Presence Of Gradient Research Articles

Rapid Quality Index (R-MaQI), based mainly on macrophyte associations, to assess the ecological status of Mediterranean transitional environments

A rapid index for the quality status assessment of Mediterranean transitional environments is proposed. It is based on the study of macrophyte associations (macroalgae and seagrasses) and the gross determination of some environmental parameters. The index was set up in 19 sampling sites of the Venice lagoon monitored during one year on a monthly basis taking into account the flora, the main contaminants and some other variables indicating the presence of gradients of stress conditions. Results were compared and intercalibrated with measurements carried out in Sacca di Goro, placed in Po delta, and in Lesina and Orbetello lagoons.

Robust, susceptibility-matched NMR probes for compensation of magnetic field imperfections in magnetic resonance imaging (MRI)

The presented paper describes a magnetic field sensor system for the real-time monitoring of magnetic resonance (MR) image encoding in the presence of gradient and main magnetic field imperfections. For this purpose, a novel simplified design for nuclear magnetic resonance (NMR) probes has been developed. The design fulfills the requirements of providing below ppm measurement accuracy in combination with long readout times. To this end, NMR is performed with a nanoliter water volume, which together with the radiofrequency (RF) solenoid coil is cast into an Epoxy holder. Based on the Larmor relation (i.e. the proportionality between the NMR resonance frequency and the local B0), time varying magnetic field information is extracted from the phase evolution of the detected RF signals. Susceptibility matching techniques are applied to homogenize the B0 field across the NMR sample and in this way to extend the readout time of the NMR probes. The presented design of NMR probe is significantly simpler compared to previous presented ones by De Zanche et al. in the sense that it omits the glass capillary plus additional matching fluidics. The optimization of the susceptibility for the Epoxy is described and results of the probe characterization measurements are presented. The feasibility of magnetic field monitored MRI is demonstrated for ultra-fast single- and multishot data acquisition schemes.

A thermodynamic based higher-order gradient theory for size dependent plasticity

A physically motivated and thermodynamically consistent formulation of small strain higher-order gradient plasticity theory is presented. Based on dislocation mechanics interpretations, gradients of variables associated with kinematic and isotropic hardenings are introduced. This framework is a two non-local parameter framework that takes into consideration large variations in the plastic strain tensor and large variations in the plasticity history variable; the equivalent (effective) plastic strain. The presence of plastic strain gradients is motivated by the evolution of dislocation density tensor that results from non-vanishing net Burgers vector and, hence, incorporating additional kinematic hardening (anisotropy) effects through lattice incompatibility. The presence of gradients in the effective (scalar) plastic strain is motivated by the accumulation of geometrically necessary dislocations and, hence, incorporating additional isotropic hardening effects (i.e. strengthening). It is demonstrated that the non-local yield condition, flow rule, and non-zero microscopic boundary conditions can be derived directly from the principle of virtual power. It is also shown that the local Clausius–Duhem inequality does not hold for gradient-dependent material and, therefore, a non-local form should be adopted. The non-local Clausius–Duhem inequality has an additional term that results from microstructural long-range energy interchanges between the material points within the body. A detailed discussion on the physics and the application of proper microscopic boundary conditions, either on free surfaces, clamped surfaces, or intermediate constrained surfaces, is presented. It is shown that there is a close connection between interface/surface energy of an interface or free surface and the microscopic boundary conditions in terms of microtraction stresses. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given. Applications of the proposed theory for size effects in thin films are presented.

Mechanical feedback as a possible regulator of tissue growth.

Regulation of cell growth and proliferation has a fundamental role in animal and plant development and in the progression of cancer. In the context of development, it is important to understand the mechanisms that coordinate growth and patterning of tissues. Imaginal discs, which are larval precursors of fly limbs and organs, have provided much of what we currently know about these processes. Here, we consider the mechanism that is responsible for the observed uniformity of growth in wing imaginal discs, which persists in the presence of gradients in growth inducing morphogens in spite of the stochastic nature of cell division. The phenomenon of "cell competition," which manifests in apoptosis of slower-growing cells in the vicinity of faster growing tissue, suggests that uniform growth is not a default state but a result of active regulation. How can a patch of tissue compare its growth rate with that of its surroundings? A possible way is furnished by mechanical interactions. To demonstrate this mechanism, we formulate a mathematical model of nonuniform growth in a layer of tissue and examine its mechanical implications. We show that a clone growing faster or slower than the surrounding tissue is subject to mechanical stress, and we propose that dependence of the rate of cell division on local stress could provide an "integral-feedback" mechanism stabilizing uniform growth. The proposed mechanism of growth control is not specific to imaginal disc growth and could be of general relevance. Several experimental tests of the proposed mechanism are suggested.

Culture of Escherichia coli under dissolved oxygen gradients simulated in a two‐compartment scale‐down system: Metabolic response and production of recombinant protein

A significant problem of large-scale cultures, but scarcely studied for recombinant E. coli, is the presence of gradients in dissolved oxygen tension (DOT). In this study, the effect of DOT gradients on the metabolic response of E. coli and production of recombinant pre-proinsulin, accumulated as inclusion bodies, was determined. DOT gradients were simulated in a two-compartment scale-down system consisting of two interconnected stirred-tank bioreactors, one maintained at anoxic conditions and the other at a DOT of at least 6%. Cells were continuously circulated between both vessels to simulate circulation times (tc) of 20, 50, 90, and 180 sec. A complete kinetic and stoichiometric characterization was performed in the scale-down system as well as in control cultures maintained at constant DOT in the range of 0-20%. The performance of E. coli cultured under oscillating DOT was significantly affected, even at a tc of 20 sec corresponding to transient exposures of only 13.3 sec to anaerobic conditions. Specific growth rate decreased linearly with tc to a maximum reduction of 30% at the highest tc tested. The negative effect of DOT gradients was even more pronounced for the overall biomass yield on glucose and the maximum concentration and yield of pre-proinsulin. In these cases, the losses were 9%, 27%, and 20%, respectively, at tc of 20 sec and 65%, 94%, and 87%, respectively, at tc of 180 sec. Acetic, lactic, formic, and succinic acids accumulated during oscillatory DOT cultures, indicating that deviation of carbon flow to anaerobic metabolism was responsible for the observed losses. The results of this study indicate that even very short exposures to anaerobic conditions, typical of large-scale operations, can substantially reduce recombinant protein productivity. The information presented here is useful for establishing improved rational scale-up strategies and understanding the behavior of recombinant E. coli exposed to DOT gradients.

Effect of oscillatory motion on heat transfer at vertical flat surfaces

The effect of oscillations on heat transfer at vertical surfaces is investigated and a model is developed that predicted both the transient and time average heat transfer rates. The transient behavior of the heat transfer indicates the presence of an oscillatory component superimposed on a larger steady one that does not reach zero during flow reversal. This was explained in terms of the interaction between a “quasi-steady oscillatory” mechanism near the leading edge, and a “pseudo-steady diffusive” far from it. The analysis further revealed that the time average heat transfer rate can be adequately estimated using a mixed “forced-natural” convections correlation, with the forced convection component estimated based on the time average oscillatory Reynolds number Re v = awL/ ν. The agreement between the model predictions and the experimental measurements makes it applicable for predicting heat transfer characteristics and velocity fluctuations near heated vertical surfaces in presence of oscillatory motion. The model is also applicable for predicting heat transfer rates under conditions where oscillatory motion is used to achieve specificity in temperature control without affecting process residence time, such as in biomedical and biochemical applications. The modest heat transfer enhancement (<2) due to oscillatory motion is attributed to the small convective term in the energy equation, which is consistent with previous investigations where increasing the axial temperature gradient in presence of oscillatory motion was shown to achieve much higher heat transfer enhancement.

In Vitro Modeling of Fatty Acid Synthesis under Conditions Simulating the Zonation of Lipogenic [13C]Acetyl-CoA Enrichment in the Liver

In the companion report (Bederman, I. R., Reszko, A. E., Kasumov, T., David, F., Wasserman, D. H., Kelleher, J. K., and Brunengraber, H. (2004) J. Biol. Chem. 279, 43207-43216), we demonstrated that, when the hepatic pool of lipogenic acetyl-CoA is labeled from [13C]acetate, the enrichment of this pool decreases across the liver lobule. In addition, estimates of fractional synthesis calculated by isotopomer spectral analysis (ISA), a nonlinear regression method, did not agree with a simpler algebraic two-isotopomer method. To evaluate differences between these methods, we simulated in vitro the synthesis of fatty acids under known gradients of precursor enrichment, and known values of fractional synthesis. First, we synthesized pentadecanoate from [U-13C3]propionyl-CoA and four gradients of [U-13C3]malonyl-CoA enrichment. Second, we pooled the fractions of each gradient. Third, we diluted each pool with pentadecanoate prepared from unlabeled malonyl-CoA to simulate the dilution of the newly synthesized compound by pre-existing fatty acids. This yielded a series of samples of pentadecanoate with known values of (i) lower and upper limits for the precursor enrichment, (ii) the shape of the gradient, and (iii) the fractional synthesis. At each step, the mass isotopomer distributions of the samples were analyzed by ISA and the two-isotopomer method to determine whether each method could correctly (i) detect gradients of precursor enrichment, (ii) estimate the gradient limits, and (iii) estimate the fractional synthesis. The two-isotopomer method did not identify gradients of precursor enrichment and underestimated fractional synthesis by up to 2-fold in the presence of gradients. ISA uses all mass isotopomers, correctly identified imposed gradients of precursor enrichment, and estimated the expected values of fractional synthesis within the constraints of the data.

Significance of thresholding processing in centroid based gradient wavefront sensors: effective modulation of the wavefront derivative

The use of thresholding processing is a very extended task in centroid based gradient wavefront sensors. In this paper we develop the expressions that include the thresholding process in the relation between the wavefront derivative and the centroid of a thresholded intensity distribution. We also analyze through numerical simulations the effective influence of thresholding on the wavefront slope. The results of the developed simulations remark: the relevancy of the centroid shift induced by the interaction between thresholding processing and comatic aberrations; and the nonlinear relation between the centroid and the phase gradient in presence of thresholding processing. Particularization of these results to Shack–Hartmann sensors has also been done.

Dynamics and stability of the Gödel universe

We use covariant techniques to describe the properties of the Gödel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Gödel model depends primarily upon the presence of gradients in the centrifugal energy, and secondarily on the equation of state of the fluid. The latter dictates the behaviour of the model when dealing with homogeneous perturbations. The vorticity of the perturbed Gödel model is found to evolve as in almost-FRW spacetimes, with some additional directional effects due to shape distortions. We also consider gravitational-wave perturbations by investigating the evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave equation, which argues for the neutral stability of the Gödel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Gödel cosmologies are also discussed.

Ground-based observations of the auroral zone and polar cap ionospheric responses to dayside transient reconnection

Abstract. Observations from the EISCAT VHF incoherent scatter radar system in northern Norway, during a run of the common programme CP-4, reveal a series of poleward-propagating F-region electron density enhancements in the pre-noon sector on 23 November 1999. These plasma density features, which are observed under conditions of a strongly southward interplanetary magnetic field, exhibit a recurrence rate of under 10 min and appear to emanate from the vicinity of the open/closed field-line boundary from where they travel into the polar cap; this is suggestive of their being an ionospheric response to transient reconnection at the day-side magnetopause (flux transfer events). Simultaneous with the density structures detected by the VHF radar, poleward-moving radar auroral forms (PMRAFs) are observed by the Finland HF coherent scatter radar. It is thought that PM-RAFs, which are commonly observed near local noon by HF radars, are also related to flux transfer events, although the specific mechanism for the generation of the field-aligned irregularities within such features is not well understood. The HF observations suggest, that for much of their existence, the PMRAFs trace fossil signatures of transient reconnection rather than revealing the footprint of active reconnection itself; this is evidenced not least by the fact that the PMRAFs become narrower in spectral width as they evolve away from the region of more classical, broad cusp scatter in which they originate. Interpretation of the HF observations with reference to the plasma parameters diagnosed by the incoherent scatter radar suggests that as the PMRAFs migrate away from the reconnection site and across the polar cap, entrained in the ambient antisunward flow, the irregularities therein are generated by the presence of gradients in the electron density, with these gradients having been formed through structuring of the ionosphere in the cusp region in response to transient reconnection.Key words. Magnetospheric physics (magnetosphere-ionosphere interaction) – ionosphere (ionospheric irregularities; plasma density and temperature)

Correlation between uncoupled ATP hydrolysis and heat production by the sarcoplasmic reticulum Ca2+-ATPase: coupling effect of fluoride.

The sarcoplasmic reticulum Ca(2+)-ATPase transports Ca(2+) using the chemical energy derived from ATP hydrolysis. Part of the chemical energy is used to translocate Ca(2+) through the membrane (work) and part is dissipated as heat. The amount of heat produced during catalysis increases after formation of the Ca(2+) gradient across the vesicle membrane. In the absence of gradient (leaky vesicles) the amount of heat produced/mol of ATP cleaved is half of that measured in the presence of the gradient. After formation of the gradient, part of the ATPase activity is not coupled to Ca(2+) transport. We now show that NaF can impair the uncoupled ATPase activity with discrete effect on the ATPase activity coupled to Ca(2+) transport. For the control vesicles not treated with NaF, after formation of the gradient only 20% of the ATP cleaved is coupled to Ca(2+) transport, and the caloric yield of the total ATPase activity (coupled plus uncoupled) is 22.8 kcal released/mol of ATP cleaved. In contrast, the vesicles treated with NaF consume only the ATP needed to maintain the gradient, and the caloric yield of ATP hydrolysis is 3.1 kcal/mol of ATP. The slow ATPase activity measured in vesicles treated with NaF has the same Ca(2+) dependence as the control vesicles. This demonstrates unambiguously that the uncoupled activity is an actual pathway of the Ca(2+)-ATPase rather than a contaminating phosphatase. We conclude that when ATP hydrolysis occurs without coupled biological work most of the chemical energy is dissipated as heat. Thus, uncoupled ATPase activity appears to be the mechanistic feature underlying the ability of the Ca(2+)-ATPase to modulated heat production.

Water uptake by roots: effects of water deficit.

The variable hydraulic conductivity of roots (Lp(r)) is explained in terms of a composite transport model. It is shown how the complex, composite anatomical structure of roots results in a composite transport of both water and solutes. In the model, the parallel apoplastic and cell-to-cell (symplastic and transcellular) pathways play an important role as well as the different tissues and structures arranged in series within the root cylinder (epidermis, exodermis, cortex, endodermis, stelar parenchyma). The roles of Casparian bands and suberin lamellae in the root's endo- and exodermis are discussed. Depending on the developmental state of these apoplastic barriers, the overall hydraulic resistance of roots is either more evenly distributed across the root cylinder (young unstressed roots) or is concentrated in certain layers (exo- and endodermis in older stressed roots). The reason for the variability of root Lp(r), is that hydraulic forces cause a dominating apoplastic flow of water around protoplasts, even in the endodermis and exodermis. In the absence of transpiration, water flow is osmotic in nature which causes a high resistance as water passes across many membranes on its passage across the root cylinder. The model allows for a high capability of roots to take up water in the presence of high rates of transpiration (high demands for water from the shoot). By contrast, the hydraulic conductance is low, when transpiration is switched off. Overall, this results in a non-linear relationship between water flow and forces (gradients of hydrostatic and osmotic pressure) which is otherwise hard to explain. The model allows for special root characteristics such as a high hydraulic conductivity (water permeability) in the presence of a low permeability of nutrient ions once taken up into the stele by active processes. Low root reflection coefficients are in line with the idea of some apoplastic bypasses for water within the root cylinder. According to the composite transport model, the switch from the hydraulic to the osmotic mode is purely physical. In the presence of heavily suberized roots, the apoplastic component of water flow may be too small. Under these conditions, a regulation of radial water flow by water channels dominates. Since water channels are under metabolic control, this component represents an 'active' element of regulation. Composite transport allows for an optimization of the water balance of the shoot in addition to the well-known phenomena involved in the regulation of water flow (gas exchange) across stomata. The model is employed to explain the responses of plants to water deficit and other stresses. During water deficit, the cohesion-tension mechanism of the ascent of sap in the xylem plays an important role. Results are summarized which prove the validity of the coehesion/tension theory. Effects of the stress hormone abscisic acid (ABA) are presented. They show that there is an apoplastic component of the flow of ABA in the root which contributes to the ABA signal in the xylem. On the other hand, (+)-cis-trans-ABA specifically affects both the cell level (water channel activity) and water flow driven by gradients in osmotic pressure at the root level which is in agreement with the composite transport model. Hydraulic water flow in the presence of gradients in hydrostatic pressure remains unchanged. The results agree with the composite transport model and resemble earlier findings of high salinity obtained for the cell (Lp) and root (Lp(r)) level. They are in line with known effects of nutrient deprivation on root Lp(r )and the diurnal rhythm of root Lp(r )recently found in roots of LOTUS.

Perkins instability revisited

A thorough review of the Perkins instability is presented in this paper. We introduce two new elements to the earlier model presented by Perkins [1973], namely, the neutral wind velocity and gradients in the background field line integrated density and Pedersen conductivity, respectively. We derive the eigenfrequencies and growth rates for a new instability and recover the limiting cases discussed by Perkins [1973] and Miller [1997]. The presence of gradients in the background density and Pedersen conductivity reveals a new branch in the dispersion relation and can possibly enhance the Perkins instability growth rate. The need for horizontal gradients, as was pointed out by Basu et al. [1981], is essential for the generation of small‐scale and kilometer‐scale irregularities. The Perkins instability is shown to be enhanced by both the presence of a neutral wind and the background density and Pedersen conductivity.

Depth profiling of residual stress in steel by laser ultrasonics

Depth profiling of residual stress in steel is of great interest in many practical applications. Conventional techniques are either destructive (x-ray diffraction and hole drilling) or with obvious restriction (Barkhausen noise). This paper presents a noncontact and nondestructive laser ultrasonics method for determining the depth profile of the residual stress layer in steel samples. It is known that surface acoustic waves penetrate into solids to a depth proportional to the wavelength. They are expected to be dispersive in the presence of gradients in physical properties such as residual stress. Based on the dispersion theory, the depth dependence of an effective velocity v(z), which is related to the stress profile S(z), can be fitted from the frequency dependence of the phase velocity v(w). Due to the advantage of wide bandwidth, laser-generated and -detected surface acoustic waves (SAW) offer a promising nondestructive stress depth profiling method. The profiles obtained by SAW are compared with the stress data obtained by other techniques. a)Also at Service de Métallurgie Physique, Université Libre de Bruxelles, Belgique.

The investigation and the thermodynamic analysis of volume properties in HgTe and CdHgTe melts

The temperature dependence of the density in pure HgTe melt and liquid Cd x Hg 1− x Te for x≤20 mol% CdTe has been investigated by the γ-ray attenuation method. The anomalous character of temperature density dependence for the investigated melts should be noted. Both the density and concentration gradient being stable in time have been found by the density measurements along the sample height. This gradient presence can be regarded as a new physical phenomenon in CMT melts (cadmium–mercury–tellurium). The concentration and density gradient formation is being related to the peculiarities of intermolecular interaction nature. The observed change of volume properties in the melts mentioned above has been analyzed on the basis of the associated solution theory. The calculation success in associated model approximation was achieved at the expense of Hg 2Te 3 associate introduction into the model of the chemical structure for these melts.

Vortex characteristics over delta wing subject to transient along-core blowing

Doppler anemometer (LDA), is around 1.2%. The blockage ratio of the half-wing model varies between 0.024 and 0.031 for different AOA. The momentum coefficient of blowing is defined as CM = (Vp/Uoo)2 (AP/AW), where Vp and U^ are the velocities issuing from the blowing slot and in the freestream and Ap and Aw are the areas of the blowing slot and the half-wing model, respectively. In this study, the momentum coefficient varied in the range of 0.025-0.181, and the reduced frequencies vary between 1.25 and 5.0, Figure la shows the direction and location where the blowing perturbation is applied. In Fig. Ib, the half-delta vfing model, with 75-deg sweep and 25-deg upward-beveled leading edge, is situated on a platform having an elliptic leading edge profile with a major/minor axes ratio of 5:1. The model is located within the region where the static pressure indicates only a negligible streamwise pressure gradient in presence of the platform. A circular disk is designed to rotate relative to the wing model to align the blowing direction with the vortex core above the wing surface. A hole is drilled through the thickness of the circular disk to align with the vortex core direction when viewed from the wing upper surface. Fluid issues from this blowing slot, 0.5 mm inner diameter, into and along the vortex core driven by a stepping motor pumping system. The AOA can be altered simply by screwing each hole to the wing model with the wing tip as a rotating center. Food-coloring dye, flowing naturally from another tiny slot very close to the wing apex, has been used as a tracer in the vortex core to identify the transient location of vortex breakdown during and after each blowing event. The vortex breakdown is qualitatively characterized by the

Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations.

In this paper we discuss the Euler-Heisenberg effective Lagrangian in nonperturbative and inhomogeneous field configurations characterized by a strong magnetic field of the form ${\mathit{B}}_{\mathit{x}}$=${\mathit{B}}_{\mathit{y}}$=0,rotectinebreak ${\mathit{B}}_{\mathit{z}}$=B(x,y). Our treatment exploits some interesting properties of the second-order Dirac Hamiltonian describing the electronic motion in the transverse plane (x,y). In particular, we take advantage of the existence of an energy gap separating the excited states from the lowest-lying modes. The latter are exactly calculable and give the leading nontrivial contribution to the effective Lagrangian. Our results show that the presence of gradients can be accounted for by introducing an effective magnetic field strength defined as the sum of the square moduli of the ground state wave functions. This surprisingly simple conclusion is mainly due to a quantum-mechanical supersymmetry of the problem, that of the second-order Dirac Hamiltonian in the transverse plane (x,y). We recall that the same supersymmetry plays an important role for the spontaneous mass generation in the Nambu\char21{}Jona-Lasinio model interacting with an external magnetic field. As a simple application of our effective Lagrangian, we discuss the asymptotic behavior of the dielectric permeability tensor of the vacuum as a function of the external field configuration. No anomalous enhancement of the effective electromagnetic coupling is observed. Implications of this result for the GSI peaks are briefly considered.

Moiré interferometry determination of residual stresses in the presence of gradients

The full-field technique of high-sensitivity moire interferometry in conjunction with a multiple-hole-drilling procedure is applied to residual-stress measurements in the presence of gradients. The method arrives at residual-stress estimates starting from in-plane displacement components. Successful applications of the method to problems simulating the nonuniform transverse residual stresses of welded joints are reported.

Sodium and calcium share the electrogenic 2 Na(+)-1 H+ antiporter in crustacean antennal glands

Na uptake by short-circuited epithelial brush-border membrane vesicles of Atlantic lobster (Homarus americanus) antennal gland labyrinth was Cl independent, amiloride sensitive, and stimulated by a transmembrane H+ gradient [( H]i greater than [H]o; i is internal, o is external). Na influx (2.5-s uptake) was a sigmoidal function of [Na]o (25-400 mM) when pHi = 5.0 and pHo = 8.0 and followed the Hill equation for binding cooperatively [apparent maximal influx (Jmax) = 271 nmol.mg protein-1.s-1, apparent affinity constant for Na (KNa) = 310 mM Na, and Hill coefficient (n) = 2.41]. Amiloride acted as a competitive inhibitor of Na binding to two external sites with markedly dissimilar apparent amiloride affinities (Ki1 = 14 microM; Ki2 = 1,340 mM). Electrogenic Na-H antiport by these vesicles was demonstrated by equilibrium-shift experiments in which an imposed transmembrane electrical potential difference was the only driving force for exchange. A transport stoichiometry of 2 Na to 1 H was demonstrated with the static-head technique in which a balance of driving forces was attained with 10:1 Na gradient and 100:1 H gradient. External Ca, like amiloride, was a strong competitive inhibitor of Na-H exchange, acting at two sites on the outer vesicular face with markedly different apparent divalent cation affinities (Ki1 = 20 microM; Ki2 = 500 microM). Ca-H exchange by electrogenic Na-H antiporter was demonstrated in complete absence of Na by use of an outward H gradient in presence and absence of amiloride. Both external amiloride (Ki1 = 70 microM; Ki2 = 500 microM) and Na (Ki1 = 12 mM; Ki2 = 380 mM) were competitive inhibitors of Ca-H exchange. These results suggest that the electrogenic 2 Na-1 H exchanger characterized for this crustacean epithelium may also have a role in organismic Ca balance.

Mathematical analysis of cell-target encounter rates in three dimensions. Effect of chemotaxis

Efficient and rapid immune response upon challenge by an infectious agent is vital to host defense. The encounter of leukocytes (white blood cells of the immune system) with their targets is the first step in this response. Analysis of the kinetics of this process is essential not only to understanding dynamic behavior of the immune response, but also to elucidating the consequences of many leukocyte functional abnormalities. The motion of leukocytes in the presence of targets typically involves a directed, or chemotactic component. These immune cells orient the direction of their motion in the presence of gradients in chemical attractants generated by pathogens. Fisher and Lauffenburger (1987. Biophys. J. 51:705-716) developed a model for macrophage/bacterium encounter in two dimensions which includes chemotaxis, and applied it to the particular system of alveolar macrophages (phagocytic leukocytes on the lung surface). Their model showed that macrophage/target encounter is likely the rate-limiting step in clearance of bacteria from the lung surface (Fisher, E. S., D. A. Lauffenburger, and R. P. Daniele. 1988. Am. Rev. Resp. Dis. 137:1129-1134). We have extended this model to analyze the effects of cell motility properties and geometric parameters on cell-target encounter in three dimensions. The differential equation governing encounter time in three dimensions is essentially the same as that in two dimensions, except for changed probability values. Our results show that more highly directed motion is necessary in three dimensions to achieve substantially decreased encounter times than in two dimensions, because of the increased search dimensionality. These general results were applied to the particular system of neutrophils operating in three dimensions in response to a bacterial challenge in connective tissue. Our results provide a plausible rationalization for both the chemotactic and chemokinetic behavior observed in neutrophils. That is, these cells exhibit in vitro a greater chemotactic bias and a more dramatic variation of speed with attractant concentration than alveolar macrophages, and our results indicate that these behaviors can have a greater influence in three-dimensional connective tissue infection situations than in two-dimensional lung surface infection cases. In addition, we show that encounter apparently is not generally the rate-limiting step in this neutrophil response. These findings have important implications for correlating in vitro measured defects in cell motility and chemotaxis properties with in vivo functions of host defense against infection.