examination. In the drug discovery pipeline, the lack of multi-scale modeling approaches able of taking into account the observation of an immunological phenomenon from the molecular to the tissue/organism levels represents a big issue. In this scenario, agent-based models can partially make up for this issue allowing them to accurately describe all the interactions that occur at the cellular level and showing the phenomenon at the tissue/organ level thanks to their capability of producing emergent global behaviors. This short review will present some of these agent-based approaches developed for the simulation of diseases and the relative immune system response that also try to explicitly include molecular-level aspects such as internal cell behavior or receptor binding, for a more real and complete representation of the immunological phenomena under immune system, Agent-based models, simulation, computational biology, multi-scale model, systems biology of new vaccines, where researchers make use of bioinfor- the natural phenomenon under study, are:
pipeline is given by the lack of multi-scale modeling approaches able of taking into account the observation of an immunological phenomenon from diferent points of view, i.e. from the molecular to the tissue/organism level.
This aspect is particularly critical for the development matics approaches only on a limited number of aspects of the phenomenon (as existing tools are usually designed to tackle specific questions, such as immunogenicity and so on) to detect possible candidate drugs or to design possible vaccines. Such compounds have to be then tested at later stages to verify their safety and eficacy. So, further studies possibly carried on expensive in vitro/in vivo setups are then needed, but the results are not always capable of supporting the previous findings. versal influenza/A has been challenging [ 1], and various attempts have fallen short during in vitro and/or in vivo verification.
To this end, simulation approaches that can be used to substitute in vivo/in vitro experiments may reduce both the time-to-market and the development costs. These approaches, referred to as in-silico approaches, must be capable of reproducing the target disease and the involved modeled using specific software such as COPASI [
2] or mathematical formalisms such as Petri nets [3, 4].
At the extracellular level, we can consider all the processes involved in recognizing non-self antigens, such as their binding to major histocompatibility complex (MHC) class molecules in antigen-presenting cells, and B and T cell epitope recognition processes. Many recent methodologies for solving these tasks are nowadays based on structural and machine learning algorithms [5, 6].
For example, it is well known that developing a uni- intracellular and extracellular molecular processes. For For the cellular level scale, in which cell-cell interac- needed since both the modeling and the simulation astions hold, the use of agent-based models (ABMs) repre- pects must be considered and developed. This entitles, sents the most natural choice. ABMs allow to accurately besides the longer developing times, the risk to have imdescribe all the interactions that occur at the cellular plementation errors that may be present not only in the level naturally and simply, making also easier the com- modeling part (i.e., biological conceptual errors), but also munication between the modeler and the domain expert in the simulation part (i.e., programming bugs). However, (i.e., the immunologist, biologist, pharmaceutical scien- there are some advantages to implement an ABM from tist, or medical doctor). Furthermore, their capability of scratch. Since both simulation and modeling parts are producing emergent global behaviors at a higher level as in general partially merged, it is possible to include and the sum of the actions of their agents makes ABMs an describe in depth any biological aspect without any limiexceptional tool to describe immunological phenomena tation, having as a result also better simulation speeds. at the cellular level, obtaining a representation at the It is of course possible to implement an ABM by using tissue/organ level. In this sense, ABMs can be already some of the general frameworks devoted to the simulaconsidered multi-scale models in immunology and can tion of ABMs. In such cases, less programming knowlbe used in substitution of continuous approaches based edge is required, as such frameworks typically require on ODE/PDE systems that are instead frequently used specific ABM-oriented programming languages that are for tissue scale representation, provided that suficient easier to understand and learn. The use of a pre-built computational resources are available [7]. ABM simulation framework allows focusing on the mod
Many agent models have been developed for repro- eling part of the problem, as the underlying simulator ducing the immune system behavior, however few of part is provided by the framework itself. This speeds them try to explicitly include also molecular-level as- up the development of the model and lowers the risk pects. These models are either developed to tackle spe- of programming bugs and errors. On the other hand, cific pathologies, or presented as general-purpose plat- such models are usually slower than custom models, and forms and then specialized each time on given diseases. the possibility of defining custom agent behaviors, propThe goal of this short review is to present some of these erties and functions, as well as the capacity to allow models and approaches. To this end, we will first recall large-scale simulations, are strictly connected to the flexsome crucial aspects of agent-based models for the im- ibility and capabilities of the chosen simulation platform. mune system and how to build them, then we summarize Some ABM frameworks have been used quite fruitfully some of the models and approaches based on ABMs that in the modeling of IS. Among these we recall Netlogo [8], include molecular aspects (either intracellular o extracel- Swarm[9], Repast[10], Flame and FlameGPU[11]. lular) in these cellular to tissue level approaches.
immune system
Although the development of an ABM does not strictly tial equations (DE) based approaches in immunology, require the same mathematical knowledge as for difer- ABM literature on this topic is far more recent, parential equations-based models, it is mandatory to possess ticularly when we concentrate on multi-scale ABM apminimal knowledge of computer science and some pro- proaches that include molecular aspects. Here we review gramming skills. the most relevant ABM models and simulators that deal,
We would like to distinguish between two diferent to some extent, with the immune system behavior, priviaspects in the implementation of an ABM of IS and that leging the most recent approaches, the approaches that may influence the required degree of computer science are still under development, or those that have given knowledge. The first aspect is the modeling aspect, which birth to descending projects that are still alive. regards the implementation of the biological knowledge, One of the first ABM approaches for the modeling of including the description of which entities are involved, the immune system function is represented by IMMSIM, and how they act and interact. The second aspect is a computer model presented by Franco Celada and Philip instead the simulation aspect, which takes instead care Seiden in the early 90’ [12, 13]. In their work, the authors of the underlying infrastructure that executes the sim- present what they call a “generalized cellular automaulation, performs the movement and the evolution of ton” (the term agent-based model was not so common the entities, manages memory allocation for the entities at that time), which was able to mimic both the cognate and the physical space, and governs all the accessory recognition and response of the immune system system activities like the storage and visualization of the results. to general pathogens. In this approach, the space rep
To build from scratch an ABM, a substantial efort is resentation is discretized by means of a hexagonal grid called lattice. At each time-step, all the entities in the that such models may include various immune system same lattice point can act and interact with each other cells and pathogens with diferent receptors, these apaccording to pre-defined rules that drive the entities’ be- proaches lack the possibility to include real antigenic havior. Entities may also difuse from a lattice point to sequences, and this limits their applicability to specific another in the neighborhood. Agents are used to either cases. Furthermore, cells’ internal dynamics are based represent cellular immune system entities of the innate on rules derived from immunology rather than driven and adaptive response, or pathogens such as viruses and by intracellular pathways. So it is not possible to predict bacteria. Moreover, this approach includes many molec- cell behaviors outside the actions established by such ular entities such as chemokines and cytokines, which predefined rules. are represented by their concentration per lattice-point. However, when the binding-afinity is known a priori it The model does not explicitly include extracellular re- is possible to translate it into a pair of binary strings, one ceptors but tries instead to mimic receptor diversity by representing a given antigenic sequence of the entity that using binary strings, and hamming distance between will challenge the immune system (i.e., a pathogen, a drug strings to measure receptor afinity. More specifically, a or a vaccine), and the other one representing a specific piece-wise function calculates an interaction probability receptor of the IS family that will be challenged, in such according to the hamming distance of two strings repre- a way that their interaction will entitle an interaction senting the cells’ receptors. Under a given threshold of probability that is proportional to the in-vivo binding mismatching bits, the function will return no afinity, so afinity. the entities will have zero probability to interact. Over This approach has been used in [22], where the authors such a threshold, the function will return a probability predicted the eficacy of some candidate citrus-derived that is proportional to the number of mismatching bits. adjuvants (to be used instead of Aluminum salts) for While this approach may appear quite simplistic, it allows influenza-A vaccines. The methodology applied some to execute many cell-cell and cell-molecules interactions virtual-screening techniques to calculate the interaction rapidly, and its adoption indeed allows to reproduce some scores of the candidate adjuvants and aluminum salts important hallmarks of the adaptive immune system re- (used as a reference value). Then, such scores were used sponse: specificity, memory and discrimination between to build-up a translation function that converts a given self and non-self. From their efort many other mod- score into a required number of mismatching bits to reels originated and, while some of them were lost on the produce the adjuvants capability to stimulate the imroad, others are still actively developed and represent the mune system. The in-silico experiment predicted Betastate-of-the-art immune system models at the cellular Sitosterol as the best potential candidate, and this result scale. was then confirmed by in vitro experiments.
Among these models we recall two frameworks named Another UISS extension to reproduce avascular tumor UISS and C-IMMSIM, defined as general-purpose immune growth and the involved immune system response was system simulators and specialized each time for the dis- presented in [23]. A lattice Boltzmann (LB) method (a ease under investigation. These two frameworks are computational fluid dynamics technique that avoids solvwritten in C, and include both the simulation and the ing the Navier–Stokes equations directly by using instead modeling aspects into one single code. a discrete lattice mesh [24]), was used for nutrient distri
UISS has been successfully used for optimizing, in bution and propagation, while the ABM infrastructure silico, the vaccination schedule of a prophylactic vac- was used to describe the immune system reaction against cine named Triplex against mammary carcinoma [14, 15]. the tumor at the cellular level.
Then it has been used, under the name Metastasim, with a Various studies extended the C-IMMSIM framework by similar goal (i.e., optimizing an administration schedule) including more features at the molecular level for better but in a diferent experimental setup, in which the same describing either intracellular or extracellular behaviors. vaccine was used as a therapeutic agent against lung A first extension (called VaccImm) was presented to remetastases derived by mammary carcinoma [16]. Then, produce in-silico peptide vaccination in cancer therapy. UISS has been recently used inside the H2020 Project The ABM infrastructure, that was already capable of reSTriTuVaD to predict the efects of combined immuniza- producing the involved cells (immune system and cancer) tion strategies against tuberculosis [17], and also special- behavior as well as molecules (antibodies, antigens and ized to suggest the best therapeutic options in patients semiochemicals), was extended by substituting part of with Multiple Sclerosis [18]. Finally, UISS-COVID was the machinery based on binary strings for receptors’ inused for predicting SARS-CoV-2 dynamics and related teractions with real amino acid sequences to represent immune system host response [19]. C-IMMSIM, used in- molecular binding sites of immune cells [25]. stead for simulating HIV alone or under HAART therapy Another C-IMMSIM version deals instead with intraadministration [20] and Epstein-Barr virus [21]. cellular aspects. Specifically, C-IMMSIM was extended
While being considered polyclonal models, in the sense to include, at the intracellular level, a Boolean network with the aim to describe the activation dynamics of a from the concepts and approaches for ABMs. To this end, gene regulatory network driving Th1 and Th2 polariza- it would be important to establish a common language tion [26]. The model has been further extended [27] to for the communication of the models at diferent scales. also include T helper cell polarization towards Th17 and On the other hand, the molecular and cellular scales can Treg, with a boolean network composed by 40 nodes. be in general developed independently, and put together
A similar approach was used by Beyer and Meyer- at later times, making easier the development of these Hermann[28], with an ABM that includes a set of ODEs multi-scale hybrid models. for chemokine receptor internalization. The ABM was Another problem with multi-scale modeling in imspecifically developed to study the formation of cell ag- munology is correlated to the diferent spatiotemporal digregates and consequent tissue instability in rheumatoid mensions of the processes that happen at diferent levels. arthritis. Usually, the phenomena at a lower scale have reduced di
Dutta-Moscato et al. [29] developed a multiscale mensions, but they happen and are repeated many times agent-based in silico Model of Liver Fibrosis Progression. during one single instance of the phenomena at a higher The liver fibrosis ABM (LFABM) includes five types of level. For example, the development of Tuberculosis may agents (parenchymal cells, inflammatory cells, collagen- require years, but the involved cells’ interactions may producing cells, and structural elements that define lob- happen billions of times in that period. However, simules). Agents can release various factors, such as tumor ulation of these processes usually does not require less necrosis factor alpha, transforming growth factor beta 1, time as the modeling scale goes down, and this makes high mobility group box protein 1, that can influence the dificult the development of comprehensive models. In agent behavior. LFABM made use of literature-derived this case, it would be (in principle) possible to make use rules to the inflammation and fibrosis in a portion of a of pre-calculated results using look-up tables for a given chemically injured liver. subset of results referring to the molecular-level mod
Using Netlogo as a starting point [8], Gary An devel- els and use interpolation (if the low-level solutions are oped the epithelial barrier agent-based model (EBABM), smooth enough) or lazy-evaluation for obtaining, when an ABM that includes the enterocytes of the gut and their needed, the missing points. response to inflammatory mediators such as nitric oxide Furthermore, the accuracy of the low-level molecular (NO) and to pro-inflammatory cytokines, including tu- models may negatively influence the results of the model mor necrosis factor, interleukin-1 and interferon-gamma. at a higher scale. For example, the accuracy of B cell To this end, tight junction protein metabolism and pro- epitope prediction tools is generally rather poor, having inflammatory signaling cascades were included in the AUC values ranging from 0.6 to 0.7 [6]. In such a case, it is model as considered responsible for gut epithelial barrier important to execute extensive robustness and sensitivity function [30]. analyses on the multi-scale models to estimate how and
ENISI-MSM is instead a multi-scale platform that in what measure these inaccuracies influence the global makes use of an agent-based framework for cell-cell in- behavior of the model. teraction and movement based on Repast. This frame- Finally, to reach a real tissue/organ scale, beyond a work is connected to a module that uses the COPASI more accurate anatomical description that should be [2] ODE/SDE (ordinary/stochastic diferential equation) taken into account for the involved organs (such as solver for representing intracellular pathways, and an lymph-nodes), it is important to have the capability of reintegrated PDE (partial diferential equation) simulator producing the behavior of (at least) millions of agents, and for molecule gradient and difusion. The model has been it is well known that this aspect represents the Achille’s used to obtain the immune response in the gut at a high heel of any ABM approach. In this case specific HPC [ 32] resolution [31] thanks to the use of the REPAST-HPC and/or GPU [11] enabled ABM infrastructures may come library [32]. to the aid to mitigate this issue.
In conclusion, despite the existing challenges and issues, we expect in the coming years that the contribu4. Conclusions tion of these multi-scale models will become even more important and substantial, helping all the researchers from the immunology and life-science fields in general in better understanding disease mechanisms and thus in developing faster more efective treatments.
The development of multi-scale ABMs of the immune system may help to address various immunological questions on how diseases happen and evolve, on what is the role of the immune system in developing and contrasting such diseases, and on if and how candidate treatments act.
However, there are still some major issues that need to be solved. Models from the molecular scale are commonly developed exploiting methodologies that are usually far system simulation framework, Proc. - 2017 Int.
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