Browsing by Author "Xing, Jianhua"

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    Actin polymerization dynamics at the leading edge
    Hu, Xiaohua (Virginia Tech, 2012-10-05)
    Actin-based cell motility plays crucial role throughout the lifetime of an organism. While the dendritic nucleation model explains the initiation and organization of the actin network in lamellipodia, two questions need to be answered. In this study, I reconstructed cellular motility in vitro to investigate how actin filaments are organized to coordinate elongation and attachment to leading edge. Using total internal reflection fluorescence microscopy of actin filaments, we tested how profilin, Arp2/3, and capping protein (CP) function together to propel beads or thin glass nanofibers coated with N-WASP WCA domains. During sustained motility, physiological concentrations of Mg²⁺ generated actin filament bundles that processively attached to the nanofiber. Reduction of total Mg²⁺ abolished particle motility and actin attachment to the particle surface without affecting actin polymerization, Arp2/3 nucleation, filament capping, or actin shell formation. Addition of other types of crosslinkers restored both comet tail attachment and particle motility. We propose a model in which polycation-induced filament bundling sustains processive barbed end attachment to the leading edge. I lowered actin, profilin, Arp2/3, and CP concentrations to address the generation of actin filament orientation during the initiation of motility. In the absence of CP, Arp2/3 nucleates barbed ends that grow away from the nanofiber surface and branches remain stably attached to nanofiber. CP addition causes shedding of short branches and barbed end capture by the nanofiber. Barbed end retention by nanofibers is coupled with capping, indicating that WWCA and CP bind simultaneously to barbed ends. In pull-down assays, saturating CP addition only blocks WWCA binding to barbed end by half. Labeled WWCA bound to barbed ends with an affinity of 14 pM and unlabeled WWCA with an affinity of 75 pM. CP addition increased WWCA binding slightly at low CP concentrations and decreased WWCA binding to 50% at high CP concentrations. Molecular models of CP and WH2 domains bound respectively to the terminal and penultimate actin subunit showed no overlap and that CP orientation might blocks WWCA dissociation from the penultimate subunit. Simultaneous binding of CP and WWCA to barbed ends is essential to the establishment of filament orientation at the leading edge.
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    Biophysics at the coffee shop: lessons learned working with George Oster
    Igoshin, Oleg A.; Chen, Jing; Xing, Jianhua; Liu, Jian; Elston, Timothy C.; Grabe, Michael; Kim, Kenneth S.; Nirody, Jasmine A.; Rangamani, Padmini; Sun, Sean X.; Wang, Hongyun; Wolgemuth, Charles (American Society for Cell Biology, 2019-07-22)
    Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition, and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists.
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    Comparative Studies of Microtubule Mechanics with Two Competing Models Suggest Functional Roles of Alternative Tubulin Lateral Interactions
    Wu, Z. H.; Nogales, Eva; Xing, Jianhua (CELL PRESS, 2012-09)
    The dynamic assembly and disassembly of microtubules and the mechanical properties of these polymers are essential for many key cellular processes. Mathematical and computational modeling, especially coupled mechanochemical modeling, has contributed significantly to our understanding of microtubule dynamics. However, critical discrepancies exist between experimental observations and modeling results that need to be resolved before further progress toward a complete model can be made. Open sheet structures ranging in length from several hundred nanometers to one micron have often been observed at the growing ends of microtubules in in vitro studies. Existing modeling studies predict these sheet structures to be short and rare intermediates of microtubule disassembly rather than important components of the assembly process. Atomic force microscopy (AFM) studies also reveal interesting step-like gaps of the force-indentation curve that cannot yet be explained by existing theoretical models. We have carried out computational studies to compare the mechanical properties of two alternative models: a more conventional model where tubulin dimers are added directly into a microtubule lattice, and one that considers an additional type of tubulin lateral interaction proposed to exist in intermediate sheet structures during the microtubule assembly process. The first model involves a single type of lateral interactions between tubulin subunits, whereas the latter considers a second type that can convert to the canonical lateral contact during microtubule closure into a cylinder. Our analysis shows that only the second model can reproduce the AFM results over a broad parameter range. We propose additional studies using different sizes of AFM tips that would allow to unambiguously distinguish the relative validity of the two models.
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    Computational Systems Biology Analysis of Cell Reprogramming and Activation Dynamics
    Fu, Yan (Virginia Tech, 2012-07-17)
    In the past two decades, molecular cell biology has transitioned from a traditional descriptive science into a quantitative science that systematically measures cellular dynamics on different levels of genome, transcriptome and proteome. Along with this transition emerges the interdisciplinary field of systems biology, which aims to unravel complex interactions in biological systems through integrating experimental data into qualitative or quantitative models and computer simulations. In this dissertation, we applied various systems biology tools to investigate two important problems with respect to cellular activation dynamics and reprograming. Specifically, in the first section of the dissertation, we focused on lipopolysaccharide (LPS)-mediated priming and tolerance: a reprogramming in cytokine production in macrophages pretreated with specific doses of LPS. Though both priming and tolerance are important in the immune system's response to pathogens, the molecular mechanisms still remain unclear. We computationally investigated all network topologies and dynamics that are able to generate priming or tolerance in a generic three-node model. Accordingly, we found three basic priming mechanisms and one tolerance mechanism. Existing experimental evidence support these in silico found mechanisms. In the second part of the dissertation, we applied stochastic modeling and simulations to investigate the phenotypic transition of bacteria E.coli between normally-growing cells and persister cells (growth-arrested phenotype), and how this process can contribute to drug resistance. We built up a complex computational model capturing the molecular mechanism on both single cell level and population level. The paper also proposed a novel way to accelerate the phenotypic transition from persister cells to normally growing cell under resonance activation. The general picture of phenotypic transitions should be applicable to a broader context of biological systems, such as T cell differentiation and stem cell reprogramming.
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    Coupled Reversible and Irreversible Bistable Switches Underlying TGF beta-induced Epithelial to Mesenchymal Transition
    Tian, X. J.; Zhang, H.; Xing, Jianhua (CELL PRESS, 2013-08)
    Epithelial to mesenchymal transition (EMT) plays an important role in embryonic development, tissue regeneration, and cancer metastasis. Whereas several feedback loops have been shown to regulate EMT, it remains elusive how they coordinately modulate EMT response to TGF-beta treatment. We construct a mathematical model for the core regulatory network controlling TGF-beta-induced EMT. Through deterministic analyses and stochastic simulations, we show that EMT is a sequential two-step program in which an epithelial cell first is converted to partial EMT then to the mesenchymal state, depending on the strength and duration of TGF-beta stimulation. Mechanistically the system is governed by coupled reversible and irreversible bistable switches. The SNAIL1/miR-34 double-negative feedback loop is responsible for the reversible switch and regulates the initiation of EMT, whereas the ZEB/nniR-200 feedback loop is accountable for the irreversible switch and controls the establishment of the mesenchymal state. Furthermore, an autocrine TGF-beta/miR-200 feedback loop makes the second switch irreversible, modulating the maintenance of EMT. Such coupled bistable switches are robust to parameter variation and molecular noise. We provide a mechanistic explanation on multiple experimental observations. The model makes several explicit predictions on hysteretic dynamic behaviors, system response to pulsed stimulation, and various perturbations, which can be straightforwardly tested.
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    A framework for understanding heterogeneous differentiation of CD4⁺ T cells
    Hong, Tian (Virginia Tech, 2013-08-05)
    CD4+ T cells are a group of lymphocytes that play critical roles in the immune system. By releasing cytokines, CD4+ T cells regulate other immune cells for maximizing the efficiency of the system. Naive CD4+ T cells are activated and become mature upon engagement with antigens, and the mature CD4+ T cells have several subsets, which play diverse regulatory functions. For the past two decades, our understanding of CD4+ T cells has been advanced through the studies on the differentiation process and the lineage specification of various subsets of these cells. Although in most experimental studies of CD4+ T cells, researchers focused on how transcription factors and signaling molecules influence the differentiation of a particular subset of these cells, many evidence have shown that the differentiation of CD4+ T cells can be heterogeneous in terms of the phenotypes of the cells involved. This dissertation describes a framework that uses mathematical models of the dynamics of the signaling pathways to explain heterogeneous differentiation. We show that the mutual inhibitions among the master regulators govern the formation of multi-stability behavior, which in turn gives rise to heterogeneous differentiation. The framework can be applied to systems with two or more master regulators, and models based on the framework can make specific predictions about heterogeneous differentiations. In addition, this dissertation describes an experimental study on CD4+ T cell differentiation. Being part of the adaptive immune system, the differentiation of CD4+ T cells was previously known to be induced by the signals from the innate immune cells. However, the expression of Toll-like receptor in CD4+ T cells suggests that microbial products can also influence the differentiation directly. Using an in vitro cell differentiation approach, we show that the differentiation and proliferation of CD4+ T cells can be influenced by lipopolysaccharide under the condition that would favor the differentiation of induced regulatory T cells. These theoretical and experimental studies give novel insights on how CD4+ T cells differentiate in response to pathogenic challenges, and help to gain deeper understanding of regulatory mechanisms of the complex immune system.
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    Functional Roles of Slow Enzyme Conformational Changes in Network Dynamics
    Wu, Z. H.; Xing, Jianhua (CELL PRESS, 2012-11)
    Extensive studies from different fields reveal that many macromolecules, especially enzymes, show slow transitions among different conformations. This phenomenon is named such things as dynamic disorder, heterogeneity, hysteretic or mnemonic enzymes across these different fields, and has been directly demonstrated by single molecule enzymology and NMR studies recently. We analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can filter upstream network noises, and can either resonantly respond to the system stimulus at certain frequencies or respond adaptively for sustained input signals of the network fluctuations. It thus can serve as a basic functional motif with properties that are normally for larger intermolecular networks in the field of systems biology. We further analyzed examples including enzymes functioning against pH fluctuations, metabolic state change of Artemia embryos, and kinetic insulation of fluctuations in metabolic networks. The study also suggests that hysteretic enzymes may be building blocks of synthetic networks with various properties such as narrow-banded filtering. The work fills the missing gap between studies on enzyme biophysics and network level dynamics, and reveals that the coupling between the two is functionally important; it also suggests that the conformational dynamics of some enzymes may be evolutionally selected.
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    The Goldbeter-Koshland Switch in the First-Order Region and Its Response to Dynamic Disorder
    Xing, Jianhua; Chen, Jing (PLOS, 2008-05-14)
    In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840–6844), Goldbeter and Koshland mathematically analyzed a reversible covalent modification system which is highly sensitive to the concentration of effectors. Its signal-response curve appears sigmoidal, constituting a biochemical switch. However, the switch behavior only emerges in the ‘zero-order region’, i.e. when the signal molecule concentration is much lower than that of the substrate it modifies. In this work we showed that the switching behavior can also occur under comparable concentrations of signals and substrates, provided that the signal molecules catalyze the modification reaction in cooperation. We also studied the effect of dynamic disorders on the proposed biochemical switch, in which the enzymatic reaction rates, instead of constant, appear as stochastic functions of time. We showed that the system is robust to dynamic disorder at bulk concentration. But if the dynamic disorder is quasi-static, large fluctuations of the switch response behavior may be observed at low concentrations. Such fluctuation is relevant to many biological functions. It can be reduced by either increasing the conformation interconversion rate of the protein, or correlating the enzymatic reaction rates in the network.
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    A Mathematical Model for the Reciprocal Differentiation of T Helper 17 Cells and Induced Regulatory T Cells
    Hong, Tian; Xing, Jianhua; Li, Liwu; Tyson, John J. (PLOS, 2011-07-01)
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    Mathematical modeling approaches for dynamical analysis of protein regulatory networks with applications to the budding yeast cell cycle and the circadian rhythm in cyanobacteria
    Laomettachit, Teeraphan (Virginia Tech, 2011-10-24)
    Mathematical modeling has become increasingly popular as a tool to study regulatory interactions within gene-protein networks. From the modeler's perspective, two challenges arise in the process of building a mathematical model. First, the same regulatory network can be translated into different types of models at different levels of detail, and the modeler must choose an appropriate level to describe the network. Second, realistic regulatory networks are complicated due to the large number of biochemical species and interactions that govern any physiological process. Constructing and validating a realistic mathematical model of such a network can be a difficult and lengthy task. To confront the first challenge, we develop a new modeling approach that classifies components in the networks into three classes of variables, which are described by different rate laws. These three classes serve as "building blocks" that can be connected to build a complex regulatory network. We show that our approach combines the best features of different types of models, and we demonstrate its utility by applying it to the budding yeast cell cycle. To confront the second challenge, modelers have developed rule-based modeling as a framework to build complex mathematical models. In this approach, the modeler describes a set of rules that instructs the computer to automatically generate all possible chemical reactions in the network. Building a mathematical model using rule-based modeling is not only less time-consuming and error-prone, but also allows modelers to account comprehensively for many different mechanistic details of a molecular regulatory system. We demonstrate the potential of rule-based modeling by applying it to the generation of circadian rhythms in cyanobacteria.
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    Mathematical modeling of pathways involved in cell cycle regulation and differentiation
    Ravi, Janani (Virginia Tech, 2011-12-01)
    Cellular processes critical to sustaining physiology, including growth, division and differentiation, are carefully governed by intricate control systems. Deregulations in these systems often result in complex diseases such as cancer. Hence, it is crucial to understand the interactions between molecular players of these control systems, their emergent network dynamics, and, ultimately, the overall contribution to cellular physiology. In this dissertation, we have developed a mathematical framework to understand two such cellular systems: an early checkpoint (START) in the budding yeast cell cycle (Chapter 1), and the canonical Wnt signaling pathway involved in cell proliferation and differentiation (Chapter 2). START transition is an important decision point where the cell commits to one round DNA replication followed by cell division. Several years of experimental research have gone into uncovering molecular details of this process, but a unified understanding is yet to emerge. In chapter one, we have developed a comprehensive mathematical model of START transition that incorporates several findings including information about the phosphorylation state of key START proteins and their subcellular localization. In the second chapter, we focus on modeling the canonical Wnt signaling pathway, a cellular circuit that plays a key role in cell proliferation and differentiation. The Wnt pathway is often deregulated in colon cancers. Based on some evidence of bistability in the Wnt signaling pathway, we proposed the existence of a positive feedback loop underlying the activation and inactivation of the core protein complex of the pathway. Bistability is a common feature of biological systems that toggle between ON and OFF states because it ensures robust switching back and forth between the two states. To study and explain the behavior of this dynamical system, we developed a mathematical model. Based on experimentally determined interactions, our simple model recapitulates the observed phenomena of bimodality (bistability) and hysteresis under the effects of the physiological signal (Wnt), a Wnt-mimic (LiCl), and a stabilizer of one of the key members of core complex (IWR-1). Overall, we believe that cell biologists and molecular geneticists can benefit from our work by using our model to make novel quantitative predictions for experimental verification.
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    Mechanical Properties of Elastomeric Proteins
    Kappiyoor, Ravi (Virginia Tech, 2014-01-23)
    When we stretch and contract a rubber band a hundred times, we expect the rubber band to fail. Yet our heart stretches and contracts the same amount every two minutes, and does not fail. Why is that? What causes the significantly higher elasticity of certain molecules and the rigidity of others? Equally importantly, can we use this information to design materials for precise mechanical tasks? It is the aim of this dissertation to illuminate key aspects of the answer to these questions, while detailing the work that remains to be done. In this dissertation, particular emphasis is placed on the nanoscale properties of elastomeric proteins. By better understanding the fundamental characteristics of these proteins at the nanoscale, we can better design synthetic rubbers to provide the same desired mechanical properties.
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    Mitotic Dynamics of Normally and Mis-attached Chromosomes and Post-mitotic Behavior of Missegregated Chromosomes
    He, Bin (Virginia Tech, 2015-06-01)
    Equal segregation of the replicated genomic content to the two daughter cells is the major task of mitotic cells. The segregation is controlled by a complex system in the cell and relies mainly on the interaction between microtubules (MTs) of the mitotic spindle and kinetochores (KTs), specialized protein structures that assemble on each chromatid of each mitotic chromosome. By combining computational modeling and quantitative light microscopy, we established a quantitative model of the forces and regulators controlling metaphase chromosome movement in the mammalian cell line derived from Potorous tridactylis kidney epithelial cells (PtK1) (Chapter 2). This model can explain key features of metaphase chromosome dynamics and related chromosome structural changes experimentally observed. Moreover, the model made predictions, which we tested experimentally, on how changes in spindle dynamics affect certain aspects of chromosome structure. This quantitative model was next used to study the metaphase dynamics of chromosomes with erroneous KT-MT attachments (Chapter 3). Once again, the model predictions were tested experimentally and showed that erroneous KT-MT attachment alters the dynamics not only of the mis-attached KT, but also of its sister KT. Even more strikingly, experimental data showed that the presence of a single mis-attached KT could perturb the dynamics of all other, normally attached, KTs in anaphase. Chapter 3 also describe how MT poleward flux ensures correct KT-MT attachment and correct chromosome segregation. Indeed, reduced flux is associated with an increase in merotelically attached anaphase lagging chromosomes (LCs). These LCs form micronuclei (MNi) upon mitotic exit. The final effort of this work focused on the fate of MNi and micronuclated (MNed) cells (Chapter 4). Experimental observations showed that most of the chromosomes in MNi missegregated at the cell division following MN formation and that frequently the chromatin in the MN displayed delayed condensation. This work, thus, established a direct link between LCs and aneuploidy through the MN cell cycle.
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    Model Studies of the Dynamics of Bacterial Flagellar Motors
    Bai, F.; Lo, C. J.; Berry, R. M.; Xing, Jianhua (CELL PRESS, 2009-04)
    The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.
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    Molecular Mechanism Underlying Persistent Induction of LCN2 by Lipopolysaccharide in Kidney Fibroblasts
    Glaros, Trevor; Fu, Yan; Xing, Jianhua; Li, Liwu (PLOS, 2012-04-13)
    The neutrophil gelatinase-associated lipocalin 2 (LCN2) is a critical inflammatory mediator persistently induced during endotoxemia, contributing to tubular damage and kidney failure. The intracellular process responsible for persistent induction of LCN2 by bacterial endotoxin Lipopolysaccharide (LPS) is not well understood. Using primary kidney fibroblasts, we observed that LPS-induced LCN2 expression requires a coupled circuit involving an early transient phase of AP-1 path and a late persistent phase of C/EBPδ path, both of which are dependent upon the interleukin 1 receptor associated kinase 1 (IRAK-1). Using immunoprecipitation analysis we observed transient binding of AP-1 to the promoters of both TNFα and C/ebpδ. On the other hand, we only observed persistent binding of C/EBPδ to its own promoter but not on TNFα. Blockage of new protein synthesis using cyclohexamide significantly reduced the expression of C/EBPδ as well as LCN2. By chromatin immunoprecipitation analyses, we demonstrated that LPS recruited C/EBPδ to the Lcn2 promoter in WT, but not IRAK-1 deficient fibroblasts. A differential equation-based computational model captured the dynamic circuit leading to the persistent induction of LCN2. In vivo, we observed elevated levels of LCN2 in kidneys harvested from LPS-injected WT mice as compared to IRAK-1 deficient mice. Taken together, this study has identified an integrated intracellular network involved in the persistent induction of LCN2 by LPS.
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    The Novel Role of Interleukin-1 Receptor-Associated Kinase 1 in the Signaling Process Controlling Innate Immunity and Inflammation
    Fang, Youjia (Virginia Tech, 2009-05-05)
    Obesity-induced chronic inflammation plays a key role in the pathogenesis of insulin resistance and the metabolic syndrome. Proinflammatory cytokines can cause insulin resistance in adipose tissue, skeletal muscle and liver by inhibiting insulin signaling transduction. Interleukin-1 receptor-associated kinase-1 (IRAK-1) is a serine/threonine kinase functioning in Toll-like Receptor signaling pathways, and plays an important role in inflammation and immune response. In our studies, we demonstrated that IRAK-1 is involved with the negative regulation of PI3K-Akt dependent signaling pathway induced by insulin and TLR 2&4 agonists. Out data also indicate that IRAK-1 can interact with IRS-1 protein both in vivo and in vitro. The binding sites for the IRAK1-IRS1 biochemical interaction are IRS-1's PH domain and IRAK-1's proline-rich LWPPPP motif. Our studies also indicate that IRAK-1 is involved with the negative regulation of glycogen synthesis through inhibiting PI3K-Akt signaling pathway and thus releasing GSK3β's inhibitory effect on glycogen synthase. Moreover, our studies also suggest that IRAK-1 is involved in the activation of transcription factors CREB and ATF-1 by stimulating CREB-Ser133 and ATF-1 phosphorylation. CREB transcription factor family induces genes involved in cellular metabolism, gene transcription, cell cycle regulation, cell survival, as well as growth factor and cytokine genes. That may partially explain our finding that IRAK-1 may be also involved with cell proliferation and survival pathway.
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    A simple theoretical framework for understanding heterogeneous differentiation of CD4(+) T cells
    Hong, Tian; Xing, Jianhua; Li, Liwu; Tyson, John J. (Biomed Central, 2012-06-14)
    Background CD4+ T cells have several subsets of functional phenotypes, which play critical yet diverse roles in the immune system. Pathogen-driven differentiation of these subsets of cells is often heterogeneous in terms of the induced phenotypic diversity. In vitro recapitulation of heterogeneous differentiation under homogeneous experimental conditions indicates some highly regulated mechanisms by which multiple phenotypes of CD4+ T cells can be generated from a single population of naïve CD4+ T cells. Therefore, conceptual understanding of induced heterogeneous differentiation will shed light on the mechanisms controlling the response of populations of CD4+ T cells under physiological conditions. Results We present a simple theoretical framework to show how heterogeneous differentiation in a two-master-regulator paradigm can be governed by a signaling network motif common to all subsets of CD4+ T cells. With this motif, a population of naïve CD4+ T cells can integrate the signals from their environment to generate a functionally diverse population with robust commitment of individual cells. Notably, two positive feedback loops in this network motif govern three bistable switches, which in turn, give rise to three types of heterogeneous differentiated states, depending upon particular combinations of input signals. We provide three prototype models illustrating how to use this framework to explain experimental observations and make specific testable predictions. Conclusions The process in which several types of T helper cells are generated simultaneously to mount complex immune responses upon pathogenic challenges can be highly regulated, and a simple signaling network motif can be responsible for generating all possible types of heterogeneous populations with respect to a pair of master regulators controlling CD4+ T cell differentiation. The framework provides a mathematical basis for understanding the decision-making mechanisms of CD4+ T cells, and it can be helpful for interpreting experimental results. Mathematical models based on the framework make specific testable predictions that may improve our understanding of this differentiation system.
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    Simulations of Tubulin Sheet Polymers as Possible Structural Intermediates in Microtubule Assembly
    Wu, Zhanghan; Wang, Hong-Wei; Mu, Weihua; Ouyang, Zhongcan; Nogales, Eva; Xing, Jianhua (PLOS, 2009-10-02)
    The microtubule assembly process has been extensively studied, but the underlying molecular mechanism remains poorly understood. The structure of an artificially generated sheet polymer that alternates two types of lateral contacts and that directly converts into microtubules, has been proposed to correspond to the intermediate sheet structure observed during microtubule assembly. We have studied the self-assembly process of GMPCPP tubulins into sheet and microtubule structures using thermodynamic analysis and stochastic simulations. With the novel assumptions that tubulins can laterally interact in two different forms, and allosterically affect neighboring lateral interactions, we can explain existing experimental observations. At low temperature, the allosteric effect results in the observed sheet structure with alternating lateral interactions as the thermodynamically most stable form. At normal microtubule assembly temperature, our work indicates that a class of sheet structures resembling those observed at low temperature is transiently trapped as an intermediate during the assembly process. This work may shed light on the tubulin molecular interactions, and the role of sheet formation during microtubule assembly.
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    Speeding up electrostatic computations for molecular dynamics
    Anandakrishnan, Ramamoorthi (Virginia Tech, 2011-10-18)
    Molecular dynamics (MD) simulations are routinely used to study the structure and function of biological molecules. However the accuracy and duration of these simulations are constrained by their computational costs, thus limiting the ability to accurately simulate systems of realistic sizes over biologically relevant time periods. The two most computationally demanding steps in these simulations are (1) determining the charge state of ionizable sites in biomolecules, which is a key input to the simulation, and (2) calculating long range electrostatic interactions during the simulation. Presented here are two novel methods, the direct interaction approximation (DIA) and the hierarchical charge partitioning (HCP) approximation, for speeding up each of these two computations. The average charge state of ionizable sites in biomolecules can be calculated as the statistical average over all possible (2N) microstates for a molecule, where N is the number of ionizable sites. In general this computation scales exponentially as O(N² 2N). The DIA is an O(²) approximation for calculating the average charge state of ionizable sites. For each site, the DIA treats direct interactions (interactions involving the site of interest) exactly, while using an average value for indirect interactions (interactions not involving the site of interest). The DIA was tested on two problems. The computation of thermal average properties for the 2-D Ising model of ferromagnetism, and the average charge state of ionizable residues in biomolecules. Compared to the commonly used non-deterministic Monte Carlo method, for the same computational cost, the deterministic DIA was found to be at least as accurate, as measured by RMS error relative to the exact computation. Thus, the DIA may be a practical alternative to the Monte Carlo method for some problems. In atomistic MD simulations, the computation of long range electrostatic interactions, scale as O(n²), where n is the number of atoms. For most biologically relevant timescales the simulations involve 1012–16 simulation steps. Thus, the computational cost of long range interactions become the limiting factor in the size and duration of MD simulations. The HCP is an O(n log n) approximation for computing long range electrostatic interactions. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of components. For components that are far from the point of interest, the charge distribution for each component is approximated by a much smaller number of charges. For nearby components, the HCP uses the full set of atomic charges. For large structures the HCP can be several orders of magnitude faster than the exact pairwise O(n²) all-atom computation. For a representative set of structures, the accuracy of the HCP is comparable to the industry standard explicit solvent particle mesh Ewald (PME), and is in general more accurate than the spherical cutoff method. And, unlike the PME, the DIA can be easily extended to implicit solvent GB models. 50 ns implicit solvent simulations for a representative set of four biomolecules suggests that the HCP could be a practical alternative for implicit solvent simulations, and preferable to the cutoff based method. The HCP is available for general use in the open source MD software, NAB within AmberTools.
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    Stochastic Simulation Methods for Biochemical Systems with Multi-state and Multi-scale Features
    Liu, Zhen (Virginia Tech, 2012-11-13)
    In this thesis we study stochastic modeling and simulation methods for biochemical systems. The thesis is focused on systems with multi-state and multi-scale features and divided into two parts. In the first part, we propose new algorithms that improve existing multi-state simulation methods. We first compare the well known Gillespie\\\'s stochastic simulation algorithm (SSA) with the StochSim, an agent-based simulation method. Based on the analysis, we propose a hybrid method that possesses the advantages of both methods. Then we propose two new methods that extend the Network-Free Algorithm (NFA) for rule-based models. Numerical results are provided to show the performance improvement by our new methods. In the second part, we investigate two simulation schemes for the multi-scale feature: Haseltine and Rawlings\\\' hybrid method and the quasi-steady-state stochastic simulation method. We first propose an efficient partitioning strategy for the hybrid method and an efficient way of building stochastic cell cycle models with this new partitioning strategy. Then, to understand conditions where the two simulation methods can be applied, we develop a way to estimate the relaxation time of the fast sub-network, and compare it with the firing interval of the slow sub-network. Our analysis are verified by numerical experiments on different realistic biochemical models.