Stochastic simulation algorithms for computational systems biology: Exact, approximate, and hybrid methods

A Novel Hybrid Logic-ODE Modeling Approach to Overcome Knowledge Gaps

Mathematical modeling allows using different formalisms to describe, investigate, and understand biological processes. However, despite the advent of high-throughput experimental techniques, quantitative information is still a challenge when looking for data to calibrate model parameters. Furthermore, quantitative formalisms must cope with stiffness and tractability problems, more so if used to describe multicellular systems. On the other hand, qualitative models may lack the proper granularity to describe the underlying kinetic processes. We propose a hybrid modeling approach that integrates ordinary differential equations and logical formalism to describe distinct biological layers and their communication. We focused on a multicellular system as a case study by applying the hybrid formalism to the well-known Delta-Notch signaling pathway. We used a differential equation model to describe the intracellular pathways while the cell-cell interactions were defined by logic rules. The hybrid approach herein employed allows us to combine the pros of different modeling techniques by overcoming the lack of quantitative information with a qualitative description that discretizes activation and inhibition processes, thus avoiding complexity.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

QSPcc reduces bottlenecks in computational model simulations

Mathematical models have grown in size and complexity becoming often computationally intractable. In sensitivity analysis and optimization phases, critical for tuning, validation and qualification, these models may be run thousands of times. Scientific programming languages popular for prototyping, such as MATLAB and R, can be a bottleneck in terms of performance. Here we show a compiler-based approach, designed to be universal at handling engineering and life sciences modeling styles, that automatically translates models into fast C code. At first QSPcc is demonstrated to be crucial in enabling the research on otherwise intractable Quantitative Systems Pharmacology models, such as in rare Lysosomal Storage Disorders. To demonstrate the full value in seamlessly accelerating, or enabling, the R&D efforts in natural sciences, we then benchmark QSPcc against 8 solutions on 24 real-world projects from different scientific fields. With speed-ups of 22000x peak, and 1605x arithmetic mean, our results show consistent superior performances.

Lombardo and colleagues present QSPcc, a computational code compiler designed to convert code from popular scientific programming languages, such as MATLAB or R, into fast-running C code. This reduces the computational load required for complex modelling approaches and reduces user investment learning additional complex languages.

History and Future Perspectives on the Discipline of Quantitative Systems Pharmacology Modeling and Its Applications

Mathematical biology and pharmacology models have a long and rich history in the fields of medicine and physiology, impacting our understanding of disease mechanisms and the development of novel therapeutics. With an increased focus on the pharmacology application of system models and the advances in data science spanning mechanistic and empirical approaches, there is a significant opportunity and promise to leverage these advancements to enhance the development and application of the systems pharmacology field. In this paper, we will review milestones in the evolution of mathematical biology and pharmacology models, highlight some of the gaps and challenges in developing and applying systems pharmacology models, and provide a vision for an integrated strategy that leverages advances in adjacent fields to overcome these challenges.

Generalized stochastic microdosimetric model: The main formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM^{2}), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM^{2}. Development of GSM^{2} can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

Towards understanding the messengers of extracellular space: Computational models of outside-in integrin reaction networks

The interactions between cells and their extracellular matrix (ECM) are critically important for homeostatic control of cell growth, proliferation, differentiation and apoptosis. Transmembrane integrin molecules facilitate the communication between ECM and the cell. Since the characterization of integrins in the late 1980s, there has been great advancement in understanding the function of integrins at different subcellular levels. However, the versatility in molecular pathways integrins are involved in, the high diversity in their interaction partners both outside and inside the cell as well as on the cell membrane and the short lifetime of events happening at the cell-ECM interface make it difficult to elucidate all the details regarding integrin function experimentally. To overcome the experimental challenges and advance the understanding of integrin biology, computational modeling tools have been used extensively. In this review, we summarize the computational models of integrin signaling while we explain the function of integrins at three main subcellular levels (outside the cell, cell membrane, cytosol). We also discuss how these computational modeling efforts can be helpful in other disciplines such as biomaterial design. As such, this review is a didactic modeling summary for biomaterial researchers interested in complementing their experimental work with computational tools or for seasoned computational scientists that would like to advance current in silico integrin models.

A QSP model of prostate cancer immunotherapy to identify effective combination therapies

Immunotherapy, by enhancing the endogenous anti-tumor immune responses, is showing promising results for the treatment of numerous cancers refractory to conventional therapies. However, its effectiveness for advanced castration-resistant prostate cancer remains unsatisfactory and new therapeutic strategies need to be developed. To this end, systems pharmacology modeling provides a quantitative framework to test in silico the efficacy of new treatments and combination therapies. In this paper we present a new Quantitative Systems Pharmacology (QSP) model of prostate cancer immunotherapy, calibrated using data from pre-clinical experiments in prostate cancer mouse models. We developed the model by using Ordinary Differential Equations (ODEs) describing the tumor, key components of the immune system, and seven treatments. Numerous combination therapies were evaluated considering both the degree of tumor inhibition and the predicted synergistic effects, integrated into a decision tree. Our simulations predicted cancer vaccine combined with immune checkpoint blockade as the most effective dual-drug combination immunotherapy for subjects treated with androgen-deprivation therapy that developed resistance. Overall, the model presented here serves as a computational framework to support drug development, by generating hypotheses that can be tested experimentally in pre-clinical models.