Stereoelectronic effects in RNase-catalysed reactions of dinucleoside phosphate cleavage

AbstractThe rate at which dinucleoside phosphates are cleaved by RNases is supposed to be determined by the mole fraction of enzyme-substrate complexes in which the phosphodiester moiety of a dinucleoside phosphate has a highly reactive conformation. The mole fraction of such complexes for a particular RNase depends on the nature of a nucleoside at the O5'-end of the phosphodiester bond. Experimental data are presented to support this hypothesis

Asymmetry of Cell Division in CFSE-Based Lymphocyte Proliferation Analysis

Flow cytometry-based analysis of lymphocyte division using carboxyfluorescein succinimidyl ester (CFSE) dye dilution permits acquisition of data describing cellular proliferation and differentiation. For example, CFSE histogram data enable quantitative insight into cellular turnover rates by applying mathematical models and parameter estimation techniques. Several mathematical models have been developed using different types of deterministic or stochastic approaches. However, analysis of CFSE proliferation assays is based on the premise that the label is halved in the two daughter cells. Importantly, asymmetry of protein distribution in lymphocyte division is a basic biological feature of cell division with the degree of the asymmetry depending on various factors. Here, we review the recent literature on asymmetric lymphocyte division and CFSE-based lymphocyte proliferation analysis. We suggest that division- and label-structured mathematical models describing CFSE-based cell proliferation should take into account asymmetry and time-lag in cell proliferation. Utilization of improved modeling algorithms will permit straightforward quantification of essential parameters describing the performance of activated lymphocytes

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4+ T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets

Examining the cooperativity mode of antibody and CD8+ T cell immune responses for vaccinology

A fundamental unsolved issue in vaccine design is how neutralizing antibodies and cytotoxic CD8+ T cells cooperate numerically in controlling virus infections. We hypothesize on a viewpoint for the multiplicative cooperativity between neutralizing antibodies and CD8+ T cells and propose how this might be exploited for improving vaccine-induced protective immunity.info:eu-repo/semantics/acceptedVersio

Neutral delay differential equations in the modelling of cell growth

In this contribution, we indicate (and illustrate by example) roles that may be played by neutral delay differential equations in modelling of certain cell growth phenomena that display a time lag in reacting to events. We explore, in this connection, questions involving the sensitivity analysis of models and related mathematical theory; we provide some associated numerical results

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search “...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle” (as highlighted recently by Tedbury & Freed, The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments

On some aspects of casual and neutral equations used in mathematical modelling

The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) roles for well-defined ad-joints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints

Numerical modelling of label-structured cell population growth using CFSE distribution data

<p>Abstract</p> <p>Background</p> <p>The flow cytometry analysis of CFSE-labelled cells is currently one of the most informative experimental techniques for studying cell proliferation in immunology. The quantitative interpretation and understanding of such heterogenous cell population data requires the development of distributed parameter mathematical models and computational techniques for data assimilation.</p> <p>Methods and Results</p> <p>The mathematical modelling of label-structured cell population dynamics leads to a hyperbolic partial differential equation in one space variable. The model contains fundamental parameters of cell turnover and label dilution that need to be estimated from the flow cytometry data on the kinetics of the CFSE label distribution. To this end a maximum likelihood approach is used. The Lax-Wendroff method is used to solve the corresponding initial-boundary value problem for the model equation. By fitting two original experimental data sets with the model we show its biological consistency and potential for quantitative characterization of the cell division and death rates, treated as continuous functions of the CFSE expression level.</p> <p>Conclusion</p> <p>Once the initial distribution of the proliferating cell population with respect to the CFSE intensity is given, the distributed parameter modelling allows one to work directly with the histograms of the CFSE fluorescence without the need to specify the marker ranges. The label-structured model and the elaborated computational approach establish a quantitative basis for more informative interpretation of the flow cytometry CFSE systems.</p

A Systems Immunology Approach to Plasmacytoid Dendritic Cell Function in Cytopathic Virus Infections

Plasmacytoid dendritic cell (pDC)-mediated protection against cytopathic virus infection involves various molecular, cellular, tissue-scale, and organism-scale events. In order to better understand such multiscale interactions, we have implemented a systems immunology approach focusing on the analysis of the structure, dynamics and operating principles of virus-host interactions which constrain the initial spread of the pathogen. Using high-resolution experimental data sets coming from the well-described mouse hepatitis virus (MHV) model, we first calibrated basic modules including MHV infection of its primary target cells, i.e. pDCs and macrophages (Mφs). These basic building blocks were used to generate and validate an integrative mathematical model for in vivo infection dynamics. Parameter estimation for the system indicated that on a per capita basis, one infected pDC secretes sufficient type I IFN to protect 103 to 104 Mφs from cytopathic viral infection. This extremely high protective capacity of pDCs secures the spleen's capability to function as a ‘sink’ for the virus produced in peripheral organs such as the liver. Furthermore, our results suggest that the pDC population in spleen ensures a robust protection against virus variants which substantially down-modulate IFN secretion. However, the ability of pDCs to protect against severe disease caused by virus variants exhibiting an enhanced liver tropism and higher replication rates appears to be rather limited. Taken together, this systems immunology analysis suggests that antiviral therapy against cytopathic viruses should primarily limit viral replication within peripheral target organs

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved