A Mathematical Model of Force Generation by Flexible Kinetochore-Microtubule Attachments

Important mechanical events during mitosis are facilitated by the generation of force by chromosomal kinetochore sites that attach to dynamic microtubule tips. Several theoretical models have been proposed for how these sites generate force, and molecular diffusion of kinetochore components has been proposed as a key component that facilitates kinetochore function. However, these models do not explicitly take into account the recently observed flexibility of kinetochore components and variations in microtubule shape under load. In this paper, we develop a mathematical model for kinetochore-microtubule connections that directly incorporates these two important components, namely, flexible kinetochore binder elements, and the effects of tension load on the shape of shortening microtubule tips. We compare our results with existing biased diffusion models and explore the role of protein flexibility inforce generation at the kinetochore-microtubule junctions. Our model results suggest that kinetochore component flexibility and microtubule shape variation under load significantly diminish the need for high diffusivity (or weak specific binding) of kinetochore components; optimal kinetochore binder stiffness regimes are predicted by our model. Based on our model results, we suggest that the underlying principles of biased diffusion paradigm need to be reinterpreted.     

In Vivo FRET Imaging Revealed a Regulatory Role of RanGTP in Kinetochore-Microtubule Attachments via Aurora B Kinase

Under the fluctuating circumstances provided by the innate dynamics of microtubules and opposing tensions resulted from microtubule-associated motors, it is vital to ensure stable kinetochore-microtubule attachments for accurate segregation. However, a comprehensive understanding of how this regulation is mechanistically achieved remains elusive. Using our newly designed live cell FRET time-lapse imaging, we found that post-metaphase RanGTP is crucial in the maintenance of stable kinetochore-microtubule attachments by regulating Aurora B kinase via the NES-bearing Mst1. More importantly, our study demonstrates that by ensuring stable alignment of metaphase chromosomes prior to segregation, RanGTP is indispensible in governing the genomic integrity and the fidelity of cell cycle progression. Our findings suggest an additional role of RanGTP beyond its known function in mitotic spindle assembly during the prometaphase-metaphase transition.     

A Novel Three-Filament Model of Force Generation in Eccentric Contraction of Skeletal Muscles

We propose and examine a three filament model of skeletal muscle force generation, thereby extending classical cross-bridge models by involving titin-actin interaction upon active force production. In regions with optimal actin-myosin overlap, the model does not alter energy and force predictions of cross-bridge models for isometric contractions. However, in contrast to cross-bridge models, the three filament model accurately predicts history-dependent force generation in half sarcomeres for eccentric and concentric contractions, and predicts the activation-dependent forces for stretches beyond actin-myosin filament overlap.     

A Mathematical Model of Pattern Formation by Swimming Microorganisms*

Bioconvection in suspensions of Tetrahymena pyriformis and Crypthecodinium cohnii is described and 2 new patterns, the toroid and the cat's-eye, which appear in shallow suspensions of C. cohnii, are reported. Except in very dense cultures, bioconvection does not arise unless the depth of the suspensions or the mean concentration exceed certain critical values, other things being equal. A mathematical model describing the hydrodynamics of suspension of negatively geotactic microorganisms is described which predicts the existence of critical depths and concentrations. The equations presented admit solutions describing the “polka-dot” patterns seen at low organism concentration in suspensions slightly deeper than the critical value. The discussion here is limited to the case of fairly dilute suspensions, but the basic approach can be applied also to richer cultures.     

A Flexible Mathematical Model Platform for Studying Branching Networks: Experimentally Validated Using the Model Actinomycete,Streptomyces coelicolor

Branching networks are ubiquitous in nature and their growth often responds to environmental cues dynamically. Using the antibiotic-producing soil bacterium Streptomyces as a model we have developed a flexible mathematical model platform for the study of branched biological networks. Streptomyces form large aggregates in liquid culture that can impair industrial antibiotic fermentations. Understanding the features of these could aid improvement of such processes. The model requires relatively few experimental values for parameterisation, yet delivers realistic simulations of Streptomyces pellet and is able to predict features, such as the density of hyphae, the number of growing tips and the location of antibiotic production within a pellet in response to pellet size and external nutrient supply. The model is scalable and will find utility in a range of branched biological networks such as angiogenesis, plant root growth and fungal hyphal networks.     

A Simple,Flexible Failure Model

A new failure model is introduced in the form of a four-parameter nonlinear differential equation, with failure probability as the dependent variable and failure time as the independent variable. The first parameter characterizes the location, the second the scale, and the other two the shape of the model. The type of the accompanying hazard function is immediately read off the shape parameters. The new model approximates the classical failure models with rather high precision, but also models cases where the failure density is skewed to the left. It can be used to analyze survival data objectively, based on the shape of the failure distribution. The computation of quantiles and moments is easy and fast. Nonlinear regression methods are used to estimate parameter values.     

Force Generation by Endocytic Actin Patches in Budding Yeast

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel. The deformation of the gel is treated using a finite-element approach. We explore the effects and interplay of three different types of force driving invagination: 1), forces perpendicular to the membrane, generated by differences between actin polymerization rates at the edge of the patch and those at the center; 2), the inherent curvature of the coat-protein layer; and 3), forces parallel to the membrane that buckle the coat protein layer, generated by an actomyosin contractile ring. We find that with optimistic estimates for the stall stress of actin gel growth and the shear modulus of the actin gel, actin polymerization can generate almost enough force to overcome the turgor pressure. In combination with the other mechanisms, actin polymerization can the force over the critical value.     

A Mathematical Model for Extrachromosomal Heredity

During embryogeny the components of the cytoplasm of a zygote are subject to certain irregularities. This has been investigated with the aid of some probability models and distribution functions. For mitochondria, which are the most important cell components with respect to extra-chromosomal heredity, a four-phase model with computer programs was developed. The complete arithmetical results total 15,000 pages from a fast printer. For the jobs a CPU-time of 500 hours, using a SIEMENS 4004 system, was required.     

A Mathematical Model for Bacterial Chemotaxis

A differential equation describing the chemotactic migration of a bacterial population in a fixed exponential gradient of attractant has been integrated using the appropriate boundary conditions. The solution predicts an initial bacterial accumulation at the concentration “knee” with the final distribution of bacteria approaching a time-independent state. Specific additional experiments to obtain further data for a rigorous test of the theory are suggested.     

一个人体运动的数学模型

本文采用L-E法和铰分解法研究了人体运动的数学模型问题,给出了一种人体运动的规范建模方法。该方法适用于多种拓扑结构形式的人体运动（如空翻、步行、滑行等）,所得方程具有适合于计算机程式求解的特点。     

A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

A Mathematical Model of Idiopathic Pulmonary Fibrosis

Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs.     

A Mathematical Model of Leaf Carbon Metabolism

A dynamic mechanistic mathematical model of C₃ leaf carbon metabolism,incorporating the Calvin cycle with starch and sucrose synthesisand degradation, is proposed. The model consists of a systemof non-linear differential equations based on biochemical andphysiological assumptions. An analytical steady-state solution,with interesting mathematical properties that are interpretedbiologically, is presented and shown to be stable. The systemequations are integrated numerically, and an approximate analyticalsolution to the sucrose sub-system is derived. Some resultsof the model are compared with experimental data. Mathematical model, Calvin cycle, leaf carbon metabolism, photosynthesis, differential equations     

A Mathematical Model of Photorespiration and Photosynthesis

A comprehensive mathematical model of C₃ leaf carbon metabolism,involving the Calvin cycle and the glycolate and glycerate pathwaysof photorespiration, is formulated in terms of a system of non-lineardifferential equations. A steady state, which is found to beeffectively stable, is derived. The model behaves realisticallywhen tested under varying external carbon dioxide and oxygenconcentrations: photosynthesis is inhibited by higher oxygenlevels, while photorespiration is inhibited by higher carbondioxide levels. Calvin cycle, differential equations, glycolate pathway, mathematical model, photorespiration, photosynthesis     

A Mathematical Model of the Enhancement of Tumor Vaccine Efficacy by Immunotherapy

TGF-β is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggests that TGF-β inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model in order to gain insight into the cooperative interaction between anti-TGF-β and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF-β concentration, activated cytotoxic effector cells, and regulatory T cells. Using numerical simulations and stability analysis, we study the following scenarios: a control case of no treatment, anti-TGF-β treatment, vaccine treatment, and combined anti-TGF-β vaccine treatments. We show that our model is capable of capturing the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy.     

Hypoxia Inducible Factors-Mediated Inhibition of Cancer by GM-CSF: A Mathematical Model

Under hypoxia, tumor cells, and tumor-associated macrophages produce VEGF (vascular endothelial growth factor), a signaling molecule that induces angiogenesis. The same macrophages, when treated with GM-CSF (granulocyte/macrophage colony-stimulating factor), produce sVEGFR-1 (soluble VEGF receptor-1), a soluble protein that binds with VEGF and inactivates its function. The production of VEGF by macrophages is regulated by HIF-1α (hypoxia inducible factor-1α), and the production of sVEGFR-1 is mediated by HIF-2α. Recent experiments measured the effect of inhibiting tumor growth by GM-CSF treatment in mice with HIF-1α-deficient or HIF-2α-deficient macrophages. In the present paper, we represent these experiments by a mathematical model based on a system of partial differential equations. We show that the model simulations agree with the above experiments. The model can then be used to suggest strategies for inhibiting tumor growth. For example, the model qualitatively predicts the extent to which GM-CSF treatment in combination with a small molecule inhibitor that stabilizes HIF-2α will reduce tumor volume and angiogenesis.