Leukocyte biophysics

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.     

Baseline mechanical characterization of J774 macrophages

Macrophage cell lines like J774 cells are ideal model systems for establishing the biophysical foundations of autonomous deformation and motility of immune cells. To aid comparative studies on these and other types of motile cells, we report measurements of the cortical tension and cytoplasmic viscosity of J774 macrophages using micropipette aspiration. Passive J774 cells cultured in suspension exhibited a cortical resting tension of ∼0.14 mN/m and a viscosity (at room temperature) of 0.93 kPa·s. Both values are about one order of magnitude higher than the respective values obtained for human neutrophils, lending support to the hypothesis that a tight balance between cortical tension and cytoplasmic viscosity is a physical prerequisite for eukaryotic cell motility. The relatively large stiffness of passive J774 cells contrasts with their capacity for a more than fivefold increase in apparent surface area during active deformation in phagocytosis. Scanning electron micrographs show how microscopic membrane wrinkles are smoothed out and recruited into the apparent surface area during phagocytosis of large targets.     

Kinematics of cytoplasmic deformation in neutrophils during active motion

A procedure is proposed to measure the cytoplasmic deformation in active motile neutrophils in the form of cytoplasmic strains and strain rates. Three neighboring microspheres in a local region of the cytoplasm serve as markers for local motion. Their positions are tracked by means of a high resolution light microscope and serve to compute nonlinear measures of strains and strain rates together with the principal strains and principal directions. Active neutrophils exhibit large cytoplasmic strains both during periodic pseudopod projections and during continuous locomotion in a polarized shape. The cytoplasmic motion is often synchronized with the whole cell deformation. The local cytoplasmic strains exceed the strains estimated for the whole cell and are not reversible except in some cases of single pseudopod projections. Large strains are observed both in attached and freely suspended cells. Strain rates are relatively constant but show an increase during the pseudopod retraction phase. Local cytoplasmic strains in neutrophils are inhomogeneous and reach large values during passage of the contraction rings. Neutrophils rendered passive by treatment with cytochalasin or EDTA show a random motion of microspheres with much smaller displacements. These observations suggest that the cytoplasm of active neutrophil exhibits large cytoplasmic strains and strain rates in the absence of an external stress resulting in a high degree of intracellular mixing. The proposed technique may be applied to a wide range of problems in cell biology.     

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.     

Leukocyte deformability: finite element modeling of large viscoelastic deformation.

An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.     

A sensitive measure of surface stress in the resting neutrophil.

The simplest parameterized model of the "passive" or "resting receptive" neutrophil views the cell as being composed of an outer cortex surrounding an essentially liquid-like highly viscous cytoplasm. This cortex has been measured to maintain a small persistent tension of approximately 0.035 dyn/cm (Evans and Yeung. 1989. Biophys. J. 56:151-160) and is responsible for recovering the spherical shape of the cell after large deformation. The origin of the cortical tension is at present unknown, but speculations are that it may be an active process related to the sensitivity of a given cell to external stimulation and the "passive-active" transition. In order to characterize further this feature of the neutrophil we have used a new micropipet manipulation method to give a sensitive measure of the surface stress as a function of the surface area dilation of the highly ruffled cellular membrane. In the experiment, a single cell is driven down a tapered pipet in a series equilibrium deformation positions. Each equilibrium position represents a balance between the stress in the membrane and the pressure drop across the cell. For most cells that seemed to be "passive," as judged by their spherical appearance and lack of pseudopod activity, area dilations of approximately 30% were accompanied by only a small increase in the membrane tension, indicative of a very small apparent elastic area expansion modulus (approximately 0.04 dyn/cm). Extrapolations back to zero area dilation gave a value for the tension in the resting membrane of 0.024 +/- 0.003 dyn/cm, in close agreement with earlier measures.(ABSTRACT TRUNCATED AT 250 WORDS)     

Viscoelastic response of fibroblasts to tension transmitted through adherens junctions.

Cytoplasmic deformation was monitored by observing the displacements of 200-nm green fluorescent beads microinjected into the cytoplasm of Swiss 3T3 fibroblasts. We noted a novel protrusion of nonruffling cell margins that was accompanied by axial flow of beads and cytoplasmic vesicles as far as 50 microm behind the protruding plasma membrane. Fluorescent analog cytochemistry and immunofluorescence localization of F-actin, alpha-actinin, N-cadherin, and beta-catenin showed that the protruding margins of deforming cells were mechanically coupled to neighboring cells by adherens junctions. Observations suggested that protrusion resulted from passive linear deformation in response to tensile stress exerted by centripetal contraction of the neighboring cell. The time dependence of cytoplasmic strain calculated from the displacements of beads and vesicles was fit quantitatively by a Kelvin-Voight model for a viscoelastic solid with a mean limiting strain of 0.58 and a mean strain rate of 4.3 x 10(-3) s(-1). In rare instances, the deforming cell and its neighbor spontaneously became uncoupled, and recoil of the protruding margin was observed. The time dependence of strain during recoil also fit a Kelvin-Voight model with similar parameters, suggesting that the kinetics of deformation primarily reflect the mechanical properties of the deformed cell rather than the contractile properties of its neighbor. The existence of mechanical coupling between adjacent fibroblasts through adherens junctions and the viscoelastic responses of cells to tension transmitted directly from cell to cell are factors that must be taken into account to fully understand the role of fibroblasts in such biological processes as wound closure and extracellular matrix remodeling during tissue development.     

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

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

Leukocyte relaxation properties.

Study of the mechanical properties of leukocytes is useful to understand their passage through narrow capillaries and interaction with other cells. Leukocytes are known to be viscoelastic and their properties have been established by micropipette aspiration techniques. Here, the recovery of leukocytes to their normal spherical form is studied after prolonged deformation in a pipette which is large enough to permit complete entry of the leukocyte. The recovery history is characterized by the time history of the major diameter (d1) and minor diameter (d2). When the cell is removed from the pipette, it shows initially a small rapid recoil followed by a slower asymptotic recovery to the spherical shape. In the presence of cell activation and formation of pseudopods, the time history for recovery is prolonged compared with passive cell recovery. If a protopod pre-existed during the holding period, the recovery only begins when the protopod starts to retract.     

Split Na+-Ca2+ exchangers. Implications for function and expression

The Na(+)-Ca(2+) exchanger has nine transmembrane segments, with a large cytoplasmic loop between the fifth and sixth transmembrane segments. The protein was split within the cytoplasmic loop into two domains consisting of the first five transmembrane segments and the last four transmembrane segments, respectively. The two domains were either expressed individually or coexpressed. Each of the two domains with different lengths of the cytoplasmic loop was fused to green fluorescent protein. We show that coexpression of both domains is required for proper membrane targeting and for expression of functional exchange activity. Fusion to green fluorescent protein does not alter biophysical properties of the exchange process. In addition, truncation of a large portion of the cytoplasmic loop does not alter important properties of the exchanger such as Na(+)-dependent inactivation, activation by chymotrypsin, or exchanger inhibitory peptide (XIP) sensitivity.     

Membrane and cytoplasmic resistivity properties of normal and sickle red blood cells

The cytoplasmic resistivities and membrane breakdown potentials of normal (AA), sickle-cell-trait (AS), as sickle (SS) red blood cells have been measured by the biophysical methodology of resistive pulse spectroscopy over a range of osmolalities. At isotonicity, the average membrane breakdown potentials are virtually identical for the three types of cells occurring at about 1150 V/cm. Average isotonic cytoplasmic resistivities are somewhat higher for the SS cells (166.7 +/- 7.49 ohm-cm) compared to the AA (147.6 +/- 1.98 ohm-cm) or AS cells (148.7 +/- 1.79 ohm-cm). As medium osmolality is varied, the differences in resistive properties become enlarged, especially at very low and very high osmolalities. At high osmolalities, both types of sickle cells show a large increase in internal resistivity compared to the normals; at low osmolality, the SS samples exhibit a distinctly different membrane breakdown characteristic, decreasing in this parameter, whereas the other two groups increase. Of the 15 SS samples tested, three displayed much higher cytoplasmic resistivities at isotonicity: 218.2 +/- 5.25 ohm-cm, compared to an average of 153.5 +/- 3.46 ohm-cm for the other 12. The relationship between these high resistivities and the subfraction of irreversibly sickled cells in the sample is discussed.     

Membrane and cytoplasmic resistivity properties of normal and sickle red blood cells

The cytoplasmic resistivities and membrane breakdown potentials of normal (AA), sickle-cell-trait (AS), and sickle (SS) red blood cells have been measured by the biophysical methodology of resistive pulse spectroscopy over a range of osmolalities. At isotonicity, the average membrane breakdown potentials are virtually identical for the three types of cells occurring at about 1150 V/cm. Average isotonic cytoplasmic resistivities are somewhat higher for the SS cells (166.7±7.49 ohm-cm) compared to the AA (147.6±1.98 ohm-cm) or AS cells (148.7±1.79 ohm-cm). As medium osmolality is varied, the differences in resistive properties become enlarged, especially at very low and very high osmolalities. At high osmolalities, both types of sickle cells show a large increase in internal resistivity compared to the normals; at low osmolality, the SS samples exhibit a distinctly different membrane breakdown characteristic, decreasing in this parameter, whereas the other two groups increase. Of the 15 SS samples tested, three displayed much higher cytoplasmic resistivities at isotonicity: 218.2±5.25 ohm-cm, compared to an average of 153.5±3.46 ohm-cm for the other 12. The relationship between these high resistivities and the subfraction of irreversibly sickled cells in the sample is discussed.     

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.     

Cable theory in neurons with active,linearized membranes

This investigation aims at exploring some of the functional consequences of single neurons containing active, voltage dependent channels for information processing. Assuming that the voltage change in the dendritic tree of these neurons does not exceed a few millivolts, it is possible to linearize the non-linear channel conductance. The membrane can then be described in terms of resistances, capacitances and inductances, as for instance in the small-signal analysis of the squid giant axon. Depending on the channel kinetics and the associated ionic battery the linearization yields two basic types of membrane: a membrane modeled by a collection of resistances and capacitances and membranes containing in addition to these components inductances. Under certain specified conditions the latter type of membrane gives rise to a membrane impedance that displays a prominent maximum at some nonzero resonant frequency f _max. We call this type of membrane quasi-active, setting it apart from the usual passive membrane. We study the linearized behaviour of active channels giving rise to quasi-active membranes in extended neuronal structures and consider several instances where such membranes may subserve neuronal function: 1. The resonant frequency of a quasi-active membrane increases with increasing density of active channels. This might be one of the biophysical mechanisms generating the large range over which hair cells in the vertebrate cochlea display frequency tuning. 2. The voltage recorded from a cable with a quasi-active membrane can be proportional to the temporal derivative of the injected current. 3. We modeled a highly branched dendritic tree (-ganglion cell of the cat retina) using a quasi-active membrane. The voltage attenuation from a given synaptic site to the soma decreases with increasing frequency up to the resonant frequency, in sharp contrast to the behaviour of passive membranes. This might be the underlying biophysical mechanism of receptive fields whose dimensions are large for rapid signals but contract to a smaller area for slow signals as suggested by Detwiler et al. (1978).     

Secretion-defective mutations in the signal sequence for Saccharomyces cerevisiae invertase.

Nine mutations in the signal sequence region of the gene specifying the secreted Saccharomyces cerevisiae enzyme invertase were constructed in vitro. The consequences of these mutations were studied after returning the mutated genes to yeast cells. Short deletions and two extensive substitution mutations allowed normal expression and secretion of invertase. Other substitution mutations and longer deletions blocked the formation of extracellular invertase. Yeast cells carrying this second class of mutant gene expressed novel active internal forms of invertase that exhibited the following properties. The new internal proteins had the mobilities in denaturing gels expected of invertase polypeptides that had retained a defective signal sequence and were otherwise unmodified. The large increase in molecular weight characteristic of glycosylation was not seen. On nondenaturing gels the mutant enzymes were found as heterodimers with a normal form of invertase that is known to be cytoplasmic, showing that the mutant forms of the enzyme are assembled in the same compartment as the cytoplasmic enzyme. All of the mutant enzymes were soluble and not associated with the membrane components after fractionation of crude cell extracts on sucrose gradients. Therefore, these signal sequence mutations result in the production of active internal invertase that has lost the ability to enter the secretory pathway. This demonstrates that the signal sequence is required for the earliest steps in membrane translocation.     

Evidence for more than one Ca2+ transport mechanism in mitochondria.

The active transport and internal binding of the Ca2+ analogue Mn2+ by rat liver mitochondria were monitored with electron paramagnetic resonance. The binding of transported Mn2+ depended strongly on internal pH over the range 7.7-8.9. Gradients of free Mn2+ were compared with K+ gradients measured on valinomycin-treated samples. In the steady state, the electrochemical Mn2+ activity was larger outside than inside the mitochondria. The observed gradients of free Mn2+ and of H+ could not be explained by a single "passive" uniport or antiport mechanism of divalent cation transport. This conclusion was further substantiated by observed changes in steady-state Ca2+ and Mn2+ distributions induced by La3+ and ruthenium red. Ruthenium red reduced total Ca2+ or Mn2+ uptake, and both inhibitors caused release of divalent cation from preloaded mitochondria. A model is proposed in which divalent cations are transported by at least two mechanisms: (1) a passive uniport and (2) and active pump, cation antiport or anion symport. The former is more sensitive to La3+ and ruthenium red. Under energized steady-state conditions, the net flux of Ca2+ or Mn2+ is inward over (1) and outward over (2). The need for more than one transport system inregulating cytoplasmic Ca2+ is discussed.     

Aspiration of THP1 into a micropipette. Mechanical deformation of monocytic THP-1 cells: occurrence of two sequential phases with differential sensitivity to metabolic inhibitors

Blood leukocytes can exhibit extensive morphological changes during their passage through small capillary vessels. The human monocytic THP-1 cell line was used to explore the metabolic dependence of these changes in shape. Cells were aspirated into micropipettes for determination of the rate of protrusion formation. They were then released and the kinetics of morphological recovery was studied. Results were consistent with Evans’ model (Blood 64:1028, 1984) of a viscous liquid droplet surrounded by a tensile membrane. The estimated values of cytoplasmic viscosity and membrane tension were 162 Pa.s and 0.0142 mN/m respectively. The influence of metabolic inhibitors on cell mechanical behavior was then studied: results strongly suggested that deformation involved two sequential phases. The cell elongation rate measured during the first 30 s following the onset of aspiration was unaffected by azide, an inhibitor of energy production, and it was about doubled by cytochalasin D, a microfilament inhibitor, and colchicine, a microtubule inhibitor. However, during the following 2 min, deformation was almost abolished in cells treated with azide and cytochalasin D, whereas the protrusion of control cells exhibited an approximately threefold increase in length. It is concluded that, although cells seemed to deform as passive objects, active metabolic processes were required to allow extensive morphological changes triggered by external forces.     

A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus.

The constitutive law of the material comprising any structure is essential for mechanical analysis since this law enables calculation of the stresses from the deformations and vice versa. To date, there is no constitutive law for actively contracting myocardial tissue. Using 2,3-butanedione monoxime to protect the myocardium from mechanical trauma, we subjected thin midwall slices of rabbit myocardium to multiaxial stretching first in the passive state and then during steady-state barium contracture or during tetani in ryanodine-loaded tissue. Assuming transverse isotropy in both the passive and active conditions, we used our previously described methods (Humphrey et al., 1990a) to obtain both passive and active constitutive laws. The major results of this study are: (1) This is the first multiaxial constitutive law for actively contracting mammalian myocardium. (2) The functional forms of the constitutive law for barium contracture and ryanodine-induced tetani are the same but differ from those in the passive state. Hence, one cannot simply substitute differing values for the coefficients of the passive law to describe the active tissue properties. (3) There are significant stresses developed in the cross-fiber direction (more than 40 percent of those in the fiber direction) that cannot be attributed to either deformation effects or nonparallel muscle fibers. These results provide the foundation for future mechanical analyses of the heart.     

Stability properties of elementary dynamic models of membrane transport

Living cells are characterized by their capacity to maintain a stable steady state. For instance, cells are able to conserve their volume, internal ionic composition and electrical potential difference across the plasma membrane within values compatible with the overall cell functions. The dynamics of these cellular variables is described by complex integrated models of membrane transport. Some clues for the understanding of the processes involved in global cellular homeostasis may be obtained by the study of the local stability properties of some partial cellular processes. As an example of this approach, I perform, in this study, the neighborhood stability analysis of some elementary integrated models of membrane transport. In essence, the models describe the rate of change of the intracellular concentration of a ligand subject to active and passive transport across the plasma membrane of an ideal cell. The ligand can be ionic or nonionic, and it can affect the cell volume or the plasma membrane potential. The fundamental finding of this study is that, within the physiological range, the steady states are asymptotically stable. This basic property is a necessary consequence of the general forms of the expressions employed to describe the active and passive fluxes of the transported ligand.     

Neuronal Spike Initiation Modulated by Extracellular Electric Fields

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.