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Multiscale models provide a unique tool for studying complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. They aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms -- coupled with a graphical interface -- is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to easily construct such models, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as a Supplementary Material and all models are provided at: https://physiboss.github.io/tutorial/.

Mechanistic learning, the synergistic combination of knowledge-driven and data-driven modeling, is an emerging field. In particular, in mathematical oncology, the application of mathematical modeling to cancer biology and oncology, the use of mechanistic learning is growing. This review aims to capture the current state of the field and provide a perspective on how mechanistic learning may further progress in mathematical oncology. We highlight the synergistic potential of knowledge-driven mechanistic mathematical modeling and data-driven modeling, such as machine and deep learning. We point out similarities and differences regarding model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Then, organizing combinations of knowledge- and data-driven modeling into four categories (sequential, parallel, intrinsic, and extrinsic mechanistic learning), we summarize a variety of approaches at the interface between purely data- and knowledge-driven models. Using examples predominantly from oncology, we discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. We see that mechanistic learning, with its intentional leveraging of the strengths of both knowledge and data-driven modeling, can greatly impact the complex problems of oncology. Given the increasing ubiquity and impact of machine learning, it is critical to incorporate it into the study of mathematical oncology with mechanistic learning providing a path to that end. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data

Computational biology has increasingly turned to agent-based modeling to explore complex biological systems. Biological diffusion (diffusion, decay, secretion, and uptake) is a key driver of biological tissues. GPU computing can vastly accelerate the diffusion and decay operators in the partial differential equations used to represent biological transport in an agent-based biological modeling system. In this paper, we utilize OpenACC to accelerate the diffusion portion of PhysiCell, a cross-platform agent-based biosimulation framework. We demonstrate an almost 40x speedup on the state-of-the-art NVIDIA A100 GPU compared to a serial run on AMD's EPYC 7742. We also demonstrate 9x speedup on the 64 core AMD EPYC 7742 multicore platform. By using OpenACC for both the CPUs and the GPUs, we maintain a single source code base, thus creating a portable yet performant solution. With the simulator's most significant computational bottleneck significantly reduced, we can continue cancer simulations over much longer times.

Increasingly sophisticated experiments, coupled with large-scale computational models, have the potential to systematically test biological hypotheses to drive our understanding of multicellular systems. In this short review, we explore key challenges that must be overcome to achieve robust, repeatable data-driven multicellular systems biology. If these challenges can be solved, we can grow beyond the current state of isolated tools and datasets to a community-driven ecosystem of interoperable data, software utilities, and computational modeling platforms. Progress is within our grasp, but it will take community (and financial) commitment.

A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate cells into 16 molecular types. The binary string value determines cell fitness, with lower fit cells (e.g. 0000) defined as healthy phenotypes, and higher fit cells (e.g. 1111) defined as malignant phenotypes. At each step of the birth-death process, the two phenotypic sub-populations compete in a prisoner's dilemma evolutionary game with healthy cells (cooperators) competing with cancer cells (defectors). Fitness and birth-death rates are defined via the prisoner's dilemma payoff matrix. Cells are able undergo two types of stochastic point mutations passed to the daughter cell's binary string during birth: passenger mutations (conferring no fitness advantage) and driver mutations (increasing cell fitness). Dynamic phylogenetic trees show clonal expansions of cancer cell sub-populations from an initial malignant cell. The tumor growth equation states that the growth rate is proportional to the logarithm of cellular heterogeneity, here measured using the Shannon entropy of the distribution of binary sequences in the tumor cell population. Nonconstant tumor growth rates, (exponential growth during sub-clinical range of the tumor and subsequent slowed growth during tumor saturation) are associated with a Gompertzian growth curve, an emergent feature of the model explained here using simple statistical mechanics principles related to the degree of functional coupling of the cell states. Dosing strategies at early stage development, mid-stage (clinical stage), and late stage development of the tumor are compared, showing therapy is most effective during the sub-clinical stage, before the cancer subpopulation is selected for growth.