrated by means of a simple neurogenetic model of a spiking neural network of the generation of local field potential. Our approach allows for investigation of how deleted or mutated genes can alter the dynamics of a model neural network. We conclude with the proposal how to extend this approach to model cognitive neurodynamics.