Modeling of the knee joint load in rehabilitative knee extension exercises under water

A biomechanical and hydrodynamic theoretical model has been developed in order to calculate the knee joint load during underwater knee extension exercises. The hydrodynamic force has been evaluated within the framework of a strip-theory approach, when a blunt rectangular resistive device is applied proximally to the shank to increase its frontal area. Analytical expressions of the patellar tendon force (F(PT)), the axial (phi(n)) and the shear (phi(t)) component of the tibiofemoral joint load have been derived as a function of joint angle (theta), angular velocity (theta ), angular acceleration (theta ), resistive device density, length (L(x)), width (L(z)) and thickness, and average hydrodynamic drag and added mass coefficients. An inverse dynamic problem has been solved, assuming for theta and theta a dependence on theta consistent with the experimental kinematic data available in the literature. The results highlight that the characteristics of the resistive device and the level of muscular activation can be adjusted reciprocally in order to control the peak value of F(PT), phi(n) and phi(t), and the position of these peaks within the joint range of motion (ROM). No anterior cruciate ligament (ACL) stress is observed (phi(t)>0) over the whole ROM, independent of the level of muscular activation, for a light resistive device with L(x) < or = 0.3 m and L(z) < or = 0.4 m. This work highlights that aquatic exercises can be usefully and safely implemented in the rehabilitation program following ACL surgery, and whenever it is important to avoid excessive shear joint forces that constrain the tibial plateau anterior translation with respect to the femur.     

Distributions of Potential in Cylindrical Coordinates and Time Constants for a Membrane Cylinder

A mathematical problem relating to membrane cylinders is stated and solved; its implications are illustrated and discussed. The problem concerns the volume distribution, in cylindrical coordinates, of the electric potential inside and outside a membrane cylinder of finite length (with sealed ends), during passive decay of an initially nonuniform membrane potential. The time constants for equalization with respect to the angle, theta, are shown to be typically about ten thousand times smaller than the time constant, tau(m) = R(m)C(m), for uniform passive membrane potential decay. The time constants for equalization with respect to length are shown to agree with those from one-dimensional cable theory; typically, they are smaller than tau(m) by a factor between 2 and 10. The relation of the membrane current density, I(m)(theta, x, t), to the values (at the outer membrane surface) of the extracellular potential phi(e)(r, theta, x, t) and of partial differential(2)phi(e)/ partial differentialx(2), is examined and it is shown that these quantities are not proportional to each other, in general; however, under certain specified conditions, all three of these quantities are proportional with each other and with phi(i)(r, theta, x, t) and partial differential(2)phi(i)/ partial differentialx(2) (at the inner membrane surface). The relation of these results to those of one-dimensional cable theory is discussed.     

Biomimetic apatite coatings--carbonate substitution and preferred growth orientation

Biomimetic apatite coatings were obtained by soaking chemically treated titanium in SBF with different HCO(3)(-) concentration. XRD, FTIR and Raman analyses were used to characterize phase composition and degree of carbonate substitution. The microstructure, elemental composition and preferred alignment of biomimetically precipitated crystallites were characterized by cross-sectional TEM analyses. According to XRD, the phase composition of precipitated coatings on chemically pre-treated titanium after exposure to SBF was identified as hydroxy carbonated apatite (HCA). A preferred c-axis orientation of the deposited crystals can be supposed due to the high relative peak intensities of the (002) diffraction line at 2theta=26 degrees compared to the 100% intensity peak of the (211) plane at 2theta=32 degrees . The crystallite size in direction of the c-axis of HCA decreased from 26 nm in SBF5 with a HCO(3)(-) concentration of 5 mmol/l to 19 nm in SBF27 with a HCO(3)(-) concentration of 27 mmol/l. Cross-sectional TEM analyses revealed that all distances correspond exactly to the hexagonal structure of hydroxyapatite. The HCO(3)(-) content in SBF also influences the composition of precipitated calcium phosphates. Biomimetic apatites were shown to have a general formula of Ca(10-x-y)Mg(y)(HPO(4))(x-z)(CO(3))(z)(PO(4))(6-x)(OH)(2-x-w)(CO(3))(w/2). According to FTIR and Raman analyses, it can be supposed that as long as the HCO(3)(-) concentration in the testing solutions is below 20 mmol/l, only B-type HCA (0相似文献   

Polymerization of rod-like macromolecular monomers studied by stopped-flow, multiangle light scattering: set-up, data processing, and application to fibrin formation

Many biological supramolecular structures are formed by polymerization of macromolecular monomers. Light scattering techniques can provide structural information from such systems, if suitable procedures are used to collect the data and then to extract the relevant parameters. We present an experimental set-up in which a commercial multiangle laser light scattering photometer is linked to a stopped-flow mixer, allowing, in principle, the time-resolved extrapolation of the weight-average molecular weight M(w) and of the z-average square radius of gyration (z) of the polymers from Zimm-like plots. However, if elongated structures are formed as the polymerization proceeds, curved plots rapidly arise, from which M(w) and (z) cannot be recovered by linear fitting. To verify the correctness of a polynomial fitting procedure, polydisperse collections of rod-like or worm-like particles of different lengths, generated at various stages during bifunctional polycondensations of rod-like macromolecular monomers, were considered. Then, the angular dependence of their time-averaged scattered intensity was calculated in the Rayleigh-Gans-Debye approximation, with random and systematic noise also added to the data. For relatively narrow size distributions, a third-degree polynomial fitting gave satisfactory results across a broad range of conversion degrees, yielding M(w) and (z) values within 2% and no greater than 10-20%, respectively, of the calculated values. When more broad size distributions were analyzed, the procedure still performed well for semiflexible polymers, but started to seriously underestimate both M(w) and (z) when rigid rod-like particles were analyzed, even at relatively low conversion degrees. The data were also analyzed in the framework of the Casassa approximation, from which the mass per unit length of the polymers can be derived. These procedures were applied to a set of data taken on the early stages of the thrombin-catalyzed polymerization of fibrinogen, a rod-like macromolecule approximately 50 nm long. The polymers, grown in the absence of Ca(2+) by rate-limiting amounts of thrombin, appeared to be characterized by a much broader size distribution than the one expected for a classical Flory bifunctional polycondensation, and they seem to behave as relatively flexible worm-like double-stranded chains. Evidence for the formation of fibrinogen-fibrin monomer complexes is also inferred from the time dependence of the mass/length ratio. However, our data are also compatible with the presence of limited amounts of single-stranded structures in the very early stages, either as a secondary, less populated pathway, or as transient intermediates to the classical double-stranded fibrils.     

Anticipatory Modulation of Digit Placement for Grasp Control Is Affected by Parkinson's Disease

Background

Successful object manipulation relies on the ability to form and retrieve sensorimotor memories of digit forces and positions used in previous object lifts. Past studies of patients affected by Parkinson''s disease (PD) have revealed that the basal ganglia play a crucial role in the acquisition and/or retrieval of sensorimotor memories for grasp control. Whereas it is known that PD impairs anticipatory control of digit forces during grasp, learning deficits associated with the planning of digit placement have yet to be explored. This question is motivated by recent work in healthy subjects revealing that anticipatory control of digit placement plays a crucial role for successful manipulation.

Methodology/Principal Findings

We asked ten PD patients off medication and ten age-matched controls to reach, grasp and lift an object whose center of mass (CM) was on the left, right or center. The only task requirement was to minimize object roll during lift. The CM remained the same across consecutive trials (blocked condition) or was altered from trial to trial (random condition). We hypothesized that impairment of the basal ganglia-thalamo-cortical circuits in PD patients would reduce their ability to anticipate digit placement appropriate to the CM location. Consequently, we predicted that PD patients would exhibit similar digit placement in the blocked vs. random conditions and produce larger peak object rolls than that of control subjects. In the blocked condition, PD patients exhibited significantly weaker modulation of fingertip contact points to CM location and larger object roll than controls (p<0.05 and p<0.01, respectively). Nevertheless, both controls and PD patients minimized object roll more in the blocked than in the random condition (p<0.01).

Conclusions/Significance

Our findings indicate that, even though PD patients may have a residual ability of anticipatory control of digit contact points and forces, they fail to implement a motor plan with the same degree of effectiveness as controls. We conclude that intact basal ganglia-thalamo-cortical circuits are necessary for successful sensorimotor learning of both grasp kinematics and kinetics required for dexterous hand-object interactions.     

Conformation transition in silk protein films monitored by time-resolved Fourier transform infrared spectroscopy: effect of potassium ions on Nephila spidroin films

We used time-resolved Fourier transform infrared spectroscopy (FTIR) to follow a conformation transition in Nephila spidroin film from random coil and/or helical structures to beta-sheet induced by the addition of KCl from 0.01 to 1.0 mol/L in D(2)O. Time series difference spectra showed parallel increases in absorption at 1620 and 1691 cm(-)(1), indicating formation of beta-sheet, together with a coincident loss of intensity of approximately 1650 cm(-)(1), indicating decrease of random coil and/or helical structures. Increase in KCl concentration produced an increased rate of the conformation transition that may attributable to weakening of hydrogen bonds within spidroin macromolecules. The conformation transition was a biphasic process with [KCl] > or = 0.3 mol/L but monophasic with [KCl] < or = 0.1 mol/L. This suggests that, at high KCl concentrations, segments of the molecular chain are adjusted first and then the whole molecule undergoes rearrangement. We discuss the possible significance of these findings to an understanding of the way that spiders spin silk.     

Effects of excluded volume and polydispersity on solution properties of lentinan in 0.1 M NaOH solution

Seven lentinan fractions of various weight-average molecular weights (M(w)), ranging from 1.45 x 10(5) to 1.13 x 10(6) g mol(-1) were investigated by static light scattering and viscometry in 0.1M NaOH solution at 25 degrees C. The intrinsic viscosity [eta] - M(w) and radius of gyration s(2)(z) (1/2) - M(w) relationships for lentinan in 0.1M NaOH solution were found to be represented by [eta] = 5.1 x 10(-3)M(w) (0.81) cm(3) g(-1) and s(2)(z) (1/2) = 2.3 x 10(-1)M(w) (0.58) nm, respectively. Focusing on the effects of the M(w) polydispersity with the Schulz-Zimm distribution function, the data of M(w), s(2)(z) (1/2), and [eta] was analyzed on the basis of the Yoshizaki-Nitta-Yamakawa theory for the unperturbed helical wormlike chain combined with the quasi-two-parameter (QTP) theory for excluded-volume effects. The persistence length, molecular weight per unit contour length, and the excluded-volume strength were determined roughly to be 6.2 nm, 980 nm(-1), and 0.1, respectively. Compared with the theoretical value calculated by the Monte Carlo model, the persistence length is longer than that of the single (1 --> 3)-beta-(D)-glucan chain. The results revealed that lentinan exists as single-stranded flexible chains in 0.1M NaOH solution with a certain degree of expansion due to the electrostatic repulsion from the interaction between the OH(-) anions and lentinan molecules.     

Valence tautomerism and macrocycle ruffling in nickel(III) porphyrins

Nonlocal density functional calculations with full geometry optimization have been carried out on the low-lying electronic states of oxidized nickel porphyrins. For [NiIII(P)(Py)2]+, the ground state corresponds to a t2g6(z2)1 configuration and the t2g6(x2-y2)1 configuration is 0.43 eV higher in energy. In contrast, the ground state of [NiIII(P)(CN)2]- corresponds to a t2g6(x2-y2)1 configuration, the t2g6(z2)1 configuration being 0.96 eV higher in energy. The results are consistent with EPR spectroscopic results on the TPP analogs of these complexes. For [Ni(P)(Py)2]+, the a2u- and a1u-type Ni(II) porphyrin cation radical states are higher in energy by 0.63 and 1.23 eV, respectively, relative to the t2g6(z2)1 Ni(III) ground state. The Ni-N(Porphyrin) distance is significantly shorter in [NiIII(P)(Py)2]+ (196 pm) than in [NiIII(P)(CN)2]- (206 pm), which is consistent with the ruffled and planar macrocycle conformations, respectively, in the two complexes.     

Preparation and characterization of two supramolecular complexes with 5-amino-2,4,6-triiodoisophthalic acid under N-donor auxiliary ligand intervention

Assemblies of 5-amino-2,4,6-triiodoisophthalic acid (H₂ATIBDC) with Cd(II) and Zn(II) in the presence of N-donor auxiliary ligand, 1,4-bis(1,2,4-triazol-1-yl)butane (btb), at ambient conditions yield two new supramolecular complexes, [Cd(ATIBDC)(btb)(H₂O)₂]·3H₂O (1), and [Zn(ATIBDC)(btb)]·2H₂O (2). Generally, these two complexes display 1D ATIBDC²⁻-bridged coordination arrays. Distinct extended 3D network architectures are further constructed with the help of weak secondary interactions especially aromatic stacking, halogen bonding, and hydrogen bonding as supramolecular driving forces. It is worthy to mention that halogen bonds (C-I?π and C-I?N/O) play important roles in the supramolecular assembly. The pentameric cluster (H₂O)₅ in 1 assembles into highly ordered helical infinite chains. Complex 2 exhibits the fascinating single-walled tube-like chain structure. It loses crystallinity rapidly in the air and leads to the formation of [Zn(ATIBDC)(btb)]·H₂O (2A). Thermal stabilities and solid state fluorescent properties of complexes 1 and 2A have been studied.     

Linkage analyses of human peptidase C (PEPC), human factor H (HF), and coagulation factor XIIIB (F13B)

Summary Linkage data on human peptidase C (PEPC), human factor H (HF), and coagulation factor XIIIB (F13B) are presented. The results confirm linkage between HF and F13B (lod=5.32 at =0.10 in males), and give strong evidence for linkage between PEPC and HF (lod=5.14 at =0.10 in males) and between PEPC and F13B (lod=3.55 at =0.10 in males). The claim that PEPA is linked with HF must be withdrawn.     

Distinctive influence of two hexafluoro solvents on the structural stabilization of Bombyx mori silk fibroin protein and its derived peptides: 13C NMR and CD studies

Employing high-resolution (13)C solution NMR and circular dichroism (CD) spectroscopic techniques, the distinctive influence of two intimately related hexafluoro solvents, 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) and hexafluoroacetone trihydrate (HFA), on the structural characteristics of Bombyx mori (B. mori) silk fibroin, the chymotrypsin precipitate (C(p)) fraction, and two synthetic peptides, (AGSGAG)(5) and (AG)(15), is described. The observed (13)C solution NMR and CD spectra of these polypeptides in HFIP and HFA revealed a distinctive influence on their conformational characteristics. The (13)C NMR spectra, as analyzed from the unique chemical shifts of C(alpha) and C(beta) resonances of constituent residues revealed that fibroin largely assumes helical conformation(s) in both solvents. However, the peak shifts were greater for the samples in HFIP, indicating that the types of helical structure(s) may be different from the one populated in HFA. Similar structural tendencies of these polypeptides were reflected in CD spectra. The observed CD patterns, i.e., a strong positive band at approximately 190 nm and negative bands at approximately 206 and 222 nm, have been attributed to the preponderance of helical structures. Of the two prevalent helical structures, alpha-helix and 3(10)-helix, the evidence emerged for the fibroin protein in favor of 3(10)-helical structure stabilization in HFIP and its significant disruption in HFA, as deduced from the characteristic R1 (=[theta](190)/[theta](202)) and R2 (=[theta](222)/[theta](206)) ratios, determined from the CD data. Conversely, the native polypeptides and synthetic peptide fragments derived from highly crystalline regions of the silk fibroin protein sustained predominantly an unordered structure in HFA solvent.     

Linkage relationships and allelic associations of the cystic fibrosis locus and four marker loci

Summary The linkage relationships between the cystic fibrosis (CF) locus and four marker loci (MET-H, MET-D, D7S8 and D7S16), allelic associations between these loci and the extent of informativity at these marker loci were investigated in a sample of 206 families with at least one child affected by CF. The data were contributed by 11 laboratories from Europe and Israel. The maximum lod scores and recombination frequency estimates ( ) (and confidence limits of ) were: 18.3 at =0.007(0.001–0.038) for CF vs. MET, 11.0 at (0.001–0.068) for CF vs. D7S8, and 5.7 at =0.0(0.0–0.064) for CF vs. D7S16. A gene order of CF-MET-D7S8 was best supported by the data, but its preference to the order D7S8-CF-MET is mainly based on one single family. There are significant allelic associations between CF, MET, D7S8 and D7S16; these allelic associations affect the risk of random individuals to be carriers of CF.     

Likely linkage: Inv with Jk

Summary In a data base consisting of 1665 pairs of loci linkage between Inv and Jk is significant . Recombination is nearly the same in the two sexes . The reason why this linkage was not noticed earlier is discussed.     

Thermally induced conformation change of succinoglycan in aqueous sodium chloride

Static and dynamic light scattering, viscosity, and optical rotation measurements have been made at eight different temperatures between 25 and 75 degrees C on two succinoglycan samples (sodium salt) with weight-average molecular weights M(w) of 7.14 x 10(5) and 3.54 x 10(5) (at 25 degrees C) in 0.01 M aqueous NaCl to investigate the thermally induced order-disorder conformation change of the polysaccharide. Additionally, viscometry and polarimetry have been performed for a sodium salt sample (M(w) = 4.55 x 10(5) at 25 degrees C) whose M(w), z-average radius of gyration (z)(1/2), and hydrodynamic radius R(H) in the aqueous salt had been determined previously. As the temperature increases, M(w), (z)(1/2), R(H), and the intrinsic viscosity for every sample sharply decrease around 55 degrees C where the specific rotation at 300 nm sigmoidally increases. In particular, M(w) at 25 degrees C (i.e., in the ordered helical state) is twice as large as that at 75 degrees C (i.e., in the disordered state). These findings substantiate that the ordered structure is composed of two chains and hence is a double helix. Data analysis shows that this helix at 25 degrees C is characterized by an unperturbed wormlike chain with a helix pitch of about 2 nm (per repeating unit) and a persistence length of about 50 nm and that upon heating, it dissociates directly (i.e., in all-or-none fashion) to disordered chains of a similar contour length but with a much smaller persistence length of about 10 nm. The temperature dependence of the light scattering second viral coefficient is discussed in relation to the association of disordered chains in the cooling process.     

Conditions under Which the Mean Fertility Is Maximized When a Population Is at a Stable Equilibrium

It is assumed that there is a population with two alleles at one locus, random mating of adults and selection only involving differential fertilities. By making use of the Kuhn-Tucker theory of optimization under constraints, conditions are derived under which stable equilibrium frequencies x, y and z of the three genotypes are the same as those that maximize the mean fertility of the population. We derive all sets of frequencies of this type for the Hadeler-Liberman symmetric fertility model and all such sets for which at least one genotype is missing for the general model. If the population has frequencies that are initially near those at which there is both a stable equilibrium and maximization of the mean fertility, then the mean fertility (t) at time t is nondecreasing with t as t -> &. It is found that it is possible for the stable equilibrium maximum points (x, y, z) to be one or two points on a ridge on which the mean fertility is maximized or the entire set of points on the ridge. Furthermore, may be smaller on this ridge than at another stable equilibrium point at which is not even locally maximized.     

Stochastic radial dose distributions and track structure theory

Measured single-event distributions of the specific energy deposited in cylindrical volumes with simulated diameters down to 150 nm for (4)He and (12)C ions with energies of 25 MeV/nucleon and (16)O ions with 21 MeV/nucleon and radial distances up to 12 microm are presented. The mean specific energy per ion , the mean specific energy per target hit z(1)(r), and the relative frequency of target hits nu(r) as a function of radial distance are evaluated and compared with the corresponding quantities of the track structure model of Kiefer and Straaten (Phys. Med. Biol. 31, 1201-1209, 1986). Though there are some discrepancies in the absolute values, the radial dependence of , z(1)(r) and v(r) for (12)C and (16)O ions is reproduced satisfactorily. The model fails to describe the data for (4)He ions. A more detailed comparison of the radial shape of the mean specific energies calculated from the experimental data from the present work and data from the literature reveals a significant projectile charge dependence which is not included in track structure models.     

Solution properties of an alpha-(1-->3)-D-glucan from Lentinus edodes and its sulfated derivatives

A water-insoluble alpha-(1-->3)-D-glucan (A) from Lentinus edodes was fractionated into 13 fractions in dimethyl sulfoxide containing 0.25 M lithium chloride (0.25 M LiCl-Me(2)SO). Five fractions were treated with sulfur trioxide-pyridine complex at 25 degrees C to synthesize water-soluble sulfated derivatives (S-A). The weight-average molecular weights, M(w), and intrinsic viscosities [eta], of the samples A and S-A were determined by multi-angler laser light scattering (MALLS), and viscosity. The M(w) dependence of [eta] and of the radius of gyration (z)(1/2), was found to be represented approximately by [eta]=4.9 x 10(-2) M(w)(0.67) (cm(3) g(-1)), and (z)(1/2)=4.8 x 10(-2) M(w)(0.54) (nm) for the alpha-glucan in 0.25 M LiCl-Me(2)SO in the M(w) range from 7.24 x 10(4) to 4.21 x 10(5), and by [eta]=6.8 x 10(-4) M(w) 1.06 (cm(3) g(-1)), and (z)(1/2)=9.4 x 10(-4) M(w)(0.92) (nm) for the sulfated alpha-glucan in aqueous 0.5 M NaCl in the M(w) range from 5.92 x 10(4) to 1.42 x 10(5) at 25 degrees C. The results indicate that the alpha-(1-->3)-D-glucan exists as a flexible chain in 0.25 M LiCl-Me(2)SO, and its sulfated derivative in 0.5 M NaCl aqueous has stiffer chains than the original. (13)C NMR indicated that intramolecular hydrogen bonding occurred in the sulfated alpha-glucan, causing the observed chain stiffness.     

Acetonitrile-induced conformational transitions in poly-l-lysine

The effect of acetonitrile on the random coil, α-helix and β-sheet conformations induced in poly-

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-lysine is studied. It is found that acetonitrile at higher concentrations transforms the backbone of polylysine from a random coil to a helical conformation. Addition of acetonitrile to polylysine (pH 11.5) in the α-helix conformation, induces conformational changes in two stages. At concentrations below 60% v/v, acetonitrile stabilizes the helical conformation and at higher concentrations (>70% v/v), it destabilizes the helix. β-sheet→α-helix→random coil conformational transitions are found to occur when polylysine in the heat-induced conformation is titrated with acetonitrile. The possible mechanism(s) of action of acetonitrile in inducing these structural transitions is discussed.     

Chain stiffness of heteropolysaccharide from Aeromonas gum in dilute solution by dynamic light scattering

Dynamic light scattering measurements have been made on 15 fractions of aeromonas (A) gum, an extracellular heteropolysaccharide produced by the strain Aeromonas nichidenii, with dimethylsulfoxide containing 0.2M lithium chloride as the solvent at 25 degrees C. Data for the translational diffusion coefficient D covering a molecular weight range from 4.5 x 10(5) to 2.1 x 10(6) and ratios of the z-average radius of gyration (z) (1/2) to the hydrodynamic radius R(H) (calculated with previous (z) data) suggest that the polymer behaves like a semiflexible chain in this solvent similar to the stiffness of cellulose derivatives. Thus the D data are analyzed on the basis of the Yamakawa-Fujii theory for the translational friction coefficient of a wormlike cylinder by coarse-graining the heteropolysaccharide molecule. Excluded-volume effects are taken into account in the quasi-two-parameter scheme, as was done previously for (z) and [eta] (the intrinsic viscosity) of A gum in the same solvent. The molecular weight dependence of R(H) is found to be explained by the perturbed wormlike chain with a persistence length of 10 nm, a linear mass density of 1350 nm(-1), an excluded-volume strength parameter of 1.3 nm, and a chain diameter of 2.8 nm. These parameters are in substantial agreement with those estimated previously from (z) and [eta] data, demonstrating that the solution properties (D, (z), and [eta]) of the heteropolysaccharide are almost quantitatively described by the current theories for wormlike chains in the molecular weight range studied.     

Dynamic contact forces on leukocyte microvilli and their penetration of the endothelial glycocalyx

We develop a theoretical model to examine the combined effect of gravity and microvillus length heterogeneity on tip contact force (F(m)(z)) during free rolling in vitro, including the initiation of L-, P-, and E-selectin tethers and the threshold behavior at low shear. F (m)(z) grows nonlinearly with shear. At shear stress of 1 dyn/cm(2), F(m)(z) is one to two orders of magnitude greater than the 0.1 pN force for gravitational settling without flow. At shear stresses > 0.2 dyn/cm(2) only the longest microvilli contact the substrate; hence at the shear threshold (0.4 dyn/cm(2) for L-selectin), only 5% of microvilli can initiate tethering interaction. The characteristic time for tip contact is surprisingly short, typically 0.1-1 ms. This model is then applied in vivo to explore the free-rolling interaction of leukocyte microvilli with endothelial glycocalyx and the necessary conditions for glycocalyx penetration to initiate cell rolling. The model predicts that for arteriolar capillaries even the longest microvilli cannot initiate rolling, except in regions of low shear or flow reversal. In postcapillary venules, where shear stress is approximately 2 dyn/cm(2), tethering interactions are highly likely, provided that there are some relatively long microvilli. Once tethering is initiated, rolling tends to ensue because F(m)(z) and contact duration will both increase substantially to facilitate glycocalyx penetration by the shorter microvilli.