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.     

Intestinal motor disorders associated with cyclical bacterial overgrowth in a rat model of enteritis

The aims of this study were: 1) to obtain an experimental model reproducing the characteristics of chronicity and spontaneous relapses found in inflammatory bowel disease (IBD) and 2) to correlate these changes with intestinal motility and bacteria translocation. For this purpose, two groups of Sprague-Dawley rats were used: a treated group that received two subcutaneous injections of indomethacin (7.5 mg/kg) 48 h apart and a control group that received saline. Blood leukocytes, TNF, and fecal parameters were monitored for 90 days after treatment. In treated rats, a cyclic oscillation of blood leukocytes and TNF concomitant with an inverse correlation of fecal output was observed. Treated rats were then selected either during their highest or lowest blood leukocyte values for motor activity and microbiological evaluation. Controls were obtained in age-matched rats. Rats with high leukocyte levels showed a decrease of motor activity. In contrast, animals with low leukocyte levels presented hypermotility. Bacterial overgrowth accompanied by bacterial translocation was found in the group with high leukocytes, whereas no differences were observed between the control and indomethacin groups during the lowest leukocyte phase. We obtained a model of IBD characterized by a chronic cyclic oscillation of intestinal motility, flora, and inflammatory blood parameters. During the high-leukocyte stage, motor activity decrease is related to bacterial translocation. This phase is followed by a reactive one characterized by hypermotility associated with a decrease in both bacterial growth and leukocytes. However, as in IBD, this reaction seems unable to prevent a return to relapse.     

Localized bacterial infection in a distributed model for tissue inflammation

Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response.Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.     

Comparison of the intracellular bacterial killing activity of leukocytes in musculocutaneous and random-pattern flaps

The in vivo physiologic response to gram-negative bacterial inoculation within wound cylinder spaces enclosed by the deep surface of paired musculocutaneous and random-pattern flaps was studied in the canine model. Leukocyte function was assessed by calculating the following values: leukocyte counts, bacterial counts, phagocytic indices, and intracellular bacterial killing ratios. The following results were observed in the wound cylinder spaces after bacterial inoculation with 5 X 10(7) of Pseudomonas aeruginosa bacteria: (1) the numbers of mobilized leukocytes within each wound cylinder space flap were not statistically different, (2) the bacterial counts were significantly lower in the musculocutaneous flap wound cylinder space at both 24 and 48 hours, (3) the phagocytic activity of the leukocytes within musculocutaneous flap wound cylinder space was 1.5 times greater than the leukocytes in the random-pattern flap wound cylinder space, and (4) the intracellular bacterial killing ratio of the musculocutaneous flap leukocyte was 83 percent versus 26 percent in the random-pattern flap leukocyte, a significant difference.     

Step-wise loss of bacterial flagellar torsion confers progressive phagocytic evasion

Phagocytosis of bacteria by innate immune cells is a primary method of bacterial clearance during infection. However, the mechanisms by which the host cell recognizes bacteria and consequentially initiates phagocytosis are largely unclear. Previous studies of the bacterium Pseudomonas aeruginosa have indicated that bacterial flagella and flagellar motility play an important role in colonization of the host and, importantly, that loss of flagellar motility enables phagocytic evasion. Here we use molecular, cellular, and genetic methods to provide the first formal evidence that phagocytic cells recognize bacterial motility rather than flagella and initiate phagocytosis in response to this motility. We demonstrate that deletion of genes coding for the flagellar stator complex, which results in non-swimming bacteria that retain an initial flagellar structure, confers resistance to phagocytic binding and ingestion in several species of the gamma proteobacterial group of Gram-negative bacteria, indicative of a shared strategy for phagocytic evasion. Furthermore, we show for the first time that susceptibility to phagocytosis in swimming bacteria is proportional to mot gene function and, consequently, flagellar rotation since complementary genetically- and biochemically-modulated incremental decreases in flagellar motility result in corresponding and proportional phagocytic evasion. These findings identify that phagocytic cells respond to flagellar movement, which represents a novel mechanism for non-opsonized phagocytic recognition of pathogenic bacteria.     

Increased recruitment but impaired function of leukocytes during inflammation in mouse models of type 1 and type 2 diabetes

Background

Patients suffering from diabetes show defective bacterial clearance. This study investigates the effects of elevated plasma glucose levels during diabetes on leukocyte recruitment and function in established models of inflammation.

Methodology/Principal Findings

Diabetes was induced in C57Bl/6 mice by intravenous alloxan (causing severe hyperglycemia), or by high fat diet (moderate hyperglycemia). Leukocyte recruitment was studied in anaesthetized mice using intravital microscopy of exposed cremaster muscles, where numbers of rolling, adherent and emigrated leukocytes were quantified before and during exposure to the inflammatory chemokine MIP-2 (0.5 nM). During basal conditions, prior to addition of chemokine, the adherent and emigrated leukocytes were increased in both alloxan- (62±18% and 85±21%, respectively) and high fat diet-induced (77±25% and 86±17%, respectively) diabetes compared to control mice. MIP-2 induced leukocyte emigration in all groups, albeit significantly more cells emigrated in alloxan-treated mice (15.3±1.0) compared to control (8.0±1.1) mice. Bacterial clearance was followed for 10 days after subcutaneous injection of bioluminescent S. aureus using non-invasive IVIS imaging, and the inflammatory response was assessed by Myeloperoxidase-ELISA and confocal imaging. The phagocytic ability of leukocytes was assessed using LPS-coated fluorescent beads and flow cytometry. Despite efficient leukocyte recruitment, alloxan-treated mice demonstrated an impaired ability to clear bacterial infection, which we found correlated to a 50% decreased phagocytic ability of leukocytes in diabetic mice.

Conclusions/Significance

These results indicate that reduced ability to clear bacterial infections observed during experimentally induced diabetes is not due to reduced leukocyte recruitment since sustained hyperglycemia results in increased levels of adherent and emigrated leukocytes in mouse models of type 1 and type 2 diabetes. Instead, decreased phagocytic ability observed for leukocytes isolated from diabetic mice might account for the impaired bacterial clearance.     

Modulation of phagocyte apoptosis by bacterial pathogens

Phagocytic leukocytes such as neutrophils and macrophages are essential for the innate immune response against invading bacteria. Binding and ingestion of bacteria by these host cells triggers potent anti-microbial activity, including production of reactive oxygen species. Although phagocytes are highly adept at destroying bacteria, modulation of leukocyte apoptosis or cell death by bacteria has emerged as a mechanism of pathogenesis. Whereas induction of macrophage apoptosis by pathogens may adversely affect the host immune response to infection, acceleration of neutrophil apoptosis following phagocytic interaction with bacteria appears essential for the resolution of infection. This idea is supported by the finding that some bacterial pathogens alter normal phagocytosis-induced neutrophil apoptosis to survive and cause disease. This review summarizes what is currently known about modulation of phagocyte apoptosis by bacteria and describes a paradigm whereby bacteria-induced neutrophil apoptosis plays a role in the resolution of infection.     

Growth rate effects on fundamental transport properties of bacterial populations

In many natural environments, bacterial populations experience suboptimal growth due to the competition with other microorganisms for limited resources. The chemotactic response provides a mechanism by which bacterial populations can improve their situation by migrating toward more favorable growth conditions. For bacteria cultured under suboptimal growth conditions, evidence for an enhanced chemotactic response has been observed previously. In this article, for the first time, we have quantitatively characterized this behavior in terms of two macroscopic transport coefficients, the random motility and chemotactic sensitivity coefficients, measured in the stopped-flow diffusion chamber assay. Escherichia coli cultured over a range of growth rates in a chemostat exhibits a dramatic increase in the chemotactic sensitivity coefficient for D-fucose at low growth rates, while the random motility coefficient remains relatively constant by comparison. The change in the chemotactic sensitivity coefficient is accounted for by an independently measured increase in the number of galactose-binding proteins which mediate the chemotactic signal. This result is consistent with the relationship between macroscopic and microscopic parameters for chemotaxis, which was proposed in the mathematical model of Rivero and co-workers. (c) 1993 John Wiley & Sons, Inc.     

Regulation of innate immunity by Rho GTPases

Leukocytes are key cellular components of innate immunity. These phagocytic cells respond to bacteria at sites of infection through chemotactic sensing and directed motility regulated by Rho GTPases. The development of sensitive probes of Rho GTPase dynamics has provided insights into the temporal and spatial aspects of GTPase regulation during chemotaxis and subsequent microbial phagocytosis. The resulting destruction of ingested bacteria by means of reactive oxygen species (ROS) depends on a Rac-regulated "molecular switch" that is modulated by antagonistic crosstalk involving Cdc42. Recent studies of leukocytes derived from Rac1- and Rac2-knockout mice have shown that these highly homologous GTPases have unique biological roles. An understanding of the biochemical basis for such distinct activities should provide novel insights into the molecular details of Rho GTPase function and regulation in innate immunity.     

Galectins as inflammatory mediators

Over the last decade a vast amount of reports have shown that galectin-1 and galectin-3 are important mediators of inflammation. In this review we describe how the galectins may be involved in several parts of the inflammatory process, including the recruitment of neutrophils into an infected tissue and the recognition and killing of bacteria by activation of the tissue destructive phagocytic respiratory burst. During bacterial infection or aseptic inflammatory processes, galectins are produced and released by e.g. infected epithelium, activated tissue-resident macrophages and endothelial cells. These extracellular galectins may facilitate binding of neutrophils to the endothelium by cross-linking carbohydrates on the respective cells. Further the galectins improve binding of the neutrophil to the extracellular matrix proteins laminin and fibronectin, and are potential chemotactic factors, inducing migration through the extracellular matrix towards the inflammatory focus. When the cells encounter bacteria, galectin-3 could function as an opsonin, cross-linking bacterial lipopolysaccharide or other carbohydrate-containing surface structures to phagocyte surface glycoconjugates. Both galectin-1 and galectin-3 have the capacity to induce a respiratory burst in neutrophils, provided that the cells have been primed by degranulation and receptor upregulation. The reactive oxygen species produced may be destructive to the invading micro-organisms as well as to the surrounding host tissue, pointing out the possible role of galectins, not only in defence toward infection, but also in inflammatory-induced tissue destruction. Published in 2004.     

Mathematical model for characterization of bacterial migration through sand cores

The migration of chemotactic bacteria in liquid media has previously been characterized in terms of two fundamental transport coefficients-the random motility coefficient and the chemotactic sensitivity coefficient. For modeling migration in porous media, we have shown that these coefficients which appear in macroscopic balance equations can be replaced by effective values that reflect the impact of the porous media on the swimming behavior of individual bacteria. Explicit relationships between values of the coefficients in porous and liquid media were derived. This type of quantitative analysis of bacterial migration is necessary for predicting bacterial population distributions in subsurface environments for applications such as in situ bioremediation in which bacteria respond chemotactically to the pollutants that they degrade.We analyzed bacterial penetration times through sand columns from two different experimental studies reported in the literature within the context of our mathematical model to evaluate the effective transport coefficients. Our results indicated that the presence of the porous medium reduced the random motility of the bacterial population by a factor comparable to the theoretical prediction. We were unable to determine the effect of the porous medium on the chemotactic sensitivity coefficient because no chemotactic response was observed in the experimental studies. However, the mathematical model was instrumental in developing a plausible explanation for why no chemotactic response was observed. The chemical gradients may have been too shallow over most of the sand core to elicit a measurable response. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 487-496, 1997.     

Chemotactic transport theory for neutrophil leukocytes

The simplest admissible phenomenological transport theory for the chemotactic migration of a population of neutrophil leukocytes is formulated along the lines of the original Keller-Segel model for bacterial chemotaxis, but with appropriate specialization of the motility and chemotactic flux coefficient to reflect their dependence on the local cytotaxin (chemoattractant) concentration, as observed experimentally by Wilkinson and other workers. By supplementing deductions from the governing transport equation with inferences from measurements and then reasoning both forwards and backwards, the functional forms of the motility and chemotactic flux coefficient can be established for any prescribed cytotaxin. This analysis is performed here with numerical details for casein, a cytotaxin which gives rise to a motility function with an increasing-then-decreasing form of dependence on the concentration and a chemotactic flux coefficient that is essentially constant with variations in the concentration. Three dimensionless numbers are associated with the chemotactic response of neutrophil leukocytes to casein.     

Biologically active peptides interacting with the G protein-coupled formylpeptide receptor

Leucocytes accumulate at sites of inflammation and microbial infection in response to locally produced chemotactic factors. N-formylpeptides produced by Gram negative bacteria were among the first chemotactic factors structurally defined which signal through G protein-coupled formylpeptide receptor (FPR) and FPR-like 1 (FPRL1) expressed by phagocytic leukocytes in human and in mouse homogogues mFPR and mFPR2. During the past few years, a number of pathogen- and host-derived agonists/antagonists for FPR, FPRL1 and another FPR variant FPR-like 2 (FPRL2) have been identified. Activation of formylpeptide receptors (FPRs) in phagocytic leukocytes by agonists results in increased cell chemotaxis, phagocytosis, and release of pro-inflammatory mediators. Peptide agonists for FPRs have also been shown to possess immune adjuvant activity when injected in mice. In addition, FPR aberrantly expressed on highly malignant human glioblastoma cells promotes tumor cell migration, proliferation and production of vascular endothelial growth factor in response to agonists released by necrotic tumor cells. Therefore, formylpeptide receptor ligands, by interacting with FPRs, play important roles in host defense and in the rapid progression of human glioblastoma.     

A Non-Poissonian Flagellar Motor Switch Increases Bacterial Chemotactic Potential

We investigate bacterial chemotactic strategies using run-tumble and run-reverse-flick motility patterns. The former is typically observed in enteric bacteria such as Escherichia coli and Salmonella and the latter was recently observed in the marine bacteria Vibrio alginolyticus and is possibly exhibited by other polar flagellated species. It is shown that although the three-step motility pattern helps the bacterium to localize near hot spots, an exploitative behavior, its exploratory potential in short times can be significantly enhanced by employing a non-Poissonian regulation scheme for its flagellar motor switches.     

Traveling bands of chemotactic bacteria in the context of population growth

A mathematical model for traveling bands of motile and chemotactic bacteria in the presence of cell growth and death is examined. It is found that asymptotic traveling wave solutions exist in the absence of chemotaxis, due to the balance of growth, death and random motility. Thus random motility confers the ecological advantage of population propagation through migration into nutrient-rich regions. The presence of chemotaxis amplifies this advantage by moving more cells into higher nutrient concentration regions, resulting in larger and faster bands. Therefore there seem to be two types of traveling bands that can be attained by chemotactic bacteria in the presence of growth and death: (1) these growth/death/motility bands; and (2) pure chemotactic ‘Keller-Segel'-type bands. Comparison to experimental observations by Chapman in 1973 indicate that the latter seem to be formed. The relationship between these two types of solution is at present uncertain. The growth/death/motility bands may have relevance on longer time or distance scales characteristic of microbial ecological systems.     

Semi-stochastic cell-level computational modeling of the immune system response to bacterial infections and the effects of antibiotics

A mathematical model for the immune system response to bacterial infections is proposed. The formalism is based on modeling the chemokine-determined transmigration of leukocytes from a venule through the venule walls and the subsequent in-tissue migration and engulfment of the pathogens that are responsible for the infection. The model is based on basic principles, such as Poiseuille blood flow through the venule, fundamental solutions of the diffusion–reaction equation for the concentration field of pathogen-released chemokines, linear chemotaxis of the leukocytes, random walk of pathogens, and stochastic processes for the death and division of pathogens. Thereby, a computationally tractable and, as far as we know, original framework has been obtained, which is used to incorporate the interaction of a substantial number of leukocytes and thereby to unravel the significance of biological processes and parameters regarding the immune system response. The developed model provides a neat way for visualization of the biophysical mechanism of the immune system response. The simulations indicate a weak correlation between the immune system response in terms of bacterial clearing time and the leukocyte stiffness, and a significant decrease in the clearing time with increasing in-blood leukocyte density, decreasing pathogen motility, and increasing venule wall transmissivity. Finally, the increase in the pathogen death rate and decrease in pathogen motility induce a decrease in the clearing time of the infection. The adjustment of the latter two quantities mimic the administration of antibiotics.     

The C-reactive protein of tongue sole Cynoglossus semilaevis is an acute phase protein that interacts with bacterial pathogens and stimulates the antibacterial activity of peripheral blood leukocytes

Pentraxins are a family of evolutionarily conserved proteins that play an important part in innate immunity. C-reactive protein (CRP) is a member of the pentraxin family and in humans is known to be the major acute phase protein. In this work, we report the identification and analysis of a CRP, CsCRP, from half-smooth tongue sole (Cynoglossus semilaevis). CsCRP is composed of 228 amino acid residues and possesses a Pentraxin/CRP domain. Expression of CsCRP occurred in a wide range of tissues and was upregulated by pathogen infection in kidney, spleen, blood, and, in particular, liver. Following bacterial infection, CsCRP level in blood rose rapidly within 12 h and was approximately 3.8 fold of that of the basal level. Purified recombinant CsCRP (rCsCRP) was able to interact with Gram-negative and Gram-positive bacteria including those of pathogenic nature in a dose-dependent manner. When peripheral blood leukocytes (PBL) were infected with bacterial pathogen in the presence of rCsCRP, the respiratory burst and phagocytic capacity of the cells were increased to significant extents. Taken together, these results indicate that CsCRP is an acute phase protein that plays a role in innate immune defense against bacterial infection.     

Inhibition of HMG-CoA reductase activity by hypercholesterolaemia reduces leukocyte recruitment and MCP-1 production

To clarify the relationship between cholesterol homeostasis and inflammation we studied the effect of hypercholesterolaemia on in vivo cytokine production and leukocyte migration, in a murine model of local inflammation. Hypercholesterolaemia reduced of 40% the leukocyte recruitment by inhibiting interleukin-6 and monocyte chemotactic protein-1 production in the pouch exudate, without affecting vascular permeability or leukocytes motility.     

Localization of chemotactic peptide receptors on rabbit neutrophils

The chemotaxis of blood leukocytes is initiated by the binding of a chemoattractant to specific receptors on the leukocyte cell surface. Although a great deal is known about the biochemical and morphological events accompanying chemotactic activation, there is very little morphological information about the chemoattractant receptors themselves. This latter information is needed so that we may understand the mechanism by which these inflammatory cells detect and respond to chemical gradients. One class of chemotactic factors extensively used to characterize the complex behavioral responses following leukocyte activation are the synthetic formylmethionyl peptides. These peptides, now known to be the analogs of the naturally occurring N-terminal peptides produced by bacteria, are released into culture medium and are believed to be responsible, at least in part, for the accumulation of leukocytes at the sites of bacterial infection. We have localized the receptors for the chemotactic hexapeptide N-formylnorleucyl-leucyl-phenylalanine-norleucyl-[125I]tyrosyl-lys ine [N-fNle-Leu-Phe-Nle-[125I]Tyr-Lys] on whole rabbit peritoneal neutrophils (PMN) using light microscope autoradiography. By this method, the inherent formylpeptide receptor distribution on cells incubated at 4 degrees C appears to be uniform over the surface of both rounded and structurally polarized PMN. Following a short 37 degrees C incubation, cells retain a large proportion of labelled hexapeptide at or near the cell surface and, in addition, polarized PMN redistribute the hexapeptide anteriorly away from the cell uropod.