NetLogo User Community Models
by Wilfred Ndifon (Submitted: 08/31/2004)
WHAT IS IT?
HIVSIM is an agent-based simulation of HIV immunodynamics that is currently being developped in NetLogo. It allows users to investigate dependencies between various components of the cellular and humoral immune responses to HIV. Users can interactively manipulate simulation parameters (e.g., the number of Th, Tc, and B cells, and the infectivity of viral particles) and, in real-time, observe graphical plots of the results. Additionally, users can simulate antibody and anti-retroviral therapies at various stages of infection (e.g., the user can introduce into the simulation antibodies with affinity for the dominant HIV epitope). HIVSIM is still a work in progress. As time permits, the underlying model will be further calibrated against experimental data to make it robust and applicable to the qualitative evaluation of hypotheses on HIV immunodynamics.
HOW IT WORKS
Described below are some of the entities, interactions, and biological processes implemented in HIVSIM. Except where otherwise noted, information regarding the various interactions and processes came from . Also, some of the parameters used in the simulation were adapted from . For detailed information about the simulation, please see comments within the code.
Let us first of all discuss the prerequisites for a "successul interaction" between two entities. Note that except for nonspecifc interactions such as those involving APCs and cell-free HIV, the outcome (e.g., successful formation of a bond) of most interactions depends on the receptors (or epitopes and paratopes) of the entities involved. Each cellular entity possesses a receptor, represented by a randomly chosen integer belonging to the closed-open interval [0, maxspec), where the upper bound maxspec is determined by the user. Cellular entities also possess HLA1 (human leukocyte antigen type 1) with similar numeric values as their receptors. In additon to HLA1, APCs and B cells also have HLA2. Among the non-cellular entities, viruses have epitopes while antibodies have paratopes. When two entities A and B, say, with receptors x and y, respectively, interact, the probability that their interaction will be successful is given by exp(|x-y|). The closer the numeric values of the interacting entities' receptors, the higher their affinities for each other and, hence, the higher the probability of a successful interaction.
Entities and interactions
T helper (Th) cells: Also known as CD4+ T cells, these cells are the orchestrators of the adaptive immune response to HIV. When a naive Th cell binds to HIV peptides presented on HLA2 surface molecules of antigen presenting cells (APCs) they become activated. Activated Th cells divide to produce memory and effector Th cells (see "Cell Division" below). The short-lived effector Th cells continuously secrete cytokines which participate in the activation of other immune system components including B cells and Tc cells (see below). Upon activation, the long-lived memory Th cells divide, as described below, producing more memory and effector Th cells. Th cells also facilitate the lysis of infected cells by natural killer (NK) cells in a process called antibody dependent cell-mediated cytotoxicity. The gradual depletion of Th cells, a hallmark of HIV pathogenesis, is thought to arise not only from direct hiv-mediated killing of infected Th cells but also from indirect killing of Th cells or activation-induced cell death (AICD) . It is assumed here that this indirect killing of Th cells is a function of the number of infected cells and virions in the vicinity of a Th cell. The parameter AICD is used to simulate this increased susceptibility of Th cells to HIV.
T cytotoxic (Tc) cells: Tc cells are very important in the control of HIV infection. They are activated either by direct contact with APC-activated Th cells or by cytokines. Once activated, they divide and produce memory and effector Tc cells. Effector Tc cells recognize HIV peptides, 9 to 11 nucleotides in length, bound to molecules called human leukocyte antigens type 1 (HLA1) found on most human cell types. Effector Tc cells bind to and kill infected cells displaying such HLA1-peptide complexes on their surfaces, at a rate that is determined by the ctl-rate parameter.Memory Tc cells, on the other hand, afford long-term protection against infection. Upon activation (see naive Tc cell activation) the memory cells divide, as described below.
Antigen-presenting cells (APCs): These include macrophages, dendrites and lymphocytes. All APCs possess HLA2 molecules. Note that if Th cell activation was exclusively dependent on B cell activation, the primary response to HIV would be very slow due to the initial low numbers of B and T cells with affinity for the HIV pathogens. Fortunately, that is not the case; APCs other than B cells can bind non-specifically to HIV. After binding, the APCs ingest, digest and present HLA2-peptide complexes on their surfaces. The binding of Th cells to these complexes activates the Th cells and causes them to divide.
Resupply: To maintain a relatively constant population of all lymphocytes, these cells are continuously produced by the bone marrow and thymus to make up for those lost through apoptosis. During each time step, the half-life and original population size of each class of lymphocytes are used to determine the number of new cells of the given class to be added to the simulation.
Necrosis: During each time step, an infected cell undergoes necrosis or lysis if the number of intracellular viral particles it contains exceeds the viral burst size (i.e., the threshold of viral particles needed to elicit the lysis of an infected cell). Following necrosis, the cell releases new viral particles and is immediately removed from the simulation.
Cell Division: Only stimulated B, Th and Tc cells undergo cell division. A stimulated B cell divides over two time steps producing 4 new cells with the same receptors/specificity as the parent B cell. Fifty percent of the new cells become memory cells while the remaining 50% become plasma cells. The division of a stimulated Th (or Tc) cell follows similar rules with the difference being that 50% of the new cells become long-lived memory Th (or Tc) cells while the remaining 50% become effector Th (or Tc) cells. Note that dividing B cells may undergo hypermutation at a rate determined by the bMut parameter.
HIV infection: During a time step, each un-bound HIV particle is allowed to infect a randomly chosen neighboring cell. The probability of infection is determined by the infectivity of the HIV epitope. If infection occurs, the HIV disappears into the cytoplasm of the infected cell where it integrates its RNA into the cell's DNA. Infected cells present viral peptides on their surface, complexed with HLA1 molecules.
Viral replication: During each time step, HIV particles, found in infected cells, are allowed to replicate - each HIV divides once, producing two new viruses. Each new virus may mutate (i.e., it can be assigned a new randomly chosen (numerical) epitope and peptide). The probability of such mutation is determined by the vMut parameter.
CTL: This denotes the killing of infected cells by Tc cells. During each time step, a Tc cell is allowed to randomly kill one infected cell in its neighborhood/vicinity. The probability that a Tc cell will kill an infected cell on contact is determined by the parameter ctl-rate.
HOW TO USE IT
The interface contains 10 sliders, two switches, six monitors, three plots, and the buttons "Setup" and "Run".
Click the "Setup" button to initialize a new simulation and click "Run" to run the simulation.
The following information is reported during a simulation:
While running a simulation, you can use the Command Center to perform the following:
2) Simulate antibody therapy
3) Simulate anti-retroviral therapy
Also, the values of about 30 global variables can be manipulated from the Procedures Tab.
THINGS TO TRY
Try to determine an optimal choice of parameter values for which each of the following occurs:
Based on your observations, suggest putative critical parameters (e.g., viral infectivity) for the immune response to HIV.
EXTENDING THE MODEL
HIVSIM is still far from being a comprehensive simulation of HIV immunodynamics. A number of other components of the immune response to HIV are yet to be implemented. Listed below are a few of them:
In addition, further calibration with experimental data is necessary in order to make the simulation more robust and less sensitive to small changes in the values of some parameters.
CREDITS AND REFERENCES
Comments and suggestions should be sent to the author, Wilfred Ndifon, at email@example.com
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