Gib Bogle

Agent-based simulation of T-cell activation and proliferation within a lymph node

Recent intravital microscopy experiments have revealed the complex behavior of T cells within lymph nodes. Modeling T‐cell responses in lymph nodes now requires integration of cell trafficking and motility with the molecular processes involved in T‐cell activation. We describe an agent‐based model that allows such integration, in which T cells undertake a random walk through a three‐dimensional representation of the lymph node paracortex, integrating signals from dendritic cells (DCs), and proliferating in response. The model accommodates simulation of a large number of T cells packed at realistic densities, and includes dynamic cell trafficking that allows the lymph nodes to swell and shrink as the immune response progresses. The results from the model, including the kinetics of cognate T‐cell proliferation and release, and the changes in their avidity profile, are similar to those observed in vivo. We therefore propose that this modeling framework is capable of successfully simulating T‐cell activation while also accounting for new spatiotemporal knowledge of how T cells and DCs interact. Although some of the parameters used to drive the model are not yet experimentally validated, the model is capable of testing the effects of alternative values for any parameter on the T‐cell response. We intend to refine each aspect of the model in collaboration with both theoreticians and experimentalists.

Simulating T-cell motility in the lymph node paracortex with a packed lattice geometry

Agent‐based simulation modelling of T‐cell trafficking, activation and proliferation in the lymph node paracortex requires a model for cell motility. Such a model must be able to reproduce the observed random‐walk behaviour of T cells, while accommodating large numbers of tightly packed cells, and must be computationally efficient. We report the development of a motility model, based on a three‐dimensional lattice geometry, that meets these objectives. Cells make discrete jumps between neighbouring lattice sites in directions that are randomly determined from specified discrete probability distributions, which are defined by a small number of parameters. It is shown that the main characteristics of the random motion of T cells as typically observed in vivo can be reproduced by suitable specification of model parameters. The model is computationally highly efficient and provides a suitable engine for a model capable of simulating the full T‐cell population of the paracortex.

On-Lattice Simulation of T Cell Motility, Chemotaxis, and Trafficking in the Lymph Node Paracortex

Agent-based simulation is a powerful method for investigating the complex interplay of the processes occurring in a lymph node during an adaptive immune response. We have previously established an agent-based modeling framework for the interactions between T cells and dendritic cells within the paracortex of lymph nodes. This model simulates in three dimensions the “random-walk” T cell motility observed in vivo, so that cells interact in space and time as they process signals and commit to action such as proliferation. On-lattice treatment of cell motility allows large numbers of densely packed cells to be simulated, so that the low frequency of T cells capable of responding to a single antigen can be dealt with realistically. In this paper we build on this model by incorporating new numerical methods to address the crucial processes of T cell ingress and egress, and chemotaxis, within the lymph node. These methods enable simulation of the dramatic expansion and contraction of the T cell population in the lymph node paracortex during an immune response. They also provide a novel probabilistic method to simulate chemotaxis that will be generally useful in simulating other biological processes in which chemotaxis is an important feature.

T cell responses in lymph nodes

Activation of T cells by antigen‐presenting cells (APCs) in lymph nodes (LNs) is a key initiating event in many immune responses. Our understanding of this process has been both improved and complicated in recent years by evidence from techniques such as intravital microscopy that has revealed new levels of dynamism in the interaction of T cells and APCs. In particular, the complex motility of T cells within LNs, and their serial interactions with many APCs, imply that earlier static models of T cell activation need to be updated. Here we review the first attempts to model T cell interactions with APCs in LNs that incorporate simulations of T cell motility, based on experimental observations. We show that lattice‐based modeling approaches are the dominant trend in these models, and then chart a possible course for development of these models toward spatially‐resolved models of immune responses within LNs. Copyright

Organ-wide 3D-imaging and topological analysis of the continuous microvascular network in a murine lymph node.

Understanding of the microvasculature has previously been limited by the lack of methods capable of capturing and modelling complete vascular networks. We used novel imaging and computational techniques to establish the topology of the entire blood vessel network of a murine lymph node, combining 63706 confocal images at 2 μm pixel resolution to cover a volume of 3.88 mm3. Detailed measurements including the distribution of vessel diameters, branch counts, and identification of voids were subsequently re-visualised in 3D revealing regional specialisation within the network. By focussing on critical immune microenvironments we quantified differences in their vascular topology. We further developed a morphology-based approach to identify High Endothelial Venules, key sites for lymphocyte extravasation. These data represent a comprehensive and continuous blood vessel network of an entire organ and provide benchmark measurements that will inform modelling of blood vessel networks as well as enable comparison of vascular topology in different organs.

Computational design of mixers and pumps for microfluidic systems, based on electrochemically-active conducting polymers

We present a theoretical description of the propagation of composition waves along a strip of electrochemically-active conducting polymer, upon electrochemical stimulation. We develop an efficient solution of the electro-neutral Nernst-Plank equations in 2-D for electromigration and diffusional transport in the solution based on an extension of the methods of Scharfetter and Gummel [D. L. Scharfetter and H. K. Gummel, IEEE Trans. Electron Devices, 1969, ED16, 64-77.] and of Cohen and Cooley [H. Cohen and J. W. Cooley, Biophys. J., 1965, 5, 145-162.], and demonstrate important effects of the geometry of the cell. Under some circumstances, waves reflecting back from the end of the strip are predicted. We then demonstrate theoretically how such waves, associated as they are with expansion of the polymer, could be employed to enhance mixing or induce pumping in microfluidic systems.

A virtual lymph node model to dissect the requirements for T-cell activation by synapses and kinapses

The initiation of T‐cell responses in lymph nodes requires T cells to integrate signals delivered by dendritic cells (DCs) during long‐lasting contacts (synapses) or more transient interactions (kinapses). However, it remains extremely challenging to understand how a specific sequence of contacts established by T cells ultimately dictates T‐cell fate. Here, we have coupled a computational model of T‐cell migration and interactions with DCs with a real‐time, flow cytometry‐like representation of T‐cell activation. In this model, low‐affinity peptides trigger T‐cell proliferation through kinapses but we show that this process is only effective under conditions of high DC densities and prolonged antigen availability. By contrast, high‐affinity peptides favor synapse formation and a vigorous proliferation under a wide range of antigen presentation conditions. In line with the predictions, decreasing the DC density in vivo selectively abolished proliferation induced by the low‐affinity peptide. Finally, our results suggest that T cells possess a biochemical memory of previous stimulations of at least 1–2 days. We propose that the stability of T‐cell–DC interactions, apart from their signaling potency, profoundly influences the robustness of T‐cell activation. By offering the ability to control parameters that are difficult to manipulate experimentally, the virtual lymph node model provides new possibilities to tackle the fundamental mechanisms that regulate T‐cell responses elicited by infections or vaccines.

Design of a microfluidic pump, based on conducting polymers

Electrochemically-active conducting polymers (ECP) swell or shrink in response to ion and solvent incorporation or ejection as a result of electrochemical reaction of the polymer. As a consequence, they are, in principle, attractive materials to consider for inducing fluid motion of electrolytes in microfluidic systems. When anodic potential is applied to an electrode attached to one end of ECP strip, the oxidation process starts from the electrode and proceeds along the polymer, propagating as a wave. This wave is driven as a consequence of the electrochemical reactions and would be coupled to a propagating front of compositional change. This property of the ECP can be used to design pumps and mixers for microfluidic systems. We in this paper set up a 2-D transport model to explain this wave phenomenon that includes both diffusion and electro-migration, that is coupled to the reaction at the polymer-solution interface, and that also includes the effects of change of polymer conductivity on the charge transport in the polymer layer. We explore the design for a microfluidic pump that uses this process and its efficiency to pump electrolytes.

An agent-based model for drug-radiation interactions in the tumour microenvironment: Hypoxia-activated prodrug SN30000 in multicellular tumour spheroids

Multicellular tumour spheroids capture many characteristics of human tumour microenvironments, including hypoxia, and represent an experimentally tractable in vitro model for studying interactions between radiotherapy and anticancer drugs. However, interpreting spheroid data is challenging because of limited ability to observe cell fate within spheroids dynamically. To overcome this limitation, we have developed a hybrid continuum/agent-based model (ABM) for HCT116 tumour spheroids, parameterised using experimental models (monolayers and multilayers) in which reaction and diffusion can be measured directly. In the ABM, cell fate is simulated as a function of local oxygen, glucose and drug concentrations, determined by solving diffusion equations and intracellular reactions. The model is lattice-based, with cells occupying discrete locations on a 3D grid embedded within a coarser grid that encompasses the culture medium; separate solvers are employed for each grid. The generated concentration fields account for depletion in the medium and specify concentration-time profiles within the spheroid. Cell growth and survival are determined by intracellular oxygen and glucose concentrations, the latter based on direct measurement of glucose diffusion/reaction (in multilayers) for the first time. The ABM reproduces known features of spheroids including overall growth rate, its oxygen and glucose dependence, peripheral cell proliferation, central hypoxia and necrosis. We extended the ABM to describe in detail the hypoxia-dependent interaction between ionising radiation and a hypoxia-activated prodrug (SN30000), again using experimentally determined parameters; the model accurately simulated clonogenic cell killing in spheroids, while inclusion of reversible cell cycle delay was required to account for the marked spheroid growth delay after combined radiation and SN30000. This ABM of spheroid growth and response exemplifies the utility of integrating computational and experimental tools for investigating radiation/drug interactions, and highlights the critical importance of understanding oxygen, glucose and drug concentration gradients in interpreting activity of therapeutic agents in spheroid models.

Bystander Effects of Hypoxia-Activated Prodrugs: Agent-Based Modeling Using Three Dimensional Cell Cultures

Intra-tumor heterogeneity represents a major barrier to anti-cancer therapies. One strategy to minimize this limitation relies on bystander effects via diffusion of cytotoxins from targeted cells. Hypoxia-activated prodrugs (HAPs) have the potential to exploit hypoxia in this way, but robust methods for measuring bystander effects are lacking. The objective of this study is to develop experimental models (monolayer, multilayer, and multicellular spheroid co-cultures) comprising ‘activator’ cells with high expression of prodrug-activating reductases and reductase-deficient ‘target’ cells, and to couple these with agent-based models (ABMs) that describe diffusion and reaction of prodrugs and their active metabolites, and killing probability for each cell. HCT116 cells were engineered as activators by overexpressing P450 oxidoreductase (POR) and as targets by knockout of POR, with fluorescent protein and antibiotic resistance markers to enable their quantitation in co-cultures. We investigated two HAPs with very different pharmacology: SN30000 is metabolized to DNA-breaking free radicals under hypoxia, while the dinitrobenzamide PR104A generates DNA-crosslinking nitrogen mustard metabolites. In anoxic spheroid co-cultures, increasing the proportion of activator cells decreased killing of both activators and targets by SN30000. An ABM parameterized by measuring SN30000 cytotoxicity in monolayers and diffusion-reaction in multilayers accurately predicted SN30000 activity in spheroids, demonstrating the lack of bystander effects and that rapid metabolic consumption of SN30000 inhibited prodrug penetration. In contrast, killing of targets by PR104A in anoxic spheroids was markedly increased by activators, demonstrating that a bystander effect more than compensates any penetration limitation. However, the ABM based on the well-studied hydroxylamine and amine metabolites of PR104A did not fit the cell survival data, indicating a need to reassess its cellular pharmacology. Characterization of extracellular metabolites of PR104A in anoxic cultures identified more stable, lipophilic, activated dichloro mustards with greater tissue diffusion distances. Including these metabolites explicitly in the ABM provided a good description of activator and target cell killing by PR104A in spheroids. This study represents the most direct demonstration of a hypoxic bystander effect for PR104A to date, and demonstrates the power of combining mathematical modeling of pharmacokinetics/pharmacodynamics with multicellular culture models to dissect bystander effects of targeted drug carriers.