Laplacian Dynamics on General Graphs

In previous work, we have introduced a “linear framework” for time-scale separation in biochemical systems, which is based on a labelled, directed graph, G, and an associated linear differential equation, $dx/dt = \mathcal{L}(G)\cdot x$ , where $\mathcal{L}(G)$ is the Laplacian matrix of G. Biochemical nonlinearity is encoded in the graph labels. Many central results in molecular biology can be systematically derived within this framework, including those for enzyme kinetics, allosteric proteins, G-protein coupled receptors, ion channels, gene regulation at thermodynamic equilibrium, and protein post-translational modification. In the present paper, in response to new applications, which accommodate nonequilibrium mechanisms in eukaryotic gene regulation, we lay out the mathematical foundations of the framework. We show that, for any graph and any initial condition, the dynamics always reaches a steady state, which can be algorithmically calculated. If the graph is not strongly connected, which may occur in gene regulation, we show that the dynamics can exhibit flexible behavior that resembles multistability. We further reveal an unexpected equivalence between deterministic Laplacian dynamics and the master equations of continuous-time Markov processes, which allows rigorous treatment within the framework of stochastic, single-molecule mechanisms.     

Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka–Volterra model

We propose an optimal control framework to describe intra-seasonal predator–prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is active, as opposed to diapausing (a state of physiological rest). The predator follows autonomous dynamics and accordingly it remains active during the season. The proposed model is a generalization of the classical Lotka–Volterra predator–prey model towards non-autonomous dynamics that furthermore includes the effect of an energy variable. The model has been inspired by a specific biological system of predatory mites (Acari: Phytoseiidae) and prey mites (so-called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees—its parameters have been instantiated based on laboratory and field studies. The goal of the work is to understand the decisions of the prey mites to enter diapause (a state of physiological rest) given the dynamics of the predatory mites: this is achieved by solving an optimization problem hinging on the maximization of the prey population contribution to the next season. The main features of the optimal strategy for the prey are shown to be that (1) once in diapause, the prey does not become active again within the same season and hence diapause is an irreversible process; (2) for the vast majority of parameter space, the portion of prey individuals entering diapause within the season does not decrease in time; (3) with an increased number of predators, the optimal population strategy for the prey is to start diapause earlier and to enter diapause more gradually. This optimal population strategy will be studied for its ESS properties in a sequel to the work presented in this article.     

Modelling and parameter identification for batch fermentations with Streptomyces tendae under phosphate limitation

Summary A simple structured model for the dynamics of phosphate-limited batch fermentations with Streptomyces tendae is presented. The model describes the influence of intracellular phosphate storage upon the growth behav our of the culture. The development of the model takes into account the possible internal regulatory processes of phosphate metabolism. These complex biochemical pathways are summarized with regard to rate-limiting steps to obtain relatively simple model equations. The model parameters are fitted to the experimental data with an identification programme based on the sequential quadratic programming algorithm. Modifications in this algorithm yield a good performance for this application. With respect to the sensitivity of the model parameters, a feedback on the modelling is given. After several loops of modelling and identification, a model was achieved that fits to a set of batch fermentations. Furthermore the simulations show that RNA measurements of some recent fermentations can be interpreted by the simulated internal state variable and that there is evidence for RNA as an intracellular phosphate reserve. Offprint requests to: K.-P. Kuhn     

Intracellular demography and the dynamics of Salmonella enterica infections

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.     

A multiscale hybrid approach for vasculogenesis and related potential blocking therapies

Solid tumors must recruit and form new blood vessels for maintenance, growth and detachments of metastases. Discovering drugs that block malignant angiogenesis is thus an important approach in cancer treatment and has given rise to multiple in vitro and in silico models. The present hybrid individual cell-based model incorporates some underlying biochemical events relating more closely the classical Cellular Potts Model (CPM) parameters to subcellular mechanisms and to the activation of specific signaling pathways. The model spans the three fundamental biological levels: at the extracellular level a continuous model describes secretion, diffusion, uptake and decay of the autocrine VEGF; at the cellular level, an extended lattice CPM, based on a system energy reduction, reproduces cell dynamics such as migration, adhesion and chemotaxis; at the subcellular level, a set of reaction-diffusion equations describes a simplified VEGF-induced calcium-dependent intracellular pathway. The results agree with the known interplay between calcium signals and VEGF dynamics and with their role in malignant vasculogenesis. Moreover, the analysis of the link between the microscopic subcellular dynamics and the macroscopic cell behaviors confirms the efficiency of some pharmacological interventions that are currently in use and, more interestingly, proposes some new therapeutic approaches, that are counter-intuitive but potentially effective.     

Embodied Choice: How Action Influences Perceptual Decision Making

Embodied Choice considers action performance as a proper part of the decision making process rather than merely as a means to report the decision. The central statement of embodied choice is the existence of bidirectional influences between action and decisions. This implies that for a decision expressed by an action, the action dynamics and its constraints (e.g. current trajectory and kinematics) influence the decision making process. Here we use a perceptual decision making task to compare three types of model: a serial decision-then-action model, a parallel decision-and-action model, and an embodied choice model where the action feeds back into the decision making. The embodied model incorporates two key mechanisms that together are lacking in the other models: action preparation and commitment. First, action preparation strategies alleviate delays in enacting a choice but also modify decision termination. Second, action dynamics change the prospects and create a commitment effect to the initially preferred choice. Our results show that these two mechanisms make embodied choice models better suited to combine decision and action appropriately to achieve suitably fast and accurate responses, as usually required in ecologically valid situations. Moreover, embodied choice models with these mechanisms give a better account of trajectory tracking experiments during decision making. In conclusion, the embodied choice framework offers a combined theory of decision and action that gives a clear case that embodied phenomena such as the dynamics of actions can have a causal influence on central cognition.     

Structure,dynamics, and biochemical characterization of ADF/cofilin Twinstar from Drosophila melanogaster

BackgroundTwinstar is an ADF/cofilin family protein, which is expressed by the tsr gene in Drosophila melanogaster. Twinstar is one of the main regulators of actin cytoskeleton remodelling and is essential for vital cellular processes like cytokinesis and endocytosis.MethodsWe have characterized the structure and dynamics of Twinstar by solution NMR spectroscopy, the interaction of Twinstar with rabbit muscle actin by ITC, and biochemical activities of Twinstar through different biochemical assays using fluorescence spectroscopy and ultra-centrifugation.ResultsThe solution structure of Twinstar shows characteristic ADF-H fold with well-formed G/F-site and F-site for interaction with actin. The structure possesses an extended F-loop, which is rigid at the base, but flexible towards its apical region. Twinstar shares similar dynamics for the G/F-site with C. elegans homologs, UNC-60A and UNC-60B. However, the dynamics of its F-loop are different from its C. elegans homologs. Twinstar shows strong affinity for ADP-G-Actin and ATP-G-Actin with K_ds of ~7.6 nM and ~0.4 μM, respectively. It shows mild F-actin depolymerizing activity and stable interaction with F-actin with a K_d of ~5.0 μM. It inhibits the rate of the nucleotide exchange in a dose dependent manner.ConclusionOn the basis of structure, dynamics, and biochemical activity, Twinstar can be taken to execute its biochemical role by facilitating directional growth and maintenance of length of actin filaments.General significanceThis study characterizes the structure, backbone dynamics, and biochemical activities of Twinstar of Drosophila, which provides an insight into the regulation of actin dynamics in the member of phylum insecta.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

Translating biochemical network models between different kinetic formats

Mechanistic biochemical network models describe the dynamics of intracellular metabolite pools in terms of substance concentrations, stoichiometry and reaction kinetics. Data from stimulus response experiments are currently the most informative source for in-vivo parameter estimation in such models. However, only a part of the parameters of classical enzyme kinetic models can usually be estimated from typical stimulus response data. For this reason, several alternative kinetic formats using different “languages” (e.g. linear, power laws, linlog, generic and convenience) have been proposed to reduce the model complexity. The present contribution takes a rigorous “multi-lingual” approach to data evaluation by translating biochemical network models from one kinetic format into another. For this purpose, a new high-performance algorithm has been developed and tested. Starting with a given model, it replaces as many kinetic terms as possible by alternative expressions while still reproducing the experimental data. Application of the algorithm to a published model for Escherichia coli's sugar metabolism demonstrates the power of the new method. It is shown that model translation is a powerful tool to investigate the information content of stimulus response data and the predictive power of models. Moreover, the local and global approximation capabilities of the models are elucidated and some pitfalls of traditional single model approaches to data evaluation are revealed.     

Stochastic models for virus and immune system dynamics

New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection. The stochastic models are derived based on the dynamics of deterministic models. The simplest deterministic model is a well-known system of ordinary differential equations which consists of three populations: uninfected cells, actively infected cells, and virus particles. This basic model is extended to include some factors of the immune response related to Human Immunodeficiency Virus-1 (HIV-1) infection. For the deterministic models, the basic reproduction number, R₀, is calculated and it is shown that if R₀<1, the disease-free equilibrium is locally asymptotically stable and is globally asymptotically stable in some special cases. The new stochastic models are systems of stochastic differential equations (SDEs) and continuous-time Markov chain (CTMC) models that account for the variability in cellular reproduction and death, the infection process, the immune system activation, and viral reproduction. Two viral release strategies are considered: budding and bursting. The CTMC model is used to estimate the probability of virus extinction during the early stages of infection. Numerical simulations are carried out using parameter values applicable to HIV-1 dynamics. The stochastic models provide new insights, distinct from the basic deterministic models. For the case R₀>1, the deterministic models predict the viral infection persists in the host. But for the stochastic models, there is a positive probability of viral extinction. It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding.     

Non-linear dynamics of the complement system activation

The complement system (CS) plays a prominent role in the immune defense. The goal of this work is to study the dynamics of activation of the classic and alternative CS pathways based on the method of mathematical modeling. The principal difficulty that hinders modeling effort is the absence of the measured values of kinetic constants of many biochemical reactions forming the CS. To surmount this difficulty, an optimization procedure consisting of constrained minimization of the total protein consumption by the CS was designed. The constraints made use of published data on the in vitro kinetics of elimination of the Borrelia burgdorferi bacteria by the CS. Special features of the problem at hand called for a significant modification of the general constrained optimization procedure to include a mathematical model of the bactericidal effect of the CS in the iterative setting. Determination of the unknown kinetic constants of biochemical reactions forming the CS led to a fully specified mathematical model of the dynamics of cell killing induced by the CS. On the basis of the model, effects of the initial concentrations of complements and their inhibitors on the bactericidal action of the CS were studied. Proteins playing a critical role in the regulation of the bactericidal action of the CS were identified. Results obtained in this work serve as an important stepping stone for the study of functioning of the CS as a whole as well as for developing methods for control of pathogenic processes.     

Protein kinase TgCDPK7 regulates vesicular trafficking and phospholipid synthesis in Toxoplasma gondii

Apicomplexan parasites are causative agents of major human diseases. Calcium Dependent Protein Kinases (CDPKs) are crucial components for the intracellular development of apicomplexan parasites and are thus considered attractive drug targets. CDPK7 is an atypical member of this family, which initial characterization suggested to be critical for intracellular development of both Apicomplexa Plasmodium falciparum and Toxoplasma gondii. However, the mechanisms via which it regulates parasite replication have remained unknown. We performed quantitative phosphoproteomics of T. gondii lacking TgCDPK7 to identify its parasitic targets. Our analysis lead to the identification of several putative TgCDPK7 substrates implicated in critical processes like phospholipid (PL) synthesis and vesicular trafficking. Strikingly, phosphorylation of TgRab11a via TgCDPK7 was critical for parasite intracellular development and protein trafficking. Lipidomic analysis combined with biochemical and cellular studies confirmed that TgCDPK7 regulates phosphatidylethanolamine (PE) levels in T. gondii. These studies provide novel insights into the regulation of these processes that are critical for parasite development by TgCDPK7.     

Bet-hedging antimicrobial strategies in macrophage phagosome acidification drive the dynamics of Cryptococcus neoformans intracellular escape mechanisms

The fungus Cryptococcus neoformans is a major human pathogen with a remarkable intracellular survival strategy that includes exiting macrophages through non-lytic exocytosis (Vomocytosis) and transferring between macrophages (Dragotcytosis) by a mechanism that involves sequential events of non-lytic exocytosis and phagocytosis. Vomocytosis and Dragotcytosis are fungal driven processes, but their triggers are not understood. We hypothesized that the dynamics of Dragotcytosis could inherit the stochasticity of phagolysosome acidification and that Dragotcytosis was triggered by fungal cell stress. Consistent with this view, fungal cells involved in Dragotcytosis reside in phagolysosomes characterized by low pH and/or high oxidative stress. Using fluorescent microscopy, qPCR, live cell video microscopy, and fungal growth assays we found that the that mitigating pH or oxidative stress reduced Dragotcytosis frequency, whereas ROS susceptible mutants of C. neoformans underwent Dragotcytosis more frequently. Dragotcytosis initiation was linked to phagolysosomal pH, oxidative stresses, and macrophage polarization state. Dragotcytosis manifested stochastic dynamics thus paralleling the dynamics of phagosomal acidification, which correlated with the inhospitality of phagolysosomes in differently polarized macrophages. Hence, randomness in phagosomal acidification randomly created a population of inhospitable phagosomes where fungal cell stress triggered stochastic C. neoformans non-lytic exocytosis dynamics to escape a non-permissive intracellular macrophage environment.     

Kinetic metabolic modelling for the control of plant cells cytoplasmic phosphate

A previously developed kinetic metabolic model for plant metabolism was used in a context of identification and control of intracellular phosphate (Pi) dynamics. Experimental data from batch flask cultures of Eschscholtiza californica cells was used to calibrate the model parameters for the slow dynamics (growth, nutrition, anabolic pathways, etc.). Perturbation experiments were performed using a perfusion small-scale bioreactor monitored by in vivo³¹P NMR. Parameter identification for Pi metabolism was done by measuring the cells dynamic response to different inputs for extracellular Pi (two pulse-response experiments and a step-response experiment). The calibrated model can describe Pi translocation between the cellular pools (vacuole and cytoplasm). The effect of intracellular Pi management on ATP/ADP and phosphomonoesters concentrations is also described by the model. The calibrated model is then used to develop a control strategy on the cytoplasmic Pi pool. From the identification of the systems dynamics, a proportional-integral controller was designed and tuned. The closed-loop control was implemented in the small-scale NMR bioreactor and experimental results were in accordance with model predictions. Thus, the calibrated model is able to predict cellular behaviour for phosphate metabolism and it was demonstrated that it is possible to control the intracellular level of cytoplasmic Pi in plant cells.     

Defects in actin dynamics lead to an autoinflammatory condition through the upregulation of CXCL5

Background

Destrin (DSTN) is a member of the ADF/cofilin family of proteins and is an important regulator of actin dynamics. The primary function of destrin is to depolymerize filamentous actin into its monomeric form and promote filament severing. While progress has been made in understanding the biochemical functions of the ADF/cofilin proteins, the study of an animal model for cells deficient for DSTN provides an opportunity to investigate the physiological processes regulated by proper actin dynamics in vivo. A spontaneous mouse mutant, corneal disease 1(corn1), is deficient for DSTN, which causes epithelial hyperproliferation and neovascularization in the cornea. Dstn^corn1 mice exhibit an actin dynamics defect in the cornea as evidenced by the formation of actin stress fibers in the epithelial cells. Previously, we observed a significant infiltration of leukocytes into the cornea of Dstn^corn1 mice as well as the upregulation of proinflammatory molecules. In this study, we sought to characterize this inflammatory condition and explore the physiological mechanism through which a loss of Dstn function leads to inflammation.

Methodology/Principal Findings

Through immunofluorescent analyses, we observed a significant recruitment of neutrophils and macrophages to the Dstn^corn1 cornea, demonstrating that the innate immune system is spontaneously activated in this mutant. The inflammatory chemokine, CXCL5, was ectopically expressed in the corneal epithelial cells of Dstn^corn1 mice, and targeting of the receptor for this chemokine inhibited neutrophil recruitment. An inflammatory reaction was not observed in the cornea of allelic mutant strain, Dstn^corn1-2J, which has a milder defect in actin dynamics in the corneal epithelial cells.

Conclusions/Significance

This study shows that severe defects in actin dynamics lead to an autoinflammatory condition that is mediated by the expression of CXC chemokines.     

植物磷脂酶D基因表达与衰老的关系

磷脂酶D (PLD)是一种重要的磷脂水解酶,在植物细胞中普遍存在。磷脂酶D能激活许多重要的细胞生理功能,包括调控细胞膜的重建、跨膜信号传导及细胞内调控、细胞骨架组装、防御反应以及种子萌发和植物的衰老等。对磷脂酶D的基本特性、磷脂酶D基因特异性表达模式及其活性抑制与植物衰老的关系进行了综述,并探讨和展望了今后植物磷脂酶D基因的研究方向。     

In vivo measurement of internal and global macromolecular motions in Escherichia coli

We present direct quasielastic neutron scattering measurements, in vivo, of macromolecular dynamics in Escherichia coli. The experiments were performed on a wide range of timescales to cover the large panel of internal and self-diffusion motions. Three major internal processes were extracted at physiological temperature: a fast picosecond process that corresponded to restricted jump diffusion motions and two slower processes that resulted from reorientational motions occurring in ∼40 ps and 90 ps, respectively. The analysis of the fast process revealed that the cellular environment leads to an appreciable increase in internal molecular flexibility and diffusive motion rates compared with those evaluated in fully hydrated powders. The result showed that the amount of cell water plays a decisive role in internal molecular dynamics. Macromolecular interactions and confinement, however, attenuate slightly the lubricating effect of water, as revealed by the decrease of the in vivo parameters compared with those measured in solution. The study demonstrated that standard sample preparations do not mimic accurately the physiological environment and suggested that intracellular complexity participates in functional dynamics necessary for biological activity. Furthermore, the method allowed the extraction of the self-diffusion of E. coli macromolecules, which presented similar parameters as those extracted for hemoglobin in red blood cells.