Abstract
The interaction among leukocytes is at the basis of the innate and adaptive immune-response and it is largely ascribed to direct cell-cell contacts. However, the exchange of a number of chemical stimuli (chemokines) allows also non-contact interaction during the immunological response. We want here to evaluate the extent of the effect of the non-contact interactions on the observed leukocyte-leukocyte kinematics and their interaction duration. To this aim we adopt a simplified mean field description inspired by the Keller-Segel chemotaxis model, of which we report an analytical solution suited for slowly varying sources of chemokines. Since our focus is on the non-contact interactions, leukocyte-leukocyte contact interactions are simulated only by means of a space dependent friction coefficient of the cells. The analytical solution of the Keller-Segel model is then taken as the basis of numerical simulations of interactions between leukocytes and their duration. The mean field interaction force that we derive has a time-space separable form and depends on the chemotaxis sensitivity parameter as well as on the chemokines diffusion coefficient and their degradation rate. All these parameters affect the distribution of the interaction durations. We draw a successful qualitative comparison between simulated data and sets of experimental data for DC-NK cells interaction duration and other kinematic parameters. Remarkably, the predicted percentage of the leukocyte-leukocyte interactions falls in the experimental range and depends (≅25% increase) upon the chemotactic parameter indicating a non-negligible direct effect of the non-contact interaction on the leukocyte interactions.
Highlights
The Immune System defends our organism from pathogens via innate and adaptive immune responses that are triggered by a cascade of interactions between different leukocytes [1]
The simulation of the Natural Killer (NK) motion around dendritic cells was developed within the simplified framework described in the Introduction
We have carried out a validation of the numerical model employed here by comparing simulated and experimental data on an extended set of additional geometrical and kinematic parameters of the NK cells motion
Summary
The Immune System defends our organism from pathogens via innate and adaptive immune responses that are triggered by a cascade of interactions between different leukocytes [1]. Recent reports showed clear evidence that DCs play a major role in the activation of Natural Killer (NK) cells This process involves direct DC-NK cell interactions [2,3,4] and release of a number of cytokines [5]. The interactions between leukocytes have been visualized with a number of imaging techniques [6] Effective to this aim are recent Two-Photon Microscopy (TPM) studies. This approach allows to quantify the cell diffusion coefficients, the statistics of the cell motion [7] and the duration and distribution of cell-cell interaction times [8,9,10,11,12,13]. Additional problems arise from the limited observation time window and by the loss of tracking due to poor signal/ noise in the images [7]
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