Mathematical analysis of cell-target encounter rates in two dimensions. The effect of chemotaxis.

The process by which cells encounter their targets is the first step of a number of cell functions involved in the immune response, such as cell-mediated cytotoxicity and phagocytic ingestion of foreign material. In many instances, this encounter may be rate-limiting, and therefore it is important to understand what factors influence the encounter rate. One key aspect of cell-target encounter is the motility behavior of the cell in the vicinity of a target. This movement may be entirely random, or there may be a directed, or chemotactic, component to it. In this paper we focus on the effects of cell motility properties, and particularly the chemotactic directional bias, on the rate of cell-target encounter. Specifically, we derive an expression for the mean encounter time of cells that meet targets in two dimensions as a function of the cells' directional orientation bias. We show that a modest degree of bias can reduce the mean encounter time by orders of magnitude, while nearly perfect directional bias offers little additional benefit. We illustrate the application of these results to a particular example system: alveolar macrophages removing inhaled particles and bacteria from the lung surface.     

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.     

Differential Effects of Serum Heat Treatment on Chemotaxis and Phagocytosis by Human Neutrophils

Neutrophils, in cooperation with serum, are vital gatekeepers of a host’s microbiome and frontline defenders against invading microbes. Yet because human neutrophils are not amenable to many biological techniques, the mechanisms governing their immunological functions remain poorly understood. We here combine state-of-the-art single-cell experiments with flow cytometry to examine how temperature-dependent heat treatment of serum affects human neutrophil interactions with “target” particles of the fungal model zymosan. Assessing separately both the chemotactic as well as the phagocytic neutrophil responses to zymosan, we find that serum heat treatment modulates these responses in a differential manner. Whereas serum treatment at 52°C impairs almost all chemotactic activity and reduces cell-target adhesion, neutrophils still readily engulf target particles that are maneuvered into contact with the cell surface under the same conditions. Higher serum-treatment temperatures gradually suppress phagocytosis even after enforced cell-target contact. Using fluorescent staining, we correlate the observed cell behavior with the amounts of C3b and IgG deposited on the zymosan surface in sera treated at the respective temperatures. This comparison not only affirms the critical role of complement in chemotactic and adhesive neutrophil interactions with fungal surfaces, but also unmasks an important participation of IgGs in the phagocytosis of yeast-like fungal particles. In summary, this study presents new insight into fundamental immune mechanisms, including the chemotactic recruitment of immune cells, the adhesive capacity of cell-surface receptors, the role of IgGs in fungal recognition, and the opsonin-dependent phagocytosis morphology of human neutrophils. Moreover, we show how, by fine-tuning the heat treatment of serum, one can selectively study chemotaxis or phagocytosis under otherwise identical conditions. These results not only refine our understanding of a widely used laboratory method, they also establish a basis for new applications of this method.     

The mechanics of heterotypic cell aggregates: insights from computer simulations

Finite element-based computer simulations are used to investigate a number of phenomena, including tissue engulfment, cell sorting, and checkerboard-pattern formation, exhibited by heterotypic cell aggregates. The simulations show that these phenomena can be driven by a single equivalent force, namely a surface (or interfacial) tension, that results from cytoskeletal components and cell-cell adhesions. They also reveal that tissue engulfment, cell sorting, and checkerboard-pattern formation involve several discernible mechanical features or stages. With the aid of analytical arguments, we identify the conditions necessary for each of these phenomena. These findings are consistent with previous experimental investigations and computer simulations, but pose significant challenges to current theories of cell sorting and tissue engulfment.     

Dynamin 2 regulates granule exocytosis during NK cell-mediated cytotoxicity

NK cells are innate immune cells that can eliminate their targets through granule release. In this study, we describe a specialized role for the large GTPase Dynamin 2 (Dyn2) in the regulation of these secretory events leading to cell-mediated cytotoxicity. By modulating the expression of Dyn2 using small interfering RNA or by inhibiting its activity using a pharmacological agent, we determined that Dyn2 does not regulate conjugate formation, proximal signaling, or granule polarization. In contrast, during cell-mediated killing, Dyn2 localizes with lytic granules and polarizes to the NK cell-target interface where it regulates the final fusion of lytic granules with the plasma membrane. These findings identify a novel role for Dyn2 in the exocytic events required for effective NK cell-mediated cytotoxicity.     

True chemotaxis in oxygen gradients of the sulfur-oxidizing bacterium Thiovulum majus.

Observations of free-swimming Thiovulum majus cells show that these bacteria exhibit a phobic response as well as true chemotaxis in oxygen gradients. Both phenomena of their chemotactic behavior are integrated into a single model of helical klinotaxis, which is demonstrated by computer simulations.     

Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations

Bone functional tissue adaptation is a multiaspect physiological process driven by interrelated mechanical and biological stimuli which requires the combined activity of osteoclasts and osteoblasts. In previous work, the authors developed a phenomenological mesoscale structural modelling approach capable of predicting internal structure of the femur based on daily activity loading, which relied on the iterative update of the cross-sectional areas of truss and shell elements representative of trabecular and cortical bones, respectively. The objective of this study was to introduce trabecular reorientation in the phenomenological model at limited computational cost. To this aim, a metamodel derived from poroelastic microscale continuum simulations was used to predict the functional adaptation of a simplified proximal structural femur model. Clear smooth trabecular tracts are predicted to form in the regions corresponding to the main trabecular groups identified in literature, at minimal computational cost.     

Protein-protein association: investigation of factors influencing association rates by brownian dynamics simulations

The rate of protein-protein association limits the response time due to protein-protein interactions. The bimolecular association rate may be diffusion-controlled or influenced, and in such cases, Brownian dynamics simulations of protein-protein diffusional association may be used to compute association rates. Here, we report Brownian dynamics simulations of the diffusional association of five different protein-protein pairs: barnase and barstar, acetylcholinesterase and fasciculin-2, cytochrome c peroxidase and cytochrome c, the HyHEL-5 antibody and hen egg lysozyme (HEL), and the HyHEL-10 antibody and HEL. The same protocol was used to compute the diffusional association rates for all the protein pairs in order to assess, by comparison to experimentally measured rates, whether the association of these proteins can be explained solely on the basis of diffusional encounter. The simulation protocol is similar to those previously derived for simulation of the association of barnase and barstar, and of acetylcholinesterase and fasciculin-2; these produced results in excellent agreement with experimental data for these protein pairs, with changes in association rate due to mutations reproduced within the limits of expected computational and modeling errors. Here, we find that for all protein pairs, the effects of mutations can be well reproduced by the simulations, even though the degree of the electrostatic translational and orientational steering varies widely between the cases. However, the absolute values of association rates for the acetylcholinesterase: fasciculin-2 and HyHEL-10 antibody: HEL pairs are overestimated. Comparison of bound and unbound protein structures shows that this may be due to gating resulting from protein flexibility in some of the proteins. This may lower the association rates compared to their bimolecular diffusional encounter rates.     

Dissipative particle dynamics simulations for biological tissues: rheology and competition

In this work, we model biological tissues using a simple, mechanistic simulation based on dissipative particle dynamics. We investigate the continuum behavior of the simulated tissue and determine its dependence on the properties of the individual cell. Cells in our simulation adhere to each other, expand in volume, divide after reaching a specific size checkpoint and undergo apoptosis at a constant rate, leading to a steady-state homeostatic pressure in the tissue. We measure the dependence of the homeostatic state on the microscopic parameters of our model and show that homeostatic pressure, rather than the unconfined rate of cell division, determines the outcome of tissue competitions. Simulated cell aggregates are cohesive and round up due to the effect of tissue surface tension, which we measure for different tissues. Furthermore, mixtures of different cells unmix according to their adhesive properties. Using a variety of shear and creep simulations, we study tissue rheology by measuring yield stresses, shear viscosities, complex viscosities as well as the loss tangents as a function of model parameters. We find that cell division and apoptosis lead to a vanishing yield stress and fluid-like tissues. The effects of different adhesion strengths and levels of noise on the rheology of the tissue are also measured. In addition, we find that the level of cell division and apoptosis drives the diffusion of cells in the tissue. Finally, we present a method for measuring the compressibility of the tissue and its response to external stress via cell division and apoptosis.     

True Chemotaxis in Oxygen Gradients of the Sulfur-Oxidizing Bacterium Thiovulum majus

Observations of free-swimming Thiovulum majus cells show that these bacteria exhibit a phobic response as well as true chemotaxis in oxygen gradients. Both phenomena of their chemotactic behavior are integrated into a single model of helical klinotaxis, which is demonstrated by computer simulations.     

Macrophages in the embryo and beyond: much more than just giant phagocytes

Originally recognized as an essential part of the innate and acquired immune systems, macrophages emerged as omnipresent and influential regulators of embryo- and organo-genesis, as well as of tissue and tumor growth. Macrophages are present essentially in all tissues, beginning with embryonic development and, in addition to their role in host defense and in the clearance of apoptotic cells, are being increasingly recognized for their trophic function and role in regeneration. Some tissue macrophages are also found to possess a substantial potential for autonomous self-renewal. Macrophages are associated with a significant proportion of malignant tumors and are widely recognized for their angiogenesis-promoting and trophic roles, making them one of the new promising targets for cancer therapies. Recent expression profiling of embryonic macrophages from different tissues revealed remarkable consistency of their gene expression profiles, independent of their tissue of origin, as well as their similarities with tumor-associated macrophages. Macrophages are also capable of fusion with other cells in tissue repair and metastasizing tumors, as well as with each other in the immune response and osteoclastogenesis.     

All-atom simulations to studying metallodrugs/target interactions

Metallodrugs are extensively used to treat and diagnose distinct disease types. The unique physical–chemical properties of metal ions offer tantalizing opportunities to tailor effective scaffolds for selectively targeting specific biomolecules. Modern experimental techniques have collected a large body of structural data concerning the interactions of metallodrugs with their biomolecular targets, although being unable to exhaustively assess the molecular basis of their mechanism of action.In this scenario, the complementary use of accurate computational methods allows uncovering the minutiae of metallodrugs/targets interactions and their underlying mechanism of action at an atomic-level of detail. This knowledge is increasingly perceived as an invaluable requirement to rationally devise novel and selective metallodrugs. Building on literature studies, selected largely from the last 2 years, this compendium encompasses a cross-section of the current role, advances, and challenges met by computer simulations to decipher the mechanistic intricacies of prototypical metallodrugs.     

Antibody-mediated cytotoxic effects in vitro and in vivo of rat cells on infective larvae of Brugia malayi

Albino rat macrophages and neutrophils in the presence of immune serum adhered to and promoted killing of Brugia malayi infective larvae in vitro. At a similar cell-target ratio, macrophages were more potent than neutrophils in inducing cytotoxic response to the larvae. Eosinophils were also effective in killing but only at a high cell-target ratio. The activity in the immune serum could be absorbed to and eluted from a Protein A-Sepharose column suggesting involvement of IgG antibody in the reaction. An indirect fluorescent antibody test confirmed the presence of IgG on the surface of larvae incubated in immune serum. Infective larvae were attacked by host cells within micropore chambers 16-24 h after implantation into immunized rats. Further, a strong cytotoxic response to the larvae was seen when they were introduced intraperitoneally into immune rats indicating the role of antibody and cells in vivo. We suggest that antibody-dependent cellular cytotoxicity may represent an important mechanism of parasite killing in an immune host.     

NK cell inhibitory receptors prevent tyrosine phosphorylation of the activation receptor 2B4 (CD244)

2B4 is an NK cell activation receptor that can provide a co-stimulatory signal to other activation receptors and whose mode of signal transduction is still unknown. We show that cross-linking of 2B4 on NK cells results in its rapid tyrosine phosphorylation, implying that this initial step in 2B4 signaling does not require coligation of other receptors. Ligation of 2B4 in the context of an NK cell-target cell interaction leads to 2B4 tyrosine phosphorylation, target cell lysis, and IFN-gamma release. Coligation of 2B4 with the inhibitory receptors killer cell Ig-like receptor (KIR)2DL1 or CD94/NKG2 completely blocks NK cell activation. The rapid tyrosine phosphorylation of 2B4 observed upon contact of NK cells with sensitive target cells is abrogated when KIR2DL1 or CD94/NKG2 are engaged by their cognate MHC class I ligand on resistant target cells. These results demonstrate that NK inhibitory receptors can interfere with a step as proximal as phosphorylation of an activation receptor.     

Mechanisms of immunity to rickettsial infection: characterization of a cytotoxic effector cell

Rickettsiae, as other intracellular bacteria, are relatively sequestered from the effects of antibody and local antibody-independent responses. Considering the obligate intracellular nature of rickettsia, the exact mechanisms by which lymphocytes and macrophages encounter rickettsial antigens and eliminate the infection depends upon the appropriate presentation of antigen to the immune system. We demonstrate here that cells taken from the spleens of Rickettsia typhi- or R. tsutsugamushi-infected mice are able to lyse specifically tissue culture targets infected with the homologous organism. This effect was eliminated upon treatment of the spleen cells with anti-Thy-1.2 + complement. Furthermore such T cells exhibit H-2-restricted killing when tested on infected targets of different genetic backgrounds. We propose that a T cell-mediated cytotoxic immune mechanism exists that may play an important role in the elimination of rickettsial organisms during infection.     

Production of proteinase A bySaccharomyces cerevesiae in a cell-recycling fermentation system: experiments and computer simulations

Overproduction of proteinase A by recombinantSaccharomyces cerevisiae was investigated by cultivations in a cell-recycling bioreactor. Memebrane filtration was used to separate cells from the broth. Recycling ratios and dilution rates were varied and the effect on enzyme production was studied both experimentally and by computer simulations. Experiments and simulations showed that cell mass and product concentration were enhanced by high ratios of recycling. Additional simulations showed that the proteinase A concentration decreased drastically at high dilution rates and the optimal volumetric productivities were at high dilution rates just below washout and at high ratios of recycling. Cell-recycling fermentation gave much higher volumetric productivities and stable product concentrations in contrast to simple continuous fermentation.     

Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations

The key role played by turbulence in the environment of plankton and larval fish populations has become appreciated in recent years. In particular, the turbulent enhancement of encounter rates between different species of microorganisms, either swimming or passively advected by the flow, is well established. However, most of the current modelling approaches are rather ad hoc, giving rise to ambiguities in the specification of certain key parameters. In this paper, the encounter problem in a turbulent flow of large Reynolds number is re-examined from first principles and a number of new formulae will be established for different swimming strategies. The key innovation is the proposal of a model form for the conditional joint probability density function of predator and prey velocities when the organisms are separated by their given contact radius, R. Particular attention will be paid to the case when a microorganism follows a random trajectory, due to a combination of its own swimming and the action of the flow. The theoretical predictions are subsequently tested against corresponding quantities derived from a series of kinematic simulations of a turbulent-like flow field. Good agreement is demonstrated between the predictions and simulations.     

Ultrastructure of Cytotoxic Cells in Frogs

Our previous work gave evidence that leopard frogs ( Rana pipiens ) possess inducible killer (IK) cells (CTL-like) and spontaneous killer (SK) cells (NK-like) that can destroy allogeneic RBC. To further characterize these cytotoxic cells we have examined their ultrastructural morphology and effector cell-target cell membrane contacts. We also studied the sensitivity of these two effector cells to low temperature (4°C). Our results showed that SK effector cells are lymphocytes (10 μm) which contain numerous vacuoles and osmiophilic granules, while IK effectors are another lymphocyte population (up to 12 μm) with a small amount of cytoplasm and few mitochondria. Both IK- and SK-mediated lytic responses were suppressed significantly by low temperature. These observations allow us to propose that frog SK and IK cells may be homologous to mammalian NK and CTL.