The simulation of density-dependent effects in the recirculation of T lymphocytes

COMPUTATIONAL MODEL OF RECIRCULATING LYMPHOCYTES

Lymphocyte recirculation plays an important role in controlling the spread of both pathogenic infections and tumor-producing cancer cells in the human body. We present a mathematical and computational framework that allows investigation of recirculating lymphocytes and estimation of model parameters using a genetic algorithm. The framework allows estimating parameters using data obtained from experiments performed in laboratory studies of rats as well as clinical studies of human subjects. Our computational model allows improved understanding of these data. Mathematical models enable investigators to obtain a quantitative picture of immune system kinetics and diversity in human health and disease outcomes. Our data-driven systems biology and immunological modeling approach contributes to a growing understanding of the dynamics of lymphocyte recirculation.

Random migration and signal integration promote rapid and robust T cell recruitment

To fight infections, rare T cells must quickly home to appropriate lymph nodes (LNs), and reliably localize the antigen (Ag) within them. The first challenge calls for rapid trafficking between LNs, whereas the second may require extensive search within each LN. Here we combine simulations and experimental data to investigate which features of random T cell migration within and between LNs allow meeting these two conflicting demands. Our model indicates that integrating signals from multiple random encounters with Ag-presenting cells permits reliable detection of even low-dose Ag, and predicts a kinetic feature of cognate T cell arrest in LNs that we confirm using intravital two-photon data. Furthermore, we obtain the most reliable retention if T cells transit through LNs stochastically, which may explain the long and widely distributed LN dwell times observed in vivo. Finally, we demonstrate that random migration, both between and within LNs, allows recruiting the majority of cognate precursors within a few days for various realistic infection scenarios. Thus, the combination of two-scale stochastic migration and signal integration is an efficient and robust strategy for T cell immune surveillance.

Mathematical modeling reveals kinetics of lymphocyte recirculation in the whole organism

The kinetics of recirculation of naive lymphocytes in the body has important implications for the speed at which local infections are detected and controlled by immune responses. With a help of a novel mathematical model, we analyze experimental data on migration of 51Cr-labeled thoracic duct lymphocytes (TDLs) via major lymphoid and nonlymphoid tissues of rats in the absence of systemic antigenic stimulation. We show that at any point of time, 95% of lymphocytes in the blood travel via capillaries in the lung or sinusoids of the liver and only 5% migrate to secondary lymphoid tissues such as lymph nodes, Peyer's patches, or the spleen. Interestingly, our analysis suggests that lymphocytes travel via lung capillaries and liver sinusoids at an extremely rapid rate with the average residence time in these tissues being less than 1 minute. The model also predicts a relatively short average residence time of TDLs in the spleen (2.5 hours) and a longer average residence time of TDLs in major lymph nodes and Peyer's patches (10 hours). Surprisingly, we find that the average residence time of lymphocytes is similar in lymph nodes draining the skin (subcutaneous LNs) or the gut (mesenteric LNs) or in Peyer's patches. Applying our model to an additional dataset on lymphocyte migration via resting and antigen-stimulated lymph nodes we find that enlargement of antigen-stimulated lymph nodes occurs mainly due to increased entrance rate of TDLs into the nodes and not due to decreased exit rate as has been suggested in some studies. Taken together, our analysis for the first time provides a comprehensive, systems view of recirculation kinetics of thoracic duct lymphocytes in the whole organism.

Directional migration of recirculating lymphocytes through lymph nodes via random walks

Naive T lymphocytes exhibit extensive antigen-independent recirculation between blood and lymph nodes, where they may encounter dendritic cells carrying cognate antigen. We examine how long different T cells may spend in an individual lymph node by examining data from long term cannulation of blood and efferent lymphatics of a single lymph node in the sheep. We determine empirically the distribution of transit times of migrating T cells by applying the Least Absolute Shrinkage & Selection Operator (LASSO) or regularised S-LASSO to fit experimental data describing the proportion of labelled infused cells in blood and efferent lymphatics over time. The optimal inferred solution reveals a distribution with high variance and strong skew. The mode transit time is typically between 10 and 20 hours, but a significant number of cells spend more than 70 hours before exiting. We complement the empirical machine learning based approach by modelling lymphocyte passage through the lymph node insilico. On the basis of previous two photon analysis of lymphocyte movement, we optimised distributions which describe the transit times (first passage times) of discrete one dimensional and continuous (Brownian) three dimensional random walks with drift. The optimal fit is obtained when drift is small, i.e. the ratio of probabilities of migrating forward and backward within the node is close to one. These distributions are qualitatively similar to the inferred empirical distribution, with high variance and strong skew. In contrast, an optimised normal distribution of transit times (symmetrical around mean) fitted the data poorly. The results demonstrate that the rapid recirculation of lymphocytes observed at a macro level is compatible with predominantly randomised movement within lymph nodes, and significant probabilities of long transit times. We discuss how this pattern of migration may contribute to facilitating interactions between low frequency T cells and antigen presenting cells carrying cognate antigen.

Lack of functional selectin ligand interactions compromises long term tumor protection by CD8+ T cells

Central memory CD8⁺ T cells expressing the adhesion molecule CD62L (L-selectin) are potent mediators of anti-cancer immunity due to their ability to proliferate extensively upon antigen re-stimulation. The interaction of selectin with its ligands mediates leukocyte rolling along high endothelial venules. Mice deficient in α(1,3) Fucosyltransferase IV and VII (FtDKO) lack functional L, P and E selectin ligands. Thus, we addressed whether the lack of selectin ligand interactions alters tumor protection by CD8⁺ T cells in FtDKO mice. Listeria monocytogenes-OVA (LM-OVA) infection evoked potent OVA-specific CD8⁺ T cells that proliferated and contracted at similar kinetics and phenotype in FtDKO and wild-type mice. Additionally, OVA-specific CD8⁺ T cells in both mouse strains exhibited similar phenotypic differentiation, in vivo cytolytic activity and IFN-γ expression. However, FtDKO mice succumbed to B16-OVA tumors significantly earlier than wild-type mice. In contrast, FtDKO mice evoked strong recall memory CD8⁺ T cell responses and protection to systemic LM-OVA re-challenge. The diminished tumor protection in FtDKO mice was not related to defective antigen presentation by dendritic cells or reduced proliferation of antigen-specific CD8⁺ T cells. However, WT or FtDKO OVA-specific CD8⁺ T cells showed significantly reduced ability to traffic to lymph nodes upon adoptive transfer into naïve FtDKO recipients. Furthermore, FtDKO OVA-specific CD8⁺ T cells displayed poor ability to infiltrate tumors growing in WT mice. These results reveal that selectin ligand expression on host endothelium as well CD8⁺ T cells may be important for their efficient and continued extravasation into peripheral tumors.

Memory T cells are enriched in lymph nodes of selectin-ligand-deficient mice

Fucosyltransferase-IV and -VII double knockout (FtDKO) mice reveal profound impairment in T cell trafficking to lymph nodes (LNs) due to an inability to synthesize selectin ligands. We observed an increase in the proportion of memory/effector (CD44(high)) T cells in LNs of FtDKO mice. We infected FtDKO mice with lymphocytic choriomeningitis virus to generate and track Ag-specific CD44(high)CD8 T cells in secondary lymphoid organs. Although frequencies were similar, total Ag-specific effector CD44(high)CD8 T cells were significantly reduced in LNs, but not blood, of FtDKO mice at day 8. In contrast, frequencies of Ag-specific memory CD44(high)CD8 T cells were up to 8-fold higher in LNs of FtDKO mice at day 60. Because wild-type mice treated with anti-CD62L treatment also showed increased frequencies of CD44(high) T cells in LNs, we hypothesized that memory T cells were preferentially retained in, or preferentially migrated to, FtDKO LNs. We analyzed T cell entry and egress in LNs using adoptive transfer of bone fide naive or memory T cells. Memory T cells were not retained longer in LNs compared with naive T cells; however, T cell exit slowed significantly as T cell numbers declined. Memory T cells were profoundly impaired in entering LNs of FtDKO mice; however, memory T cells exhibited greater homeostatic proliferation in FtDKO mice. These results suggest that memory T cells are enriched in LNs with T cell deficits by several mechanisms, including longer T cell retention and increased homeostatic proliferation.

Scaling aspects of lymphocyte trafficking

We consider the long lived pool of B and T cells that recirculate through blood, tissues and the lymphatic system of an animal with body mass M. We derive scaling rules (allometric relations) for: (1) the rate of production of mature lymphocytes, (2) the accumulation of lymphocytes in the tissues, (3) the flux of lymphocytes through the lymphatic system, (4) the number of lymph nodes, (5) the number of lymphocytes per clone within a lymph node, and (6) the total number of lymphocytes within a lymph node. Mass-dependent aspects of immune learning and of the immunological self are shown to be not very significant. Our treatment is somewhat heuristic and aims at combining immunological data with recent progress in biological scaling.

Identification of two mutually exclusive groups after long-term monitoring of HIV DNA 2-LTR circle copy number in patients on HAART

BACKGROUND

Anti-retroviral drug therapy reduces but does not abolish HIV transmission and replication throughout the body. HIV DNA 2-long terminal repeat (2-LTR) circles have been shown in point-based studies to persist in some patients whose plasma HIV RNA was undetectable. However, the degree of fluctuation of circle copy number over time has not been determined.

METHODS

A reliable, reproducible and robust quantitative LightCycler (LC qPCR)-based assay for HIV DNA 2-LTR circles in peripheral blood mononuclear (PBMN) cells was established. A prospective, longitudinal study of these circles was undertaken in HIV-1-positive patients on anti-retroviral therapy whose plasma HIV RNA was undetectable at < 50 copies/ml. Patients starting therapy for the first time were also monitored.

RESULTS

A cohort of 60 patients whose plasma HIV RNA was undetectable for 32 +/- 2 months were monitored for circles for 15 +/- 2 months. The circle copy number ranged from < 10 to 620 copies/106 PBMN cells. The circle-negative (< 10 copies/1 x 106 PBMN) cells group of 36 patients and the circle-positive (> 10 copies/106 PBMN cells) group of 24 patients were mutually exclusive (P < 0.0001). The mean circle half-life in seven of the 10 patients starting anti-retroviral therapy for the first time was 5.7 days.

CONCLUSION

The circle assay is useful for identifying those patients in whom transmission of infectious virus continues despite prolonged periods of time during which plasma HIV RNA is undetectable. New drug combinations and new therapeutic approaches should be aimed at those patients whose plasma HIV RNA is undetectable but who remain positive for 2-LTR circles.

An application of linear output error modelling for studying lymphocyte migration in peripheral lymphoid tissues

Lymphocyte recirculation between lymphatic and blood vessels and migration through tissues are essential mechanisms underlying immunological surveillance. However, the kinetics of lymphocyte migration through lymphoid tissues remains poorly understood. The present study of lymphocyte migration, based on a sheep model and entailing the long term cannulation of blood vessels and lymphatic vessels efferent from lymph nodes, represents the first attempt to apply control engineering based models to overcome some of the experimental impediments to understanding the complex phenomena involved in lymphocyte migration. An output error model order (1,2,nk) was systematically selected under given criteria from four classes of Linear Time-Invariant Single-Input Single-Output, (LTI-SISO) systems to represent the peripheral lymph node system. The unit impulse responses were simulated under noise free conditions and their features were extracted to describe the dynamics of the system. The findings from this study revealed novel information about several aspects of the dynamics of lymphocyte migration.

Modelling of peripheral lymphocyte migration: system identification approach

This is the first application of the prediction error method (PEM) of system identification to modelling lymphocyte migration through peripheral lymphoid tissue. The PEM was applied to the emergence of labelled lymphocytes from the efferent lymphatic of a lymph node following their intravenous administration. Advantages of PEM included the capacity to calculate the response to a unit impulse stimulus, unavailable to direct observation, and to allow for the return to the node of labelled cells that had already recirculated once. Calculation of the system delay (time between introduction of cells into the blood and their first appearance in lymph) indicated 4.67 +/- 1.05 h for the total lymphocyte population. The peak in efferent lymph occurred at 11.91 +/- 4.68 h, much earlier than previous reports, which were affected by cells that had already recirculated. While 75% of labelled cells had emerged in efferent lymph by 20.77 +/- 5.62 h, 86.38 +/- 29.44 h was required for 100% emergence. The considerable heterogeneity in migratory behaviour is likely to reflect frequency and duration of binding of lymphocytes by dendritic cells in paracortical cord corridors. It is proposed that differences in the speed with which lymphocytes pass along corridors depend on their functional status, in particular whether they are naïve or memory cells.