One-dimensional steady continuum model of retraction of pseudopod in leukocytes

Fluid shear stress-mediated mechanotransduction in circulating leukocytes and its defect in microvascular dysfunction

Leukocytes (neutrophils, monocytes) in the active circulation exhibit multiple phenotypic indicators for a low level of cellular activity, like lack of pseudopods and minimal amounts of activated, cell-adhesive integrins on their surfaces. In contrast, before these cells enter the circulation in the bone marrow or when they recross the endothelium into extravascular tissues of peripheral organs they are fully activated. We review here a multifaceted mechanism mediated by fluid shear stress that can serve to deactivate leukocytes in the circulation. The fluid shear stress controls pseudopod formation via the FPR receptor, the same receptor responsible for pseudopod projection by localized actin polymerization. The bioactivity of macromolecular factors in the blood plasma that interfere with receptor stimulation by fluid flow, such as proteolytic cleavage in the extracellular domain of the receptor or the membrane actions of cholesterol, leads to a defective ability to respond to fluid shear stress by actin depolymerization. The cell reaction to fluid shear involves CD18 integrins, nitric oxide, cGMP and Rho GTPases, is attenuated in the presence of inflammatory mediators and modified by glucocorticoids. The mechanism is abolished in disease models (genetic hypertension and hypercholesterolemia) leading to an increased number of activated leukocytes in the circulation with enhanced microvascular resistance and cell entrapment. In addition to their role in binding to biochemical agonists/antagonists, membrane receptors appear to play a second role: to monitor local fluid shear stress levels. The fluid shear stress control of many circulating cell types such as lymphocytes, stem cells, tumor cells remains to be elucidated.

Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry

Cell motility plays an essential role in many biological systems, but precise quantitative knowledge of the biophysical processes involved in cell migration is limited. Better measurements are needed to ultimately build models with predictive capabilities. We present an improved force cytometry method and apply it to the analysis of the dynamics of the chemotactic migration of the amoeboid form of Dictyostelium discoideum. Our explicit calculation of the force field takes into account the finite thickness of the elastic substrate and improves the accuracy and resolution compared with previous methods. This approach enables us to quantitatively study the differences in the mechanics of the migration of wild-type (WT) and mutant cell lines. The time evolution of the strain energy exerted by the migrating cells on their substrate is quasi-periodic and can be used as a simple indicator of the stages of the cell motility cycle. We have found that the mean velocity of migration v and the period of the strain energy T cycle are related through a hyperbolic law v = L/T, where L is a constant step length that remains unchanged in mutants with adhesion or contraction defects. Furthermore, when cells adhere to the substrate, they exert opposing pole forces that are orders of magnitude higher than required to overcome the resistance from their environment.

A dedication in memoriam of Dr. Richard Skalak

Richard Skalak (1923-1997) played a leadership role in the formative decades of the discipline of biomedical engineering through his technical contributions in biomechanics, his educational influence on students, and his service to many developing societies and journals. But always, the distinguishing marks of his involvement with any activity or person were his generosity, respect and tolerance for others, integrity, and curiosity. These very qualities are what first brought him as a traditional engineering trained in engineering mechanics into the young field of biomedical engineering in the 1960s, and they are what led him to new approaches to cellular and molecular engineering, tissue engineering, and orthopedic biomechanics. His technical papers and lectures on blood cell mechanics, pulmonary circulation, dental implants, and tissue growth were models of clarity and often pointed the way to new areas of exploration, while his personal writings offer advice on life, academic organizations, and the pursuit of significant work. He would be deeply appreciative that this first volume of the Annual Review of Biomedical Engineering is dedicated to his memory.

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.

Mechanical properties of cytoskeletal polymers

The mechanical properties of cytoplasm are dominated by microfilaments, microtubules, and intermediate filaments, collectively termed the cytoskeleton. This review discusses how the physical properties of these biopolymer systems are related to their molecular structures and interactions, and how remodelling of these biopolymers in vivo affects cell shape and motility.

Leukocyte biophysics. An invited review

The biophysical properties of leukocytes in the passive and active state are discussed. In the passive unstressed state, leukocytes are spherical with numerous membrane folds. Passive leukocytes exhibit viscoelastic properties, and the stress is carried largely by the cell cytoplasm and the nucleus. The membrane is highly deformable in shearing and bending, but resists area expansion. Membrane tension can usually be neglected but plays a role in cases of large deformation when the membrane becomes unfolded. The constant membrane area constraint is a determinant of phagocytic capacity, spreading of cells, and passage through narrow pores. In the active state, leukocytes undergo large internal cytoplasmic deformation, pseudopod projection, and granule redistribution. Several different measurements for assessment of biophysical properties and the internal cytoplasmic deformation in form of strain and strain rate tensors are presented. The current theoretical models for active cytoplasmic motion in leukocytes are discussed in terms of specific macromolecular reactions.

Cytoplasmic strains and strain rates in motile polymorphonuclear leukocytes

A new method is presented to measure local cytoplasmic deformation and rate of deformation in motile active neutrophils. The deformation is expressed in terms of biomechanical strains and strain rates. For this purpose small phagocytosed latex microspheres were used as intracellular markers. Planar Lagrangian and Eulerian strains and the rate of strain were estimated from the positions of a triad of internalized markers. Principal strains, stretch ratios, and principal directions were computed. The intracellular strains were found to be large relative to the overall cell shape change. Principal cytoplasmic stretch ratios showed large extension in the direction of pseudopod formation and cell locomotion and contraction in perpendicular directions. Regional strain analysis showed contractile strains to predominate in the vicinity of the pseudopod or leading edge of motion. The transitional region between the pseudopod and the main cell body exhibited large shear strains. The posterior region, where the uropod is located, also revealed large extensions but small contractile strains. The rate of strains are relatively small, nonuniform in time, and largely independent of the strain. The method we propose to measure cytoplasmic strain can be applied to a variety of problems in cell mechanics.