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.     

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 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.     

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.     

Stochastic dynamics of actin filaments in guard cells regulating chloroplast localization during stomatal movement

Actin filaments and chloroplasts in guard cells play roles in stomatal function. However, detailed actin dynamics vary, and the roles that they play in chloroplast localization during stomatal movement remain to be determined. We examined the dynamics of actin filaments and chloroplast localization in transgenic tobacco expressing green fluorescent protein (GFP)-mouse talin in guard cells by time-lapse imaging. Actin filaments showed sliding, bundling and branching dynamics in moving guard cells. During stomatal movement, long filaments can be severed into small fragments, which can form longer filaments by end-joining activities. With chloroplast movement, actin filaments near chloroplasts showed severing and elongation activity in guard cells during stomatal movement. Cytochalasin B treatment abolished elongation, bundling and branching activities of actin filaments in guard cells, and these changes of actin filaments, and as a result, more chloroplasts were localized at the centre of guard cells. However, chloroplast turning to avoid high light, and sliding of actin fragments near the chloroplast, was unaffected following cytochalasin B treatment in guard cells. We suggest that the sliding dynamics of actin may play roles in chloroplast turning in guard cells. Our results indicate that the stochastic dynamics of actin filaments in guard cells regulate chloroplast localization during stomatal movement.     

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.     

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.     

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.     

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.     

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。     

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.     

Sequence analysis of leukocyte chemoattractant peptides secreted by periovulatory ovine follicles.

Cells of the white blood series infiltrate ovarian follicles during the ovulatory process. A segment of the wall of periovulatory ovine follicles was incubated and conditioned media subjected to ultrafiltration. Leukocyte chemoattractant activity of media was measured using a linear under-agarose migration assay. Bioactivity was recovered following filtration through a 3000 molecular weight cut-off membrane. Filtrate was then fractionated by reverse phase high performance liquid chromatography. Peptides recovered from two fractions with significant chemoattractant activity were sequenced. One fraction contained 16 amino acid residues with repeating triplets of Gly-X-Y, where X and Y were often proline and hydroxyproline, respectively. Because this motif is characteristic of alpha collagens, and since thecal collagen is degraded during the mechanics of ovulation, it appears that this chemoattractant is derived from the connective tissue matrix of the follicle. Peptide isolated from the other bioactive chromatographic fraction was 15 amino acids in length, and rich in glycine, but did not contain imino acids. To our knowledge this is the first report of purification of leukocyte chemoattractants of reproductive tissue origin. Resident follicular granulocytes and mononuclear cells are capable of secreting a broad spectrum of potent chemicals that could be involved in the mechanisms of ovulation and luteinization.     

A model of flagellar movement based on cooperative dynamics of dynein-tubulin cross-bridges

A theoretical model based on molecular mechanisms of both dynein cross-bridges and radial spokes is used to study bend propagation by eukaryotic flagella. Though nine outer doublets are arranged within an axoneme, a simplified model with four doublets is constructed on the assumption that cross-bridges between two of the four doublets are opposed to those between the other two, corresponding to the geometric array of cross-bridges on the 6-9 and the 1-4 doublets in the axoneme. We also assume that external viscosity is zero, whereas internal viscosity is non-zero in order to reduce numerical complexity. For demonstrating flagellar movement, computer simulations are available by dividing a long flagellum into many straight segments. Considering the fact that dynein cross-bridge spacing is almost equal to attachment site spacing, we may use a localized cross-bridge distribution along attachment sites in each straight segment. Dynamics of cross-bridges are determined by a three-state model, and effects of radial spokes are represented by a periodic mechanical potential whose periodicity is considered to be a stroke distance of the radial spoke. First of all, we examine the model of a short segment to know basic properties of the system. Changing parameters relating to "activation" of cross-bridges, our model demonstrates various phenomena; for example "excitable properties with threshold phenomena" and "limit cycle oscillation". Here, "activation" and "inactivation" (i.e. switching mechanisms) between a pair of oppositely-directed cross-bridges are essential for generation of excitable or oscillatory properties. Next, the model for a flagellar segment is incorporated into a flagellum with a whole length to show bending movement. When excitable properties of cross-bridges, not oscillatory properties, are provided along the length of the flagellum and elastic links between filaments are presented at the base, then our model can demonstrate self-organization of bending waves as well as wave propagation without special feedback control by the curvature of the flagellum. Here, "cooperative interaction" between adjacent short segments, based on "cooperative dynamics" of cross-bridges, is important for wave propagation.