A case for the reuse and adaptation of mechanistic computational models to study transplant immunology

Abstract

Computational mechanistic models constitute powerful tools to summarize our knowledge in quantitative terms, provide mechanistic understanding, and generate new hypotheses. The present review emphasizes the advantages of reusing publicly available computational models as a way to capitalize on existing knowledge, reduce the number of parameters that need to be adjusted to experimental data, and facilitate hypothesis generation. Finally, it includes a step-by-step example of the reuse and adaptation of an existing model of immune responses to tuberculosis, tumor growth, and blood pathogens, to study donor-specific antibody (DSA) responses. This review aims to illustrate the benefit of leveraging the currently available computational models in immunology to accelerate the study alloimmune responses, and to encourage modelers to share their models to further advance our understanding of transplant immunology.

INTRODUCTION

When deciding whether to use computational models to study transplant immunology mechanisms, researchers are faced with two main questions: (i) what are computational models useful for?, and (ii) should I build my own model or use one that already exists and adapt it?

This review aims to provide answers to these questions by explaining the advantages in the use of computational models, reviewing examples of how the use of computational models has successfully furthered our understanding of alloimmune responses, and presenting the advantages of the reuse of publicly available immune mechanistic computational models to study key questions immune questions in transplant.

STRENGTHS of MECHANISTIC COMPUTATIONAL MODELS

Computational models are mathematical descriptions of biological processes that are useful tools (i) to summarize knowledge in quantitative terms, (ii) to provide mechanistic understanding of biological processes, and (iii) to generate new hypotheses (1–3).

To summarize knowledge in quantitative terms.

Building computational models is indeed not conceptually different from performing a literature search of the biological system under study (e.g. immune system, lungs, cells, etc.) and constructing a diagram with all the relevant players (e.g. cell types, molecular entities) and processes (e.g. chemical reactions, cell-to-cell interactions) that influence its response or behavior. Creating this type of diagram or working model is a task commonly used by most researchers to help guide the design of experiments. However, some key biological features are difficult to incorporate in this type of representation, namely the fact that different processes typically act at different time scales and with different strengths. The quantitative nature of a computational model not only overcomes this limitation, but also provides the opportunity to scale up the number of molecules/cells/processes followed in the model to a degree which quickly becomes too complicated for a classic ‘pen-and-paper’ diagram.

To provide mechanistic understanding of biological processes.

Biological processes and physiological responses are tightly regulated. Regulation mechanisms are typically redundant and activated in certain physiological circumstances. A computational model provides the opportunity to simulate different environmental conditions and understand which mechanisms are responsible for shaping the response of the biological system in each situation.

To generate new hypotheses.

Computational models allow us to test hypotheses in silico through simulation in a fraction of the time and at a reduced cost when compared to experiments. As an example, a research group could generate predictions on the effects of selectively blocking in their relevant computational model key chemical reactions along a signaling pathway of interest and simulating the cell’s response. In turn, this would allow these researchers to rank targets based on their likelihood to have an impact on the overall signaling response and to prioritize the experiments needed to be performed, which will maximize the chances of success in finding the right inhibitor.

SHARING COMPUTATIONAL MODELS in IMMUNOLOGY and ADVANTAGES of REUSING an EXISTING MODEL

Sharing computational models with the research community is deemed of such importance (4, 5) that different unifying formats have been created to standardize model sharing in a platform-agnostic fashion (6–8), one of the most extensively used being the Systems Biology Markup Language (SBML). SBML is a free and open interchange file format for computer models of biological processes (http://sbml.org). By using SBML as input/output format to describe the computational model, different tools and platforms can all operate on an identical representation of the model, removing opportunities for translation errors and guaranteeing a common starting point for analyses and simulations (9, 10). Although not all models are currently available in SBML, the modeling community is putting a significant effort into publishing models in this format, and creating tools to convert SBML models developed in different platforms/languages such as MATLAB to SBML (11), simulate SBML models, and test them (see Table 1)

Table 1.

Relevant resources available to the research community for computational model reuse

Name / Location	Resource Description
BioModels (www.ebi.ac.uk/biomodels)	Model Repository. 255 Immune Models
CellML (www.cellml.org)	Model Repository. 65 Immune Models
ModelDB (www.senselab.med.yale.edu)	Model Repository. Mostly Neuronal Models but also Macrophage and B cell signaling
DOQCS Database of Quantitative Cellular Signaling (www.doqcs.ncbs.res.in)	Model repository. Focused on signaling networks.
COPASI (www.copasi.org)	Freeware software for simulation analysis of biochemical networks and their dynamics. Imports and exports SBML formats.
NetLogo	Multi-agent programmable modeling environment to create and simulate agent-based models (ABM)
Cell Designer (www.celldesigner.com)	Structure diagram editor for drawing gene-regulatory and biochemical networks
SBML Team Github (www.github.com/sbmlteam)	Repository of SBML-related tools to test, curate, and convert models in other formats.
Web Plot Digitizer (https://automeris.io/WebPlotDigitizer/)	Freeware tool to digitize data from graphs.

Numerous public repositories of computational models are available (Table 1). Although frequently models are attached as supplementary materials to a given manuscript, public repositories increase accessibility/visibility and improve model usability by providing accurate descriptions and appropriate values for all of the elements in the model (curation) and working together with the authors to ensure that the major findings of the paper can be recapitulated. Most publicly available models in immunology describe immune responses in cancer and to viral infection (e.g. 235 immune models in Biomodels, and 65 immune models in CellML). These models are available for use, and more importantly, can be either expanded or adapted to study transplant immunology questions, as outlined below.

Reusing existing computational models has major advantages: (i) it capitalizes on the existing knowledge, (ii) it reduces the number of parameters that need to be adjusted to the experimental data of interest since most of them are reused and have been previously curated, (iii) it results in models whose behavior is more versatile as reused models are typically fit (i.e. their parameters adjusted to experimental data) to reproduce multiple behaviors observed experimentally, and (iv) allows researchers to test new hypotheses faster. The major limitations in reusing a model instead of building the model from scratch include the lack of availability of an existing model that describes the biology the researcher is interested in and the potential low ‘usability’ of the model if it is not well curated, which might make the original intent of the model and its assumptions unclear to the user. The current emphasis put on sharing and curating computational models should mitigate the effect of these limitations.

COMPUTATIONAL MODELS in TRANSPLANT IMMUNOLOGY

The use of mechanistic computational models in transplant is lagging behind other immunology fields such as infection and cancer immunology (see (12–16) for recent representative examples and (17, 18) for relevant reviews). Multiple processes are involved in the alloimmune response to a transplanted organ. These processes can be grouped in phases, all of which are amenable to be studied with the aid of computational models: early inflammation and ischemia/reperfusion injury, antigen recognition, activation and expansion of donor-reactive T and B cells, effector functions of these cells, and resolution of the response with residual memory. In this section, we provide an outline of three of these phases in the context of solid organ transplant, discuss mechanistic models that have been implemented, and provide ideas on how alternative implementations and/or additional expansions might help provide mechanistic insight.

Early inflammation and Ischemia/Reperfusion Injury (IRI).

Ischemia reperfusion and surgical trauma elicit production of oxygen radicals and damage-associated molecular patterns (DAMPS) which in turn activate the complement cascade, toll-like receptor (TLR) signaling, and mediate chemokine production and recruitment of neutrophils. Importantly, this inflammatory milieu renders the organ more susceptible to T cell and antibody damage.

A useful tool to study this process would be a three compartment (graft, secondary lymphoid organs, and blood) ordinary differential equation (ODE) mechanistic model that incorporates different inflammatory cascades and has as outputs inflammatory cytokine levels in each compartment, such as tumor-necrosis factor alpha (TNFα, interleukin (IL)1β and IL6, as well as the number of neutrophils and lymphocytes in the graft. The model could then be fitted to both to experimental data from a mouse transplant model of IRI in which the graft BALB/c hearts are exposed to different cold ischemia time before being transplanted into C57BL/6 mice (19, 20), and to measurements of human inflammatory cytokine levels in serum of peripheral blood of transplant recipients. One such model, could allow us to interpret mechanistically the effects of drugs that target early-inflammation cytokines currently in clinical trials on different cell subsets and their contribution to the overall aggregate immune response in the graft (e.g. infliximab, a monoclonal antibody against TNFα in kidney transplant, Clinical Trials in Organ Transplantation (CTOT)-19, or tocilizumab a monoclonal humanized anti-IL6 receptor antibody in cardiac transplantation, NCT03644667). It could also generate new mechanistic hypotheses for these therapeutics and help explore potential synergistic effects of these agents for induction. Simulations of one such model, an ODE compartment model by Day and colleagues (21), suggest that the extent of graft damage and the IRI can be well-tolerated by the recipient when each is present alone, but that their combination along with antigenic mismatch may lead to acute rejection. The authors also used the model to hypothesize that low-level DAMP release can tolerize the recipient to a mismatched allograft.

T cell activation and polarization.

T cell activation and polarization play a major role in transplantation outcome. Alloreactive T cell differentiation in the lymph nodes and the spleen yields CD4⁺ T helper (T_H)1, and CD8⁺ cytotoxic T lymphocytes, which can then circulate to the graft and mediate injury. CD4⁺ T cell differentiation is a critical step in promoting allograft tolerance. Evidence from many research labs using preclinical animal models support the conclusion that CD4⁺ Foxp3⁺ regulatory T cells (T_REG) inhibit effector T cells (T_eff) including T_H1, limit allograft injury, and promote allograft tolerance (22, 23).

Examples of computational models that integrate innate immune responses with T cell-mediated graft injury are found in the mechanistic ODE model developed by Arciero and colleagues (24) and a model in which each graft cell and immune cell is simulated and followed individually (ABM, agent-based model) and that studies the non-linear interactions of effector and regulatory immune responses as well as immunosuppression in the graft at the levels of individual cells (25). ODE models have also been employed to study the direct and indirect mechanism of T cell activation during transplant (26), and the interplay between immunosuppression and effective immune system control of viral infections on renal transplant patients (27).

Computational models of CD4⁺ T cell polarization calibrated to alloimmune responses could prove invaluable to understand how different cytokine combinations promote a more favorable T_REG/T_eff balance in the graft. Several mechanistic computational models of T cell polarization with different levels of detail are available in BioModels repository databases (Table 1) including cytokine signaling in the cells and regulation of transcriptional programs through master transcription factor regulators associated with different T cell subsets. One of these existing models, for example the ODE two-compartment deterministic model from the Virginia Computational Biology Group (28) (10 cytokine inputs, 56 reactions, 98 molecular species) could be expanded to include molecular targets of current transplant drugs (tacrolimus, co-stimulatory blockade), and subsequently calibrated and fitted to alloimmune response human and murine experimental data both from in vitro T cell polarization experiments and from alloimmune responses in transplant. The resulting model could then be used to explore the effects of new proposed drugs on T cell polarization (anti-IL6 or anti-IL6R) in vivo, their effects on key master regulator dynamics (T-bet, RORγt, GATA-3 and Foxp3) in order to devise new strategies to promote endogenous T_REG. It could also be utilized to simulate the induction and expansion of T_REG in vitro and generate hypotheses on how to enhance their stability for autologous T_REG infusions, a strategy currently pursued by several labs.

B cell activation and production of donor-specific antibodies and memory.

Activation of B cells and their differentiation into antibody-producing plasma cells is a tightly orchestrated process which involves activation of B cells by T cells and migration to the germinal center, B cell proliferation, somatic mutation and affinity maturation (isotype switching), and exit of the germinal center as high-affinity antibody-secreting cells (plasma cells) or memory B cells. This whole process is regulated at different time scales and locations (e.g. dark zone vs. light zone of the germinal center). Understanding the interplay between these mechanisms and which ones are more amenable to being targeted in order to prevent the formation of de novo donor-specific antibodies (DSA) could be aided by a computational model. More specifically, and as an example, one could build an ABM in which we could simulate individual B cell journeys since their activation by a T cell through the germinal center to their final fate as short-lived plasma cells or alloreactive B cell memory cells. Calibrating this model using mouse experimental data on the number of donor-reactive plasma cells and memory B cells formed following a transplant as function of time would allow us to start testing in silico which molecules control the balance between short-lived plasma cells and alloreactive B memory cells which might have deleterious effects upon reactivation (29–31). A different strategy would be to reuse an existing ODE B cell mechanistic model and adapt it for alloimmune responses as described in the following section.

EXAMPLE of the REUSE and ADAPTATION OF a PUBLICLY AVAILABLE COMPUTATIONAL MODEL to STUDY DSA FORMATION

As a direct illustration of how to reuse publicly available models, we describe how to adapt an existing model of immune responses to TB, tumor growth, and bloodborne pathogens from the BioModels repository (32) to study DSA formation (Fig. 1).

Figure 1. DSA production model obtained through the reuse existing publicly available model.

A model of B cell responses publicly available (32) (52 state variables, 140 reactions or fluxes, 278 constants) was simplified/adapted to be reused as a model to study DSA formation with 30 state variables, 39 fluxes and 42 constants, as described in the main text. The model expands 3 compartments (Immunization Site, Lymph Node, and Blood) and the lymphatics connecting these compartments are not explicitly represented. The most relevant state variables (15) and fluxes (27) are depicted in the figure. Interactions are depicted in grey dashed lines and represent the modulatory effects of the concentration of one species on a flux, but do not always imply direct interactions among species.

Step 1. Model download and appropriate model description.

In order to expand/simplify mechanistic ODE models, it is useful to utilize a general governing equation to describe the dynamics of cell and mass balance as dx/dt = S*v(x;k), where x is the vector of state variables (concentrations of various cell types and molecules) and v is the vector of fluxes from one state to the next (i.e. movement of cells between compartments or migration, reaction rates, cellular fate processes such as apoptosis, etc., expressed in concentrations per unit time). S is a matrix that describes the structure of the network and its topology and .. Each column in S represents a flux, each row, a state variable. Vector k contains the numerical values of kinetic and physical constants characterizing transport and reaction processes. Most ODE models can be mathematically summarized using formalism, which is versatile for integrating different models with different compartments and allows the user to expand/remove features as needed. The model was downloaded in SBML format and imported in the COPASI (33) environment, which supports this type of formalism, to perform next steps (the model files are available as supplemental material).

Step 2. Model simplification (or expansion).

The downloaded model (52 state variables, 140 reactions, 278 constants) contained multiple processes of no relevance to our study (e.g. replication of TB in macrophages or tumor debris formation) and was thus simplified to create a model of the DSA formation in response to alloantigen. The new model contains 30 state variables (x) distributed among 3 compartments (graft, lymph nodes, and blood), 39 fluxes (v) characterized by 42 constants (k), and a connectivity matrix as illustrated (Fig. 1). Included in the model are alloantigen concentration in the graft, DC maturation, migration, presentation of antigen to T cells in the lymph node, B cell activation by the antigen and T cell help, plasma cell and B cell memory (Bmem) generation, and antibody secretion by plasma cells. This was achieved through the removal of the irrelevant state variables (x_R) and fluxes (v_R) in a stepwise fashion from the network. To ensure quality control of the simplified model, prior to removing any population of cells or molecules, all fluxes related to that state variable were turned off one at a time and conservation of mass was confirmed, thus ensuring that no arbitrary gains or losses occur during model simplification (34, 35). The simplified model contained the same compartments as the original model, hence no flux correction for volume heterogeneity was required (36).

Step 3. Calibrate model to primary immunization.

In order to calibrate the model to responses without pre-existing immunity, the model was simulated with no initial donor-specific cells (Bmem=0, Plasma cells=0, Antibody=0). The model simulation (using a dose of alloantigen as input) was then fitted to published experimental time course data of IgG DSA measured during first 10 weeks post subcutaneous immunization of C57BL/6 mice with BALB/c splenocytes from Chong’s group (37), which was digitized using a freeware tool to digitize plots (Table 1). In order to calibrate the first immunization we adjusted simultaneously 3 of the 42 constants which characterize fluxes v21, v26 and v24 on of the model (Fig. 1) to the 5 data points available (Genetic Algorithm (38): # generations=200, # population size 20, available in COPASI) while keeping other values to those based on literature and calibrated in the original model (Fig. 2A).

Figure 2. Calibration of the DSA production model.

(A) Overlay of the fitted model (red line) to DSA flow cytometry data (mean fluorescence intensity MFI) experimental data available from the literature (37) of antibody responses following primary (week 0) and secondary (week 10) immunizations of C57BL/6 mice with BALB/c spleen cells. (B) Model simulations of plasma cells and B memory cell numbers over time, which should be calibrated in subsequent steps with additional experimental data.

Step 4. Calibrate the model to recall responses.

In order to calibrate the model to the second immunization recall responses, we simulated it for 10 weeks to induce B cell memory in the model (Fig. 2B and 2C), and then re-challenged the model with an additional dose of alloantigen. The model was fitted simultaneously to 2 parameters which characterize fluxes v20 and v27 using the the 7 experimental data points available for the recall response, as in the previous step.

The results indicate a good fit of model to the dynamics of IgG DSA in blood for both the primary and the recall responses (Fig. 2A), which although it needs to be further constrained by additional experimental data related to other species in the model such as B cell memory and plasma cells, indicate that this model can recapitulate essential features of the immune response of interest. At this stage, this model could constitute the backbone of a computational model to study DSA formation which can be refined and expanded to generate hypotheses based on the researcher’s question of interest.

CONCLUSIONS

Computational models are powerful tools to guide experimental immunology research and provide mechanistic insight. Leveraging the trove of already existing immune computational models through model reuse could accelerate the advancement of our understanding of alloimmune responses in transplant and guide therapeutic intervention.

ABBREVIATIONS

DSA

donor-specific antibody

TB

tuberculosis

SBML

systems biology markup language

DAMPS

damage-associated molecular patterns

TLR

toll-like receptor

ODE

ordinary differential equation

TNFα

tumor-necrosis factor Alpha

IL

interleukin

IRI

ischemia/reperfusion injury

T_H

helper T cell

T_REG

regulatory T cell

T_eff

effector T cell

ABM

agent-based model

CTOT

Clinical Trials in Organ Transplantation