Directional Persistence Time Research Articles

Deciphering chemokine properties by a hybrid agent-based model of Aspergillus fumigatus infection in human alveoli.

The ubiquitous airborne fungal pathogen Aspergillus fumigatus is inhaled by humans every day. In the lung, it is able to quickly adapt to the humid environment and, if not removed within a time frame of 4–8 h, the pathogen may cause damage by germination and invasive growth. Applying a to-scale agent-based model of human alveoli to simulate early A. fumigatus infection under physiological conditions, we recently demonstrated that alveolar macrophages require chemotactic cues to accomplish the task of pathogen detection within the aforementioned time frame. The objective of this study is to specify our general prediction on the as yet unidentified chemokine by a quantitative analysis of its expected properties, such as the diffusion coefficient and the rates of secretion and degradation. To this end, the rule-based implementation of chemokine diffusion in the initial agent-based model is revised by numerically solving the spatio-temporal reaction-diffusion equation in the complex structure of the alveolus. In this hybrid agent-based model, alveolar macrophages are represented as migrating agents that are coupled to the interactive layer of diffusing molecule concentrations by the kinetics of chemokine receptor binding, internalization and re-expression. Performing simulations for more than a million virtual infection scenarios, we find that the ratio of secretion rate to the diffusion coefficient is the main indicator for the success of pathogen detection. Moreover, a subdivision of the parameter space into regimes of successful and unsuccessful parameter combination by this ratio is specific for values of the migration speed and the directional persistence time of alveolar macrophages, but depends only weakly on chemokine degradation rates.

PilT2 enhances the speed of gonococcal type IV pilus retraction and of twitching motility

Type IV pilus (T4P) dynamics is important for various bacterial functions including host cell interaction, surface motility, and horizontal gene transfer. T4P retract rapidly by depolymerization, generating large mechanical force. The gene that encodes the pilus retraction ATPase PilT has multiple paralogues, whose number varies between different bacterial species, but their role in regulating physical parameters of T4P dynamics remains unclear. Here, we address this question in the human pathogen Neisseria gonorrhoeae, which possesses two pilT paralogues, namely pilT2 and pilU. We show that the speed of twitching motility is strongly reduced in a pilT2 deletion mutant, while directional persistence time and sensitivity of speed to oxygen are unaffected. Using laser tweezers, we found that the speed of single T4P retraction was reduced by a factor of ≈ 2 in a pilT2 deletion strain, whereas pilU deletion showed a minor effect. The maximum force and the probability for switching from retraction to elongation under application of high force were not significantly affected. We conclude that the physical parameters of T4P are fine-tuned through PilT2.

Passive control of cell locomotion using micropatterns: the effect of micropattern geometry on the migratory behavior of adherent cells

Directed cell migration is critical to a variety of biological and physiological processes. Although simple topographical patterns such as parallel grooves and three-dimensional post arrays have been studied to guide cell migration, the effect of the dimensions and shape of micropatterns, which respectively represent the amount and gradient of physical spatial cues, on cell migration has not yet been fully explored. This motivates a quantitative characterization of cell migration in response to micropatterns having different widths and divergence angles. The changes in the migratory (and even locational) behavior of adherent cells, when the cells are exposed to physical spatial cues imposed by the micropatterns, are explored here using a microfabricated biological platform, nicknamed the "Rome platform". The Rome platform, made of a biocompatible, ultraviolet (UV) curable polymer (ORMOCOMP), consists of 3 μm thick micropatterns with different widths of 3 to 75 μm and different divergence angles of 0.5 to 5.0°. The migration paths through which NIH 3T3 fibroblasts move on the micropatterns are analyzed with a persistent random walk model, thus quantifying the effect of the divergence angle of micropatterns on cell migratory characteristics such as cell migration speed, directional persistence time, and random motility coefficient. The effect of the width of micropatterns on cell migratory characteristics is also extensively investigated. Cell migration direction is manipulated by creating the gradient of physical spatial cues (that is, divergence angle of micropatterns), while cell migration speed is controlled by modulating the amount of them (namely, width of micropatterns). In short, the amount and gradient of physical spatial cues imposed by changing the width and divergence angle of micropatterns make it possible to control the rate and direction of cell migration in a passive way. These results offer a potential for reducing the healing time of open wounds with a smart wound dressing engraved with micropatterns (or microscaffolds).

Control of cell migration using a conducting polymer device

Control of cell migration is receiving a great deal of attention due to its relevance to the engineering of tissues. Here we report a device that contains a conducting polymer stripe and achieves a continuum of microenvironments for cell growth under the influence of an applied bias. Marked differences are observed in the migration behaviour of bovine aortic endothelial cells (ECs) as a function of location along the polymer stripe, and a 3-fold variation is achieved in EC migration speed and directional persistence time. Moreover, the device induces directional cell migration along the conducting polymer stripe. A gradient in adsorbed fibronectin indicates that a spatial variation in cell adhesion is at play. The ability to control cell migration behaviour using external electrical stimuli highlights the potential of using conducting polymers as “active” substrates for the non-invasive control of cell behaviour.

Micropatterned Structural Control Suppresses Mechanotaxis of Endothelial Cells

Vascular endothelial cell migration is critical in many physiological processes including wound healing and stent endothelialization. To determine how preexisting cell morphology influences cell migration under fluid shear stress, endothelial cells were preset in an elongated morphology on micropatterned substrates, and unidirectional shear stress was applied either parallel or perpendicular to the cell elongation axis. On micropatterned 20-μm lines, cells exhibited an elongated morphology with stress fibers and focal adhesion sites aligned parallel to the lines. On 115-μm lines, cell morphology varied as a function of distance from the line edge. Unidirectional shear stress caused unpatterned cells in a confluent monolayer to exhibit triphasic mechanotaxis behavior. During the first 3h, cell migration speed increased in a direction antiparallel to the shear stress direction. Migration speed then slowed and direction became spatially heterogeneous. Starting 11–12h after the onset of shear stress, the unpatterned cells migrated primarily in the downstream direction, and migration speed increased significantly. In contrast, mechanotaxis was suppressed after the onset of shear stress in cells on micropatterned lines during the same time period, for the cases of both parallel and perpendicular flow. The directional persistence time was much longer for cells on the micropatterned lines, and it decreased significantly after flow onset. Migration trajectories were highly correlated among micropatterned cells within a three-cell neighborhood, and shear stress disrupted this spatially correlated migration behavior. Thus, presetting structural morphology may interfere with mechanisms of sensing local physical cues, which are critical for establishing mechanotaxis in response to hemodynamic shear stress.

Spreading and motility of human glioblastoma cells on sheets of silicone rubber depend on substratum compliance

Although there is a substantial quantity of experimental data examining the effects of adhesion on the morphology and migration of tissue cells, little attention has been focused on how changes in substratum mechanical properties affect these cellular behaviours. To determine whether the ability of a substratum mechanically to support traction influences cell morphology and motility, measurements are taken of the spreading, the fraction of a population with pseudopodia, the number of pseudopodia and the translocation of human SNB-19 glioblastoma cells cultured on films of poly(methylphenyl)siloxane possessing a range of mechanical compliances. Cells cultured on these films generate deformations (i.e. 'wrinkles') that are used as a basis to estimate effective substratum compliances. The average projected cell area decreases by over 60%, with a two-orders-of-magnitude increase in compliance. Time-lapse videomicroscopy reveals that cell migration also decreases with increasing compliance: the average cell speed decreases from approximately 8 microns h-1 on the most rigid substrata to 1.2 microns h-1 on the most compliant substrata examined. Changes in compliance do not alter mean directional persistence time. These results are interpreted in terms of the predictions of mathematical models for the effects of substratum compliance on motility.

Quantitative analysis of adhesion-mediated cell migration in three-dimensional gels of RGD-grafted collagen.

Adhesion-mediated migration is required in a number of physiological and pathological processes. A further quantitative understanding of the relationship between cell migration and cell-substratum adhesiveness may aid in therapeutic or tissue engineering applications. The aim of this work was to quantify three-dimensional cell migration as a function of increasing cell-substratum adhesiveness within reconstituted collagen gels. Cell-substratum adhesiveness was controlled by grafting additional adhesive peptides containing the well-characterized arginine-glycine-aspartic acid sequence to collagen. The three-dimensional migration of multiple individual cells was tracked in real time in an automated fashion for extended periods. Cell displacements were statistically analyzed and fit to a correlated persistent random walk model to estimate root-mean-square speed, directional persistence time, and random motility coefficient. Based on model parameter estimates, cell speed was found to be a monotonically decreasing function of increasing substratum adhesiveness, while the directional persistence time and random motility coefficient exhibited a biphasic dependence, with maximum values at approximately intermediate concentrations of grafted adhesive peptide and hence intermediate cell-substratum adhesiveness. In conclusion, these studies suggest an optimal adhesiveness for three-dimensional random migration, consistent with previous studies on two-dimensional surfaces. However, the maximum in random motility corresponded to a maximum in directional persistence, not in cell speed.

Deconstructing (and reconstructing) cell migration.

An overriding objective in cell biology is to be able to relate properties of particular molecular components to cell behavioral functions and even physiology. In the "traditional" mode of molecular cell biology, this objective has been tackled on a molecule-by-molecule basis, and in the "future" mode sometimes termed "functional genomics," it might be attacked in a high-throughput, parallel manner. Regardless of the manner of approach, the relationship between molecular-level properties and cell-level function is exceedingly difficult to elucidate because of the large number of relevant components involved, their high degree of interconnectedness, and the inescapable fact that they operate as physico-chemical entities-according to the laws of kinetics and mechanics-in space and time within the cell. Cell migration is a prominent representative example of such a cell behavioral function that requires increased understanding for both scientific and technological advance. This article presents a framework, derived from an engineering perspective regarding complex systems, intended to aid in developing improved understanding of how properties of molecular components influence the function of cell migration. That is, cell population migration behavior can be deconstructed as follows: first in terms of a mathematical model comprising cell population parameters (random motility, chemotaxis/haptotaxis, and chemokinesis/haptokinesis coefficients), which in turn depend on characteristics of individual cell paths that can be analyzed in terms of a mathematical model comprising individual cell parameters (translocation speed, directional persistence time, chemotactic/haptotactic index), which in turn depend on cell-level physical processes underlying motility (membrane extension and retraction, cell/substratum adhesion, cell contractile force, front-vs.-rear asymmetry), which in turn depend on molecular-level properties of the plethora of components involved in governance and regulation of these processes. Hence, the influence of any molecular component on cell population migration can be understood by reconstructing these relationships from the molecular level to the physical process level to the individual cell path level to the cell population distribution level. This approach requires combining experimental, theoretical, and computational methodologies from molecular biology, biochemistry, biophysics, and bioengineering.

Transport Equations and Indices for Random and Biased Cell Migration Based on Single Cell Properties

A mathematical-modeling-and-analysis framework is presented to predict quantitative indices for random and biased cell migration based on mechanistic parameters describing the receptor-mediated motility of an individual cell. A general set of stochastic differential equations is derived to model cell movement on the time scale of the molecular processes that govern cell locomotion. Then, by adiabatic elimination of the fast variables with projector operator formalism, we derive approximate Fokker–Planck equations (FPEs) for the resultant cell movement on longer time scales. Analysis of these FPEs provides expressions for statistical indices that are commonly used to characterize cell movement, such as root-mean–squared cell speed, directional persistence time, mean-squared displacement, random motility coefficient, and drift velocity, in terms of the mechanistic parameters. As specific examples, we apply this approach to adhesion-mediated directed cell migration (haptotaxis) and chemoattractant-mediated directed cell migration (chemotaxis).

A Model of Neurite Extension across Regions of Nonpermissive Substrate: Simulations Based on Experimental Measurement of Growth Cone Motility and Filopodial Dynamics

The guidance of pioneer neurites in the developing embryo occurs through a variety of mechanisms, including chemotaxis, haptotaxis, contact inhibition, and mechanical guidance. In each of these processes, the growth cone serves as a sensory-motile mediator of the neurite response to a directional cue. However, the role of growth cone dynamics in determining the neurite path is not well-defined. To provide a quantitative basis for investigating this relationship, we have developed a mathematical model that describes two major aspects of growth cone motility during neurite outgrowth: the continuous but erratic motion frequently observed on homogeneous substrates such as laminin or collagen and the more directed movement along filopodial that have contacted a remote cue. Model parameters include the rate and angle of filopodial initiation, rates of filopodial extension and retraction, maximum filopodial length, and the root-mean square speed and directional persistence time of growth cone advance. Experimental estimates of these parameters were obtained from in vitro measurements on chick dorsal root ganglion and rat superior cervical ganglion neurons and used to compare model results with previously reported experimental data for neurite outgrowth on a patterned laminin/albumin substrate. The model represents a conceptual framework for further investigation and elucidation of the role of growth cone dynamics in neurite outgrowth and guidance.

Role of microtubules in random cell migration: stabilization of cell polarity.

The role of microtubules in random cell migration was investigated using time-lapse videomicroscopy to record in vitro the shape and motile behavior of guinea pig alveolar macrophages before and after disrupting microtubules with colcemid. Cell migration was quantified in terms of directional persistence time and speed. Motility was also correlated with morphological polarity: cells having a single lamellipodal region (monopolar cells) migrated, whereas those lacking a lamellipod (apolar cells) or with opposing lamellipodal regions (bipolar cells) did not migrate. Within 2 hours, colcemid caused a shift in polarity from 80% monopolar cells to 40% monopolar and 40% bipolar cells and a corresponding decrease from 80% to 40% in the fraction of migrating cells. Mean persistence time and speed decreased only slightly (approximately 20%) for those cells (still monopolar) which continued to migrate in the presence of colcemid. Persistence time and speed actually increased for many individual cells, indicating that random migration did not require intact microtubules. We conclude that colcemid treatment destabilizes monopolarity, leading to the gradual loss of monopolarity and consequent inhibition of migration. While a cell remains monopolar, it will continue to migrate even in the absence of intact microtubules, but microtubules are required for the long-term maintenance of cellular monopolarity and, thus, for continued motility.

Optimal estimation of cell movement indices from the statistical analysis of cell tracking data

AbstractActive cell migration is essential in many physiological processes and in the function of some bioartificial tissues. Therefore, several investigators have recently attempted to quantitatively characterize random cell movement on isotropic substrata in vitro. A popular approach is to fit a theoretical expression for mean‐squared cell displacement deriving from correlated random walk models to cell tracking data, yielding three objective cell movement indices: root‐mean‐squared speed, directional persistence time, and random motility coefficient (analogous to a molecular diffusion coefficient). The data are obtained typically by averaging cell displacements over a cell track composed of cell positions measured at equal time increments and frequently by further pooling such displacement data from tracks of different cells from the same population. We identify pitfalls introduced if an ordinary nonlinear least‐squares regression analysis is used to fit the theoretical expression to the data as is commonly done and propose a generalized least‐squares regression analysis as a remedy. This method estimates the cell movement indices and associated uncertainties much more accurately. It also predicts the precision of the indices based on their assumed true values and provides a means to address such issues as optimal sampling methods for data acquisition from cell tracks and handling errors associated with measuring cell position.

A stochastic model for adhesion-mediated cell random motility and haptotaxis.

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood. A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration. Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis), kinesis, and orthotaxis, of which taxis appears to be predominant given estimates of the model parameters.

Transport models for chemotactic cell populations based on individual cell behavior

A simple, generalized transport equation for the migration of chemotactic cell populations is derived from a probabilistic model in one spatial dimension. This general equation is then made specific for the cases of flagellar bacteria and polymorphonuclear leukocytes, based on quantitative information concerning chemosensory movement behavior of individual cells of these types. The resulting specialized equations allow a priori estimation of the polulation transport coefficients (μ, the random motility coefficient, and x, the chemotaxis coefficient) in terms of individual cell movement properties (such as speed, directional persistence time, and directional orientation bias). Thus, our model permits cell population migration to be related quantitatively to individual cell behavior. Examples of application of our models to experimental data are provided. Despite the simplifying approximations involved in our derivations, especially in the extrapolation to higher spatial dimensions, the models demonstrate a satisfactory and very useful ability to quantitatively interpret population assays for bacterial and leukocyte chemotactic migration.

Stochastic model of leukocyte chemosensory movement.

We propose a hypothesis for a unified understanding of the persistent and biased random walk behavior of leukocytes exhibiting random motility and chemotaxis, respectively. This hypothesis is based on a description of the leukocyte as an integrated system sensing and responding to a "noisy" receptor signal: random fluctuations inherent in receptor-sensing of chemo-attractant concentrations underlie the random walk behavior. Noise arises from real fluctuations in the receptor binding process, which translate into perceived fluctuations in receptor-measured concentration. The unbiased random walk characteristic of random motility arises from perceived fluctuating gradients without a mean reference direction and the biased random walk in chemotaxis arises due to the occurrence of perceived concentration fluctuations around the mean gradient. Analysis of a stochastic model based on this hypothesis yields an objective index of directional randomness in random motility, the directional persistence time, in terms of model parameters associated with receptor binding, receptor signal transduction, and the cell turning response. Simulation of the model equations yields cell paths from which the orientation behavior in a chemoattractant gradient is characterized in terms of the same model parameters. Our results provide a theoretical relationship between directional persistence and orientation bias and suggest quantitative answers to the questions: Is there an optimal level of persistence with respect to maximizing orientation bias? Do directional persistence and orientation bias both display the same parametric sensitivity? How does this sensitivity depend on the sensing, transduction, and response components of the cell system?