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R T Tranquillo

Publications and source records attributed to R T Tranquillo.

At least 37 records · Page 2Linked to original sources

Self-organization of tissue-equivalents: the nature and role of contact guidance.

The morphology and behaviour of tissue cells when surrounded by a network of protein fibres, such as for a tissue-equivalent comprising cells entrapped in a type I collagen gel, is distinct from that when cells are cultured on a rigid surface, and physiologically relevant. The highly elongated and apparently bipolar morphology leads to a 'reversing' type of cell movement in gels, as opposed to a directionally persistent movement characteristic of highly spread, polar cells on surfaces. However, the hallmark of a tissue-equivalent is consolidation of the fibrillar network, or gel compaction, resulting from traction exerted by the cells. When the gel is mechanically constrained from compacting, alignment of the fibrils occurs, inducing cell alignment through a contact guidance response. In order to understand this 'self-organization' of tissue-equivalents, some relevant structural and mechanical properties of collagen gel are considered first, followed by a review of seminal studies of cell traction and tissue-equivalent compaction. Random cell migration in an isotropic gel is then discussed, including a modification of the persistent random walk model used to analyse cell migration on surfaces, followed by a review of contact guidance studies in gels with fibrils having defined alignment. With this background, observations of self-organization of mechanically constrained compacting tissue-equivalents are summarized and explained using a mechanical theory that relates traction-induced compaction to fibre alignment and consequent contact guidance, i.e. a strain-based rather than stress-based cell response to gel compaction. Data in support of this theory obtained from studies involving the controlled applied compression of tissue-equivalents are then presented. Finally, possible mechanisms of contact guidance are discussed.

Cell Adhesion↗

Engineered alignment in media equivalents: magnetic prealignment and mandrel compaction.

We predicted and measured the evolution of smooth muscle cell (SMC) orientation in media-equivalents (MEs) for four fabrication conditions (F-, M-, F+, M+) under Free or Mandrel compaction (F/M) with and without magnetic prealignment of the collagen fibrils in the circumferential direction (+/-). Mandrel compaction refers to SMC-induced compaction of the ME that is constrained by having a nonadhesive mandrel placed in the ME lumen. Predictions were made using our anisotropic biphasic theory (ABT) for tissue-equivalent mechanics. Successful prediction of trends of the SMC orientation data for all four fabrication cases was obtained: maintenance of the initial isotropic state for F-, loss of initial circumferential alignment for F+, development of circumferential alignment for M-, and enhancement of initial circumferential alignment for M+. These results suggest two mechanisms by which the presence of the mandrel leads to much greater mechanical stiffness in the circumferential direction reported for mandrel compacted MEs relative to free compacted MEs: (1) by inducing an increasing circumferential alignment of the SMC and collagen, and (2) by inducing a large stress on the SMC, resulting in secretion and accumulation of stiffening components.

Animals↗

An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance.

We present a general mathematical theory for the mechanical interplay in tissue-equivalents (cell-populated collagen gels): Cell traction leads to compaction of the fibrillar collagen network, which for certain conditions such as a mechanical constraint or inhomogeneous cell distribution, can result in inhomogeneous compaction and consequently fibril alignment, leading to cell contact guidance, which affects the subsequent compaction. The theory accounts for the intrinsically biphasic nature of collagen gel, which is comprised of collagen network and interstitial solution. The theory also accounts for fibril alignment due to inhomogeneous network deformation, that is, anisotropic strain, and for cell alignment in response to fibril alignment. Cell alignment results in anisotropic migration and traction, as modeled by a cell orientation tensor that is a function of a fiber orientation tensor, which is defined by the network deformation tensor. Models for a variety of tissue-equivalents are shown to predict qualitatively the alignment that arises due to inhomogeneous compaction driven by cell traction.

Anisotropy↗

A finite element solution for the anisotropic biphasic theory of tissue-equivalent mechanics: the effect of contact guidance on isometric cell traction measurement.

We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo's (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load.

Algorithms↗

Stochastic model of receptor-mediated cytomechanics and dynamic morphology of leukocytes.

The proposed mathematical model investigates the simplified cytomechanics of cell shape change driven by stochastic stimulation from chemosensory receptors. The cytomechanical component of our model describes the dynamical distribution of F-actin and associated forces in an idealized cortical actin network around the cell periphery. The chemosensory component describes the distribution of chemotactic receptors in the cell membrane surrounding the cortex, where bound receptors give rise to an intracellular signal which modulates some property of the cortical network. As in our earlier models, an account is made for (1) the reactive, contractive properties of cortical actin, but here also for a stress induced by curvature of the cortex-membrane complex which carries an effective surface tension, and (2) statistical fluctuations in receptor binding, but generalized here to include statistical fluctuations in the spatial distribution of receptors, entirely determined by the additional prescription of membrane diffusion coefficients along with total receptor number, receptor binding rate constants and the local concentration field of chemotactic factor. We simplify the analysis by restricting the model to a prototype in which viscous stresses in the cortical network are negligible and the radial extension of the cell cortex is a prescribed function of the cortical actin concentration. We assume in particular that the assembly rate of cortical actin depends on the local density of bound receptors. These assumptions lead to a 4th-order parabolic differential equation on the unit circle coupled to a system of stochastic differential equations. We characterize via bifurcation analysis, stochastic simulations, and analytical correlation functions the spatial-temporal pattern of cell morphology under the influence of fluctuations in the bound receptor distribution for the case of a uniform concentration field of chemotactic factor. In addition to addressing the biological significance of our model, we remark on its relevance to the generic problem of the influence of correlated stochastic perturbations on spatial patterns in morphogenetic media.

Actins↗

Magnetically orientated tissue-equivalent tubes: application to a circumferentially orientated media-equivalent.

Circumferential orientation of collagen fibrils in a media-equivalent (ME) is achieved in a simple and effective way using the orientating effects of a strong magnetic field during collagen fibrillogenesis when the ME is first created. Circumferential orientation of the entrapped smooth muscle cells (SMC) is achieved subsequently via cell contact guidance, the induced SMC orientation along orientated fibrils. After describing the methods used, several lines of evidence are provided showing that the magnetically orientated ME is circumferentially orientated, including collagen birefringence, circumferential SMC orientation, accelerated ME compaction and increased ME stiffness with reduced creep in the circumferential direction as compared to control MEs not exposed to a magnetic field during fibrillogenesis. The optimization of these methods is discussed in order to better mimic the circumferential orientation and mechanical properties of a natural medium. Other applications of magnetically orientated tissue-equivalents are indicated.

Animals↗

Cytokine-stimulated chemotaxis of human neutrophils in a 3-D conjoined fibrin gel assay.

The ability of neutrophils to migrate through three-dimensional (3-D) tissues in response to chemical stimuli is critical to their host defense function. However, studies characterizing stimulated migration in vitro have been largely limited to two-dimensional (2-D) surfaces. In this study, we have employed direct observation methods to quantify human neutrophil migration in 3-D fibrin gel using time-lapse video microscopy and automated cell tracking methods. A novel 3-D conjoined gel assay was developed to establish experimentally quantifiable and theoretically predictable diffusion gradients of chemotactic factors. This assay was used to measure objective migration parameters, namely the random motility and chemotaxis coefficients, in response to the cytokine, interleukin-8 (IL-8). The random motility coefficient, mu, showed a biphasic dependence on IL-8 concentration with a maximum of 1.1 x 10(-8) cm2/s at 5 x 10(-8) M IL-8; no significant motility was observed in the absence of IL-8. We further established the dependence of cell orientation bias, phi, on the concentration and gradient steepness (i.e., specific gradient, SG) of IL-8. Results indicate that phi increases with increasing SG, provided the concentration is maintained sufficiently low, which we conjecture to result from minimizing IL-8 receptor down-regulation. The chemotaxis coefficient, chi, was maximum at an intermediate SG for both IL-8 concentrations studied. We also examined the applicability of this assay to estimate mu and chi from indirect measurements of chemotaxis, namely the simpler measurement of cell redistribution after a prescribed incubation time, as opposed to direct cell tracking measurements. By virtue of measuring chi, this is the first quantitatively objective study of mammalian cell chemotaxis in a physiologically relevant 3-D gel and, in particular, of neutrophil chemotaxis on any substratum in response to the physiologically relevant chemotactic factor, IL-8.

Chemotactic Factors↗

The fibroblast-populated collagen microsphere assay of cell traction force--Part 2: Measurement of the cell traction parameter.

In Part 1 of this work, we formulated and analyzed a mathematical model for our fibroblast-populated collagen microsphere (FPCM) assay of cell traction forces (Moon and Tranquillo, 1993). In this assay, the FPCM diameter decreases with time as the cells compact the gel by exerting traction on collagen fibrils. In Part 1 we demonstrated that the diameter reduction profiles for varied initial cell concentration and varied initial FPCM diameter are qualitatively consistent with the model predictions. We show here in Part 2 how predictions of a model similar to that of Part 1, along with the determination of the growth parameters of the cells and the viscoelastic parameters of the gel, allow us to estimate the magnitude of a cell traction parameter, the desired objective index of cell traction forces. The model is based on a monophasic continuum-mechanical theory of cell-extracellular matrix (ECM) mechanical interactions, with a species conservation equation for cells (1), a mass conservation equation for ECM (2), and a mechanical force balance for the cell/ECM composite (3). Using a constant-stress rheometer and a fluids spectrometer in creep and oscillatory shear modes, respectively, we establish and characterize the linear viscoelastic regime for the reconstituted type 1 collagen gel used in our FPCM traction assay and in other assays of cell-collagen mechanical interactions. Creep tests are performed on collagen gel specimens in a state resembling that in our FPCM traction assay (initially uncompacted, and therefore nearly isotropic and at a relatively low collagen concentration of 2.1 mg/ml), yielding measurements of the zero shear viscosity, mu 0 7.4 x 10(6) Poise), and the steady-state creep compliance, J0e. The shear modulus, G (155 dynes/cm2), is then determined from the inverse of J0e in the linear viscoelastic regime. Oscillatory shear tests are performed in strain sweep mode, indicating linear viscoelastic behavior up to shear strains of approximately 10 percent. We discuss the estimation of Poisson's ratio, v, which along with G and mu 0 specifies the assumed isotropic, linear viscoelastic stress tensor for the cell/collagen gel composite which appears in (3). The proliferation rate of fibroblasts in free floating collagen gel (appearing in (1)) is characterized by direct cell counting, yielding an estimate of the first-order growth rate constant, k (5.3 x 10(-6) s-1). These independently measured and estimated parameter values allow us to estimate that the cell traction parameter, tau 0, defined in the active stress tensor which also appears in (3), is in the range of 0.00007-0.0002 dyne.cm4/mg collagen.cell.(ABSTRACT TRUNCATED AT 400 WORDS)

Biomechanical Phenomena↗

Stochastic model of chemoattractant receptor dynamics in leukocyte chemosensory movement.

Mammalian white blood cells are known to bias the direction of their movement along concentration gradients of specific chemical stimuli, a phenomenon called chemotaxis. Chemotaxis of leukocyte cells is central to the acute inflammatory response in living organisms and other critical physiological functions. On a molecular level, these cells sense the stimuli termed chemotactic factor (CF) through specific cell surface receptors that bind CF molecules. This triggers a complex signal transduction process involving intracellular biochemical pathways and biophysical events, eventually leading to the observable chemotactic response. Several investigators have shown theoretically that statistical fluctuations in receptor binding lead to "noisy" intracellular signals, which may explain the observed imperfect chemotactic response to a CF gradient. The most recent dynamic model (Tranquillo and Lauffenburger, J. Math. Biol. 25, 229-262. 1987) couples a scheme for intracellular signal transduction and cell motility response with fluctuations in receptor binding. However, this model employs several assumptions regarding receptor dynamics that are now known to be oversimplifications. We extend the earlier model by accounting for several known and speculated chemotactic receptor dynamics, namely, transient G-protein signaling, cytoskeletal association, and receptor internalization and recycling, including statistical fluctuations in the numbers of receptors among the various states. Published studies are used to estimate associated constants and ensure the predicted receptor distribution is accurate. Model analysis indicates that directional persistence in uniform CF concentrations is enhanced by increasing rate constants for receptor cytoskeletal inactivation, ternary complex dissociation, and binary complex dissociation, and by decreasing rate constants for receptor internalization and recycling. For most rate constants, we have detected an optimal range that maximizes orientation bias in CF gradients. We have also examined different desensitization and receptor recycling mechanisms that yield experimentally documented orientation behavior. These yield novel insights into the relationship between receptor dynamics and leukocyte chemosensory movement behavior.

Animals↗

Mechanistic model of wound contraction.

The interplay between cellular, biochemical, and biomechanical phenomena which result in wound contraction is examined with the aid of a mathematical model. The model accounts for fibroblasts repopulating the wound extracellular matrix (ECM) by a combination of migration and proliferation and, in the course of exerting traction forces associated with their motility, their deformation of the local ECM, which has a viscoelastic character. A base model, which assumes that cell and tissue properties are the same irrespective of position with respect to the wound center, is found to be inconsistent with wound contraction. Extensions of the base model which account for the possible influence of a concentration gradient of an inflammation-derived mediator on the traction, growth, or chemotactic properties of the fibroblasts do predict the qualitative features of a contracting wound. In particular, the case where traction is prescribed to increase as fibroblasts approach the wound center is shown to obey the commonly observed exponential rate contraction law and to be largely consistent with the findings of McGrath and Simon (Plast. Reconstr. Surg. 72, 66, 1983) concerning the independence of the contraction rate constant and final extent of contraction from initial wound size and geometry.

Animals↗

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.

Animals↗

A methodology for the systematic and quantitative study of cell contact guidance in oriented collagen gels. Correlation of fibroblast orientation and gel birefringence.

Despite the likely role of contact guidance in every physiological process involving cell migration, its study in a three-dimensional tissue-equivalent environment has been precluded, heretofore, by inherent difficulties in systematically preparing well-defined contact guidance fields and quantifying the resultant contact guidance. Here, we describe a novel use of a magnetic field to orient collagen fibrils during fibrillogenesis, entrapping cells dispersed in the collagen solution. Using computer-controlled staging and image analysis, we show from automated birefringence measurements of the resultant slab of cell-populated gel contained in a specially designed observation chamber that the fibril orientation is biased along the long axis of the chamber uniformly throughout the chamber. Further, we show that the degree of fibril orientation, and consequently the elicited contact guidance, can be controlled by independently varying the magnetic field strength or temperature during fibrillogenesis. We characterize the contact guidance response to the imposed contact guidance field by measuring cell orientation relative to the axis of fibril orientation from still images obtained in time-lapse via automated image analysis. We present the first quantitative correlation of contact guidance (based on cell orientation) with collagen fibril orientation (based on birefringence) for human foreskin fibroblasts cultured in a collagen gel, by using gels of varying orientation resulting from different magnetic field strengths and temperatures during fibrillogenesis, and by using sufficiently low cell concentrations and early observation times.

Birefringence↗

Cell surface CD44-related chondroitin sulfate proteoglycan is required for transforming growth factor-beta-stimulated mouse melanoma cell motility and invasive behavior on type I collagen.

Tumor cell metastasis involves a complex series of events, including the adhesion, migration and invasive behavior of tumor cells on components of the extracellular matrix. Multiple cell surface receptors mediate interactions with the surrounding extracellular matrix and thereby influence cell adhesion, motility and invasion. We have previously described a cell surface CD44-related chondroitin sulfate proteoglycan on highly metastatic melanoma cells. CD44-chondroitin sulfate proteoglycan was shown to be important in melanoma cell motility and invasive behavior on type I collagen matrices. In our current studies, the role of cell surface CD44-chondroitin sulfate proteoglycan in collagen-mediated mouse melanoma cell migration and invasive behavior is further evaluated using transforming growth factor-beta 1. We report that transforming growth factor-beta 1 stimulates the migratory and invasive behavior of mouse melanoma cells on type I collagen. Transforming growth factor-beta 1 stimulated cell surface CD44-chondroitin sulfate proteoglycan synthesis in mouse melanoma cells, specifically through an upregulation of chondroitin sulfate production, while the expression of CD44-chondroitin sulfate proteoglycan core protein was not affected. Furthermore, transforming growth factor-beta 1-mediated enhancement of cell polarity, migration and invasive behavior on type I collagen gels was markedly inhibited in the presence of beta-D-xyloside, an agent that blocks chondroitin sulfate addition to the core protein. Collectively, our findings indicate that mouse melanoma cell surface CD44-chondroitin sulfate proteoglycan is required for transforming growth factor-beta 1-enhanced cell motility and invasion, and that CD44-chondroitin sulfate proteoglycan may play a role in forming and/or maintaining a dominant leading lamella, which is required for efficient locomotion.

Aggrecans↗

Continuum model of fibroblast-driven wound contraction: inflammation-mediation.

We propose a mathematical model to aid the understanding of how events in wound healing are orchestrated to result in wound contraction. Ultimately, a validated model could provide a predictive means for enhancing or mitigating contraction as is appropriate for managing a particular wound. The complex nature of wound healing and the lack of a modeling framework which can account for both the relevant cell biology and biomechanics are major reasons for the absence of models to date. Here we adapt a model originally proposed by Murray and co-workers to show how cell traction forces can result in spatial patterns of cell aggregates since it offers a framework for understanding how traction exerted by wound fibroblasts drives wound contraction. Since it is a continuum model based on conservation laws which reflect assumed cell and tissue properties, it is readily extended to account for emerging understanding of the cell biology of wound healing and its relationship to inflammation. We consider various sets of assumed properties, based on current knowledge, within a base model of dermal wound healing and compare predictions of the rate and extent of wound contraction to published experimental results.

Extracellular Matrix↗

Tissue engineering science: consequences of cell traction force.

Blood and tissue cells mechanically interact with soft tissues and tissue-equivalent reconstituted collagen gels in a variety of situations relevant to biomedicine and biotechnology. A key phenomenon in these interactions is the exertion of traction force by cells on local collagen fibers which typically constitute the solid network of these tissues and gels and impart gross mechanical integrity. Two important consequences of cells exerting traction on such collagen networks are first, when the cells co-ordinate their traction, resulting in cell migration, and second, when their traction is sufficient to deform the network. Such cell-collagen network interactions are coupled in a number of ways. Network deformation, for example, can result in net alignment of collagen fibers, eliciting contact guidance, wherein cells move with bidirectional bias along an axis of fiber alignment, potentially leading to a nonuniform cell distribution. This may govern cell accumulation in wounds and be exploited to control cell infiltration of bioartificial tissues and organs. Another consequence of cell traction is the resultant stress and strain in the network which modulate cell protein and DNA synthesis and differentiation. We summarize, here, relevant mathematical theories which we have used to describe the inherent coupling of cell dynamics and tissue mechanics in cell-populated collagen gels via traction. The development of appropriate models based on these theories, in an effort to understand how events in wound healing govern the rate and extent of wound contraction, and to measure cell traction forces in vitro, are described. Relevant observations and speculation from cell biology and medicine that motivate or serve to critique the assumptions made in the theories and models are also summarized.

Biomechanical Phenomena↗

Chemotactic movement of single cells.

Two central features of polymorphonuclear neutrophil leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, neutrophils exhibit a persistent random walk, with a characteristic directional persistence time between significant changes in direction. In attractant 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 attractant requires that both persistence and bias be explained within a unifying framework. We offer the hypothesis that "noise" in the cellular chemical signal detection/response process can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell chemosensory movement based on kinetic fluctuations in attractant-receptor binding. This model is capable of simulating cell paths observed experimentally in uniform concentrations as well as concentration gradients. It also quantitatively predicts both persistence time in uniform attractant concentrations and orientation bias in gradients, and the predictions compare favorably to data for neutrophils responding to chemotactic peptide. Further, the model analysis elucidates how persistence time and orientation bias depend on the model parameters associated with receptor binding, receptor signal transduction, and the cell turning response. 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.

Animals↗

Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay.

Clinical and scientific investigations of leukocyte chemotaxis will be greatly aided by an ability to measure quantitative parameters characterizing the intrinsic random motility, chemokinetic, and chemotactic properties of cell populations responding to a given attractant. Quantities typically used at present, such as leading front distances, migrating cell numbers, etc., are unsatisfactory in this regard because their values are affected by many aspects of the assay system unrelated to cell behavioral properties. In this paper we demonstrate the measurement of cell migration parameters that do, in fact, characterize the intrinsic cell chemosensory movement responses using cell density profiles obtained in the linear under-agarose assay. These parameters are the random motility coefficient, mu, and the chemotaxis coefficient, chi, which appear in a theoretical expression for cell population migration. We propose a priori the dependence of chi on attractant concentration, based on an independent experimental correlation of individual cell orientation bias in an attractant gradient with a spatial difference in receptor occupancy. Our under-agarose population migration results are consistent with this proposition, allowing chemotaxis to be reliably characterized by a chemotactic sensitivity constant, chi 0, to which chi is directly proportional. Further, chi 0 has fundamental significance; it represents the reciprocal of the difference in number of bound receptors across cell dimensions required for directional orientation bias. In particular, for the system of human peripheral blood polymorphonuclear neutrophil leukocytes responding to FNLLP, we find that the chemotaxis coefficient is a function of attractant concentration, a following the expression: chi = chi 0NT0 f(a) S(a) Kd/(Kd + a)2 where Kd is the FNLLP-receptor equilibrium dissociation constant and NT0 is the total number of cell surface receptors for FNLLP. f(a) is the fraction of surface receptors remaining after down-regulation, and S(a) is the cell movement speed, both known functions of FNLLP concentration. We find that chi 0NT0 = 0.2 cm; according to a theoretical argument outlined in the Appendix this means that these cells exhibit 75% orientation toward higher attractant concentration when the absolute spatial difference in bound receptors is 0.0025NT0 over 10 micron. (For example, if NT0 = 50,000 this would correspond to a spatial difference of 125 bound receptors over 10 micron.) This result can be compared with estimates obtained from visual studies of individual neutrophils.

Cell Movement↗