Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders

It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean-squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has, however, focused on characterizing the properties of trajectories that do not interact with cell borders (e.g., cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis, however, require particles to be near a membrane. This study investigates the consequences of a canonical type of subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive motion leads to the formation of significant zones of depleted particle density near boundaries and that this effect is independent of the specific model details encoding those dynamics. Rather, these depletion layers are a natural and robust consequence of the anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.     

Correlation analysis of frequency distributions of residues in proteins

Autocorrelation and spectrum analyses of amino acid residues along protein chains in a large data base has been performed. Results reveal the presence of general long range correlations. Similar analyses of simulated (random) peptides do not exhibit any such long range correlations. Based on the results of nur analysis, an attempt has been made to model the distribution of residues in protein sequences on a fractional Brownian motion and individual sequences as multi-fractals. For this purpose, the characteristics of an fractional Brownian motion namely, the scaling parameterH. the spectral exponent β and the fractal dimensionD, have been described     

Persistence of direction increases the drift velocity of run and tumble chemotaxis

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. Previous models of run and tumble chemotaxis neglect one or more features of the motion, namely (a) a cell cannot directly detect a chemoattractant gradient but rather makes temporal comparisons of chemoattractant concentration, (b) rather than being entirely random, tumbles exhibit persistence of direction, meaning that the new direction after a tumble is more likely to be in the forward hemisphere, and (c) rotational Brownian motion makes it impossible for an E. coli cell to swim in a straight line during a run. This paper presents an analytic calculation of the chemotactic drift velocity taking account of (a), (b) and (c), for weak chemotaxis. The analytic results are verified by Monte Carlo simulation. The results reveal a synergy between temporal comparisons and persistence that enhances the drift velocity, while rotational Brownian motion reduces the drift velocity. This work was supported by an Oliver Gatty Studentship from the University of Cambridge.     

Traction forces of neutrophils migrating on compliant substrates

Proper functioning of the innate immune response depends on migration of circulating neutrophils into tissues at sites of infection and inflammation. Migration of highly motile, amoeboid cells such as neutrophils has significant physiological relevance, yet the traction forces that drive neutrophil motion in response to chemical cues are not well characterized. To better understand the relationship between chemotactic signals and the organization of forces in motile neutrophils, force measurements were made on hydrogel surfaces under well-defined chemotactic gradients created with a microfluidic device. Two parameters, the mean chemoattractant concentration (C_M) and the gradient magnitude (Δc/Δx) were varied. Cells experiencing a large gradient with C_M near the chemotactic receptor K_D displayed strong punctate centers of uropodial contractile force and strong directional motion on stiff (12 kPa) surfaces. Under conditions of ideal chemotaxis—cells in strong gradients with mean chemoattractant near the receptor K_D and on stiffer substrates—there is a correlation between the magnitude of force generation and directional motion as measured by the chemotactic index. However, on soft materials or under weaker chemotactic conditions, directional motion is uncorrelated with the magnitude of traction force. Inhibition of either β₂ integrins or Rho-associated kinase, a kinase downstream from RhoA, greatly reduced rearward traction forces and directional motion, although some vestigial lamellipodium-driven motility remained. In summary, neutrophils display a diverse repertoire of methods for organizing their internal machinery to generate directional motion.     

Quantitative Microscopy: Protein Dynamics and Membrane Organisation

The mobility of membrane proteins is a critical determinant of their interaction capabilities and protein functions. The heterogeneity of cell membranes imparts different types of motion onto proteins; immobility, random Brownian motion, anomalous sub-diffusion, 'hop' or confined diffusion, or directed flow. Quantifying the motion of proteins therefore enables insights into the lateral organisation of cell membranes, particularly membrane microdomains with high viscosity such as lipid rafts. In this review, we examine the hypotheses and findings of three main techniques for analysing protein dynamics: fluorescence recovery after photobleaching, single particle tracking and fluorescence correlation spectroscopy. These techniques, and the physical models employed in data analysis, have become increasingly sophisticated and provide unprecedented details of the biophysical properties of protein dynamics and membrane domains in cell membranes. Yet despite these advances, there remain significant unknowns in the relationships between cholesterol-dependent lipid microdomains, protein-protein interactions, and the effect of the underlying cytoskeleton. New multi-dimensional microscopy approaches may afford greater temporal and spatial resolution resulting in more accurate quantification of protein and membrane dynamics in live cells.     

Dynamics of asynchronous random Boolean networks with asynchrony generated by stochastic processes

An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897-923] for a varying number of parents. In both these papers the authors consider an asynchronous updating of all nodes, with asynchrony generated by various random distributions. We supplement those results by using various stochastic processes as generators for the number of nodes to be updated at each time point. In this paper we use the following stochastic processes: Poisson process, random walk, birth and death process, Brownian motion, and fractional Brownian motion. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed-point analysis. The dynamics of the system show that the number of nodes to be updated at each time point is of great importance, especially for the random walk, the birth and death, and the Brownian motion processes. Small or moderate values for the number of updated nodes generate order, while large values may generate chaos depending on the underlying parameters. The Poisson process generates order. With fractional Brownian motion, as the values of the Hurst parameter increase, the system exhibits order for a wider range of combinations of the underlying parameters.     

A stochastic description of Dictyostelium chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells.     

Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure.     

Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method

An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss what we believe are new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions (MMEs), i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean-squared displacement we show that the MME analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the MME method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.     

A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

CXCR3/CXCR3 ligand biological axis impairs RENCA tumor growth by a mechanism of immunoangiostasis

Metastatic renal cell carcinoma (RCC) responds poorly to chemo- or radiation therapy but appears to respond to systemic immunotherapy (i.e., IL-2 and/or IFN-alpha), albeit with only 5-10% durable response. The CXCR3/CXCR3 ligand biological axis plays an important role in mediating type 1 cytokine-dependent cell-mediated immunity, which could be beneficial for attenuating RCC if optimized. We found that systemic IL-2 induced the expression of CXCR3 on circulating mononuclear cells but impaired the CXCR3 ligand chemotactic gradient from plasma to tumor by increasing circulating CXCR3 ligand levels in a murine model of RCC. Moreover, the antitumor effect of systemic IL-2 was CXCR3-dependent, as IL-2 failed to inhibit tumor growth and angiogenesis in CXCR3-/- mice. We hypothesized that the immunotherapeutic effect of the CXCR3/CXCR3 ligand biological axis could be optimized by first priming with systemic IL-2 to induce CXCR3 expression on circulating mononuclear cells followed by enhancing the intratumor CXCR3 ligand levels to establish optimal CXCR3-dependent chemotactic gradient. We found that combined systemic IL-2 with an intratumor CXCR3 ligand (CXCL9) lead to significantly greater reduction in tumor growth and angiogenesis, increased tumor necrosis, and increased intratumor infiltration of CXCR3+ mononuclear cells, as compared with either IL-2 or CXCL9 alone. The enhanced antitumor effect of the combined strategy was associated with a more optimized CXCR3-dependent chemotactic gradient and increased tumor-specific immune response. These data suggest that the combined strategy of systemic IL-2 with intratumor CXCR3 ligand is more efficacious than either strategy alone for reducing tumor-associated angiogenesis and augmenting tumor-associated immunity, the concept of immunoangiostasis.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

趋化因子CXCL9/Mig的研究进展

趋化因子CXCL9又称为mig,即monokine induced by IFN-γ(IFN-γ诱导的单核因子),是趋化因子CXC亚族的一员,体内主要由IFN-γ刺激的巨噬细胞和神经胶质细胞产生,体外则可由内皮细胞、粒细胞等在IFN-γ和TLR配体协同作用下产生。CXCL9的受体CXCR3为七次跨膜的G蛋白偶联受体。CXCL9对激活的T淋巴细胞和肿瘤浸润淋巴细胞具有趋化作用,但是对粒细胞和单核细胞没有作用。本文主要就CXCL9的结构与生化特征,其在免疫、移植排斥、肿瘤治疗等方面所起的作用,进行了较为系统的综述。     

Exogenous nitric oxide elicits chemotaxis of neutrophils in vitro

Nitric oxide (NO) has been shown to be both an intercellular and intracellular messenger. We propose here that exogenous NO induces chemotactic locomotion of human neutrophils. Indeed, when human neutrophils were placed in a gradient of a nitric oxide donor (S-nitroso-N-acetylpenicillamine; SNAP), a directed locomotion was induced, as evidenced by experiments of chemotaxis under agarose. Degraded SNAP (i.e., SNAP solution which had previously released NO) did not induce directed locomotion. Moreover, oxyhemoglobin, a scavenger of free NO, suppressed the chemotactic effect of SNAP, whereas LY-83583, a soluble guanylate cyclase inhibitor, inhibited the SNAP-mediated chemotaxis in a dose-response manner. Other unrelated NO donors, SIN-1 and S-nitroso-cysteine—a natural S-nitroso-compound, also induced a directed locomotion of neutrophils. Taken together, these in vitro experiments indicate that exogenous NO could mediate the chemotaxis of neutrophils and thus suggest that NO could contribute to neutrophil recruitment in vivo. © 1995 Wiley-Liss Inc.     

An updated algorithm for the generation of neutral landscapes by spectral synthesis

Background

Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts.

Methodology

We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm.

Conclusion/Significance

The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales.     

Identification of a common receptor for three types of rat cytokine-induced neutrophil chemoattractants (CINCs)

Rat cytokine-induced neutrophil chemoattractant-1 (CINC-1), CINC-2 and CINC-3/macrophage inflammatory protein-2 (MIP-2), members of the CXC chemokine family, are potent chemotactic factors for neutrophils. In order to identify the receptor for CINCs, rat CXC chemokine receptor 2 (CXCR2) was cloned and expressed in HEK293 cells. CINC-1, CINC-2 and CINC-3 induced calcium mobilizations dose-dependently in CXCR2-transfected cells, whereas formyl-methionyl-leucyl-phenylalanine (FMLP) did not. CINC-3 induced enhancement of cytoplasmic calcium concentration more potently than CINC-1 and CINC-2, and desensitized calcium transients induced by CINC-1 and CINC-2, which were essentially identical to those observed in rat neutrophils. In addition, anti-CXCR2 serum inhibited neutrophil chemotactic activities of three types of CINCs almost completely. The mutant CINC-3, whose amino-terminal amino acid sequence (SELR) was replaced to AAR, lost chemotactic activity of its own but inhibited that of CINC-1 and CINC-2 potently, and that of CINC-3 weakly. The results indicate that rat CXCR2 on neutrophils is the unique receptor for all three types of CINCs, and CINC-1/-2 and CINC-3 exert different biological activities through the common receptor.     

Testing human sperm chemotaxis: how to detect biased motion in population assays

Biased motion of motile cells in a concentration gradient of a chemoattractant is frequently studied on the population level. This approach has been particularly employed in human sperm chemotactic assays, where the fraction of responsive cells is low and detection of biased motion depends on subtle differences. In these assays, statistical measures such as population odds ratios of swimming directions can be employed to infer chemotactic performance. Here, we report on an improved method to assess statistical significance of experimentally determined odds ratios and discuss the strong impact of data correlations that arise from the directional persistence of sperm swimming.     

Molecular dynamics simulations on SDF-1alpha: binding with CXCR4 receptor

Insights into the interacting mode of CXCR4 with SDF-1alpha are crucial in understanding the structural and functional characteristics of CXCR4 receptor. In this paper a computational pipeline, integrating protein structure prediction, molecular dynamics simulations, automated molecular docking, and Brownian dynamics simulations were employed to investigate the dynamic and energetic aspects of CXCR4 associating with SDF-1alpha. The entire simulation revealed the surface distribution feature of electrostatic potentials and conformational "open-close" process of the receptor. The possible binding conformation of CXCR4 was identified, and the CXCR4-SDF-1alpha binding complex was generated. Arg188-Glu277 salt bridge plays an important role for both the extracellular domain conformational change and SDF-1alpha binding. Two binding sites were mapped at the extracellular domain (Site 1) and inside the transmembrane domain (Site 2), which are composed of conserved residues. Sites 1 and 2 contribute approximately 60% and 40% to the binding affinity with SDF-1alpha, respectively. The binding model is in agreement with most of the experimental data. Transmembrane VI has more significant motion in the harmonious conformational transition of CXCR4 during SDF-1alpha binding, which may be possibly associated with signal transduction. Based on the modeling and simulation, a binding mechanism hypothesis between CXCR4 and SDF-1alpha and its relationship to the signal transduction has been proposed.     

Lithium down-regulates the expression of CXCR4 in human neutrophils

The CXC chemokine receptor CXCR4 and its unique ligand SDF-1 (stromal-derived factor-1) play critical roles for the retention of hematopoietic cells within the bone marrow (BM) and for their mobilization into the circulation. Lithium often produces neutrophilia in psychiatric patients, but the mechanism of mobilization related to neutrophilia has not been fully clarified. We showed here that lithium dose-dependently reduces the levels of surface CXCR4 protein and mRNA in neutrophils, but not in lymphocytes. The chemotactic migration of neutrophils in response to SDF-1 was reduced after a pre-incubation with lithium. We provide evidence that lithium down-regulates the CXCR4 expression of neutrophils and it attenuates their responsiveness to SDF-1. Our studies support the concept that down-regulation of CXCR4 is one of the mechanisms by which causes neutrophilia.