Stochastic model of leukocyte chemosensory movement

Journal of Mathematical Biology - We propose a hypothesis for a unified understanding of the persistent and biased random walk behavior of leukocytes exhibiting random motility and chemotaxis,...     

A model of canine leukocyte telomere dynamics

Recent studies have found associations of leukocyte telomere length (TL) with diseases of aging and with longevity. However, it is unknown whether birth leukocyte TL or its age-dependent attrition--the two factors that determine leukocyte TL dynamics--explains these associations because acquiring this information entails monitoring individuals over their entire life course. We tested in dogs a model of leukocyte TL dynamics, based on the following premises: (i) TL is synchronized among somatic tissues; (ii) TL in skeletal muscle, which is largely postmitotic, is a measure of TL in early development; and (iii) the difference between TL in leukocytes and muscle (ΔLMTL) is the extent of leukocyte TL shortening since early development. Using this model, we observed in 83 dogs (ages, 4-42 months) no significant change with age in TLs of skeletal muscle and a shorter TL in leukocytes than in skeletal muscle (P<0.0001). Age explained 43% of the variation in ΔLMTL (P<0.00001), but only 6% of the variation in leukocyte TL (P=0.035) among dogs. Accordingly, muscle TL and ΔLMTL provide the two essential factors of leukocyte TL dynamics in the individual dog. When applied to humans, the partition of the contribution of leukocyte TL during early development vs. telomere shortening afterward might provide information about whether the individual's longevity is calibrated to either one or both factors that define leukocyte TL dynamics.     

Actin dynamics rapidly reset chemoattractant receptor sensitivity following adaptation in neutrophils

Neutrophils are cells of the innate immune system that hunt and kill pathogens using directed migration. This process, known as chemotaxis, requires the regulation of actin polymerization downstream of chemoattractant receptors. Reciprocal interactions between actin and intracellular signals are thought to underlie many of the sophisticated signal processing capabilities of the chemotactic cascade including adaptation, amplification and long-range inhibition. However, with existing tools, it has been difficult to discern actin''s role in these processes. Most studies investigating the role of the actin cytoskeleton have primarily relied on actin-depolymerizing agents, which not only block new actin polymerization but also destroy the existing cytoskeleton. We recently developed a combination of pharmacological inhibitors that stabilizes the existing actin cytoskeleton by inhibiting actin polymerization, depolymerization and myosin-based rearrangements; we refer to these processes collectively as actin dynamics. Here, we investigated how actin dynamics influence multiple signalling responses (PI3K lipid products, calcium and Pak phosphorylation) following acute agonist addition or during desensitization. We find that stabilized actin polymer extends the period of receptor desensitization following agonist binding and that actin dynamics rapidly reset receptors from this desensitized state. Spatial differences in actin dynamics may underlie front/back differences in agonist sensitivity in neutrophils.     

Stochastic computer model of cellular microtubule dynamics

A computer model of the system of microtubules has been developed to study the mechanisms of action of various factors on this system. The model describes the process of polymerization/depolymerization of microtubules as a set of chemical reactions with certain rate constants using a stochastic approach. Microtubules are visualized in the program field, which makes the model visual. The program imitates the dynamics and structure of the system of cellular microtubules with great, reliability. The parameters generated by the model correlate with the corresponding parameters of microtubules in living cells. We are going to develop this approach to modeling microtubules and similar structures to bring them into a better accord with living systems and to study the influence of various factors on these systems.     

Fluid dynamics and microscale chemical movement in the chemosensory appendages of the lobster, Homarus americanus

Every chemosensory structure has a boundary layer surroundingit through which chemical signals must pass before contactingreceptor cells. Fluid motion in this boundary layer is slowand odor movement is mainly by diffusion. The boundary layerstructure depends upon external fluid velocities and the morphologyof the appendage. High-speed (10–200 Hz) electrochemicalrecordings from microchemical electrodes were used to quantifychemical transport in the microscale environment of three morphologicallydifferent chemosensory appendages of the lobster, Homarus americanus:lateral antennule, medial antennule and walking legs. Controlledpulses of the odor tracer (dopamine) were delivered to the threeappendages at three different flow speeds (0, 3, 6 cm/s). Theamplitudes of the pulses increased with increasing flow speed,indicating that boundary layer thickness decreased with increasingflow speed. Larger pulse amplitudes were measured in the walkinglegs than in the lateral or medial antennules at all flow speeds.In addition, larger amplitudes were recorded in the medial antennulethan the lateral antennule. Changes in pulse amplitude withincreasing flow speed were larger than changes in pulse duration.These results demonstrate that pulse amplitude is affected morethan pulse duration by boundary layer thickness and that themorphology of the receptor strucure helps determine the structureof signals arriving at receptor cells. This may explain whyanimals have adopted sampling strategies that reduce boundarylayer thickness.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes, thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger is extended here to assess the consequences of recently discovered receptor phenomena: "down-regulation" of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference in relative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference in absolute receptor occupancy). However, in the context of receptor "signal noise," the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond. From this cell orientation model we can estimate the effective time-averaging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Stochastic disease dynamics of a hospital infection model

A stochastic model for hospital infection incorporating both direct transmission and indirect transmission via free-living bacteria in the environment is investigated. We examine the long term behavior of the model by calculating a stationary distribution and normal approximation of the distribution. The quasi-stationary distribution of the model is studied to investigate the models’ behavior before extinction and the time to extinction. Numerical results show agreement between the calculated distributions and results of event-driven simulations. Hand hygiene of volunteers is more effective in terms of reducing the mean (or standard deviation) of the stationary distribution of colonized patients and the expected time to extinction compared to hand hygiene of health care workers (HCWs), on the basis of our parameter values. However, the indirect (or direct) transmission rate can lead to either increase or decrease in the standard deviation of the stationary distribution, but the impact of the indirect transmission is much greater than that of the direct transmission. The findings suggest that isolation of new admitted colonized patients is most effective in reducing both the mean and standard deviation of the stationary distribution and measures related to indirect transmission are secondary in their effects compared to other interventions.     

Stochastic computer model of the cell microtubule dynamics

To study the effect of various factors on the microtubule system, one of the main cytoskeletal elements in the cell, which organizes the intracellular transport of different organelles and is necessary for mitosis and meiosis, a computer model of this system is created. Using a stochastic approach, the model describes the microtubule assembly/disassembly as a set of chemical reactions with certain rate constants. Microtubules are visualized in the computer program field, which makes the model vivid. The program imitates the dynamics and structure of the microtubule system with high reliability. The parameters calculated by the model correlate with the corresponding parameters of microtubules in living cells. This approach to modeling microtubules and similar systems continues to be developed so that the models would better describe living systems and the effect of a still broader range of factors could be studied.     

Robustness analysis of the E. coli chemosensory system to perturbations in chemoattractant concentrations

MOTIVATION: Cells of Escherichia coli sense and move toward chemical attractants. This is done through an intricate sensory system that eventually directs the movements of flagellae which regulate the 'runs' and 'tumbles' of the cells. Under realistic conditions, chemical stimuli often fluctuate due to noise from the environment. The effect of noise on the chemosensory system has been investigated here through the sensitivity coefficients of the concentrations of four key proteins--the phosphorylated forms of CheA, CheB and CheY, and the FliM-CheY-P complex--that govern chemotactic motility. The letter P denotes phosphorylation. RESULTS: All sensitivities increased with time and then stabilized. However, the four sets of sensitivities differed in their magnitudes and the durations of their transient phases before stabilization. CheA-P was the least sensitive and CheY-P the most sensitive. Moreover, while the sensitivities of CheA-P, CheB-P and CheY-P increased with chemoattractant concentration, that of the FliM complex decreased. These differences have been interpreted in terms of the mechanism of the chemosensory system and they have important implications for practical applications of chemotaxis.     

Stochastic modelling of animal movement

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal''s movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.     

A stochastic model for chemosensory cell movement: application to neutrophil and macrophage persistence and orientation

Two central features of leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic “persistence time” between significant changes in direction. In chemoattractant concentration gradients, they demonstrate a biased random walk, with an “orientation bias” characterizing the fraction of cells moving up the gradient. A coherent picture of cell-movement responses to chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper we offer the possibility that “noise” in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we report on a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant receptor binding. This model proves to be capable of stimulating cell paths similar to those observed experimentally for two cell types examined to date: neutrophils and alveolar macrophages, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Further, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. The model also successfully predicts that an increase in persistence time is associated with a decrease in orientation for typical system parameter values, as is observed for alveolar macrophages in comparison to neutrophils. Thus, the concept of signal “noise” can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients. This suggests that chemosensory cell movement behavior may be based on a “usefully” imperfect integrated signal response system, which allows both random and directed searches under appropriate conditions.     

Electron-conformational model of ryanodine receptor lattice dynamics

We propose a simple, physically reasonable electron-conformational model for the ryanodine receptor (RyR) and, on that basis, present a theory to describe RyR lattice responses to L-type channel triggering as an induced non-equilibrium phase transition. Each RyR is modelled with a single open and a single closed (electronic) state only, described utilizing a s=12 pseudospin approach. In addition to the fast electronic degree of freedom, the RyR channel is characterized by a slow classical conformational coordinate, Q, which specifies the RyR channel calcium conductance and provides a multimodal continuum of possible RyR states. The cooperativity in the RyR lattice is assumed to be determined by inter-channel conformational coupling. Given a threshold sarcoplasmic reticulum (SR) calcium load, the RyR lattice fires due to a nucleation process with a step-by-step domino-like opening of a fraction of lattice channels, providing for a sufficient release to generate calcium sparks. The optimal mode of RyR lattice functioning during calcium-induced calcium release implies a fractional release with a robust termination due to a decrease in SR calcium load, accompanied by a respective change in effective conformational strain of the lattice. SR calcium overload is shown to result in excitation of RyR lattice auto-oscillations with spontaneous RyR channel opening and closure.     

Stochastic tunnels in evolutionary dynamics

We study a situation that arises in the somatic evolution of cancer. Consider a finite population of replicating cells and a sequence of mutations: type 0 can mutate to type 1, which can mutate to type 2. There is no back mutation. We start with a homogeneous population of type 0. Mutants of type 1 emerge and either become extinct or reach fixation. In both cases, they can generate type 2, which also can become extinct or reach fixation. If mutation rates are small compared to the inverse of the population size, then the stochastic dynamics can be described by transitions between homogeneous populations. A "stochastic tunnel" arises, when the population moves from all 0 to all 2 without ever being all 1. We calculate the exact rate of stochastic tunneling for the case when type 1 is as fit as type 0 or less fit. Type 2 has the highest fitness. We discuss implications for the elimination of tumor suppressor genes and the activation of genetic instability. Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances.     

CRDB: database of chemosensory receptor gene families in vertebrate

Chemosensory receptors (CR) are crucial for animals to sense the environmental changes and survive on earth. The emergence of whole-genome sequences provides us an opportunity to identify the entire CR gene repertoires. To completely gain more insight into the evolution of CR genes in vertebrates, we identified the nearly all CR genes in 25 vertebrates using homology-based approaches. Among these CR gene repertoires, nearly half of them were identified for the first time in those previously uncharacterized species, such as the guinea pig, giant panda and elephant, etc. Consistent with previous findings, we found that the numbers of CR genes vary extensively among different species, suggesting an extreme form of 'birth-and-death' evolution. For the purpose of facilitating CR gene analysis, we constructed a database with the goals to provide a resource for CR genes annotation and a web tool for exploring their evolutionary patterns. Besides a search engine for the gene extraction from a specific chromosome region, an easy-to-use phylogenetic analysis tool was also provided to facilitate online phylogeny study of CR genes. Our work can provide a rigorous platform for further study on the evolution of CR genes in vertebrates.     

Propagating chemoattractant waves coordinate periodic cell movement in Dictyostelium slugs.

Migration and behaviour of Dictyostelium slugs results from coordinated movement of its constituent cells. It has been proposed that cell movement is controlled by propagating waves of cAMP as during aggregation and in the mound. We report the existence of optical density waves in slugs; they are initiated in the tip and propagate backwards. The waves reflect periodic cell movement and are mediated by cAMP, as injection of cAMP or cAMP phosphodiesterase disrupts wave propagation and results in effects on cell movement and, therefore, slug migration. Inhibiting the function of the cAMP receptor cAR1 blocks wave propagation, showing that the signal is mediated by cAR1. Wave initiation is strictly dependent on the tip; in decapitated slugs no new waves are initiated and slug movement stops until a new tip regenerates. Isolated tips continue to migrate while producing waves. We conclude from these observations that the tip acts as a pacemaker for cAMP waves that coordinate cell movement in slugs.     

单核细胞趋化蛋白受体的研究进展

单核细胞趋化蛋白及其受体在机体免疫应答中(免疫调节、器官形成、调节造血和神经元通讯)发挥了重要作用,同时也广泛参与某些疾病的发病机制(动脉粥样硬化、感染炎症性疾病及肿瘤等)。因此,有关趋化性细胞因子的新理论和技术可为临床治疗某些疾病提供了新思路。本文简要地综述单核细胞趋化蛋白受体的生物学特性、生物学作用及对心血管疾病的影响作用。     

Stochastic dynamics of metastasis formation

Tumor metastasis accounts for the majority of deaths in cancer patients. The metastatic behavior of cancer cells is promoted by mutations in many genes, including activation of oncogenes such as RAS and MYC. Here, we develop a mathematical framework to analyse the dynamics of mutations enabling cells to metastasize. We consider situations in which one mutation is necessary to confer metastatic ability to the cell. We study different population sizes of the main tumor and different somatic fitness values of metastatic cells. We compare mutations that are positively selected in the main tumor with those that are neutral or negatively selected, but faster at forming metastases. We study whether metastatic potential is the property of all (or the majority of) cells in the main tumor or only the property of a small subset. Our theory shows how to calculate the expected number of metastases that are formed by a tumor.     

Stochastic models of neuronal dynamics

Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs.We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker-Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have already been established for deterministic systems. The potential importance of modelling density dynamics (as opposed to more conventional neural mass models) is that they include interactions among the moments of neuronal states (e.g. the mean depolarization may depend on the variance of synaptic currents through nonlinear mechanisms).Here, we formulate a population model, based on biologically informed model-neurons with spike-rate adaptation and synaptic dynamics. Neuronal sub-populations are coupled to form an observation model, with the aim of estimating and making inferences about coupling among sub-populations using real data. We approximate the time-dependent solution of the system using a bi-orthogonal set and first-order perturbation expansion. For didactic purposes, the model is developed first in the context of deterministic input, and then extended to include stochastic effects. The approach is demonstrated using synthetic data, where model parameters are identified using a Bayesian estimation scheme we have described previously.     

Stochastic dynamics of cancer initiation

Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population.