A scalable, open-source implementation of a large-scale mechanistic model for single cell proliferation and death signaling

Artificial-intelligence-driven Innovations in Mechanistic Computational Modeling and Digital Twins for Biomedical Applications

Understanding of complex biological systems remains a significant challenge due to their high dimensionality, nonlinearity, and context-specific behavior. Artificial intelligence (AI) and mechanistic modeling are becoming essential tools for studying such complex systems. Mechanistic modeling can facilitate the construction of simulatable models that are interpretable but often struggle with scalability and parameters estimation. AI can integrate multi-omics data to create predictive models, but it lacks interpretability. The gap between these two modeling methods limits our ability to develop comprehensive and predictive models for biomedical applications. This article reviews the most recent advancements in the integration of AI and mechanistic modeling to fill this gap. Recently, with omics availability, AI has led to new discoveries in mechanistic computational modeling. The mechanistic models can also help in getting insight into the mechanism for prediction made by AI models. This integration is helpful in modeling complex systems, estimating the parameters that are hard to capture in experiments, and creating surrogate models to reduce computational costs because of expensive mechanistic model simulations. This article focuses on advancements in mechanistic computational models and AI models and their integration for scientific discoveries in biology, pharmacology, drug discovery and diseases. The mechanistic models with AI integration can facilitate biological discoveries to advance our understanding of disease mechanisms, drug development, and personalized medicine. The article also highlights the role of AI and mechanistic model integration in the development of more advanced models in the biomedical domain, such as medical digital twins and virtual patients for pharmacological discoveries.

From FAIR to CURE: Guidelines for Computational Models of Biological Systems

Guidelines for managing scientific data have been established under the FAIR principles requiring that data be Findable, Accessible, Interoperable, and Reusable. In many scientific disciplines, especially computational biology, both data and models are key to progress. For this reason, and recognizing that such models are a very special type of "data", we argue that computational models, especially mechanistic models prevalent in medicine, physiology and systems biology, deserve a complementary set of guidelines. We propose the CURE principles, emphasizing that models should be Credible, Understandable, Reproducible, and Extensible. We delve into each principle, discussing verification, validation, and uncertainty quantification for model credibility; the clarity of model descriptions and annotations for understandability; adherence to standards and open science practices for reproducibility; and the use of open standards and modular code for extensibility and reuse. We outline recommended and baseline requirements for each aspect of CURE, aiming to enhance the impact and trustworthiness of computational models, particularly in biomedical applications where credibility is paramount. Our perspective underscores the need for a more disciplined approach to modeling, aligning with emerging trends such as Digital Twins and emphasizing the importance of data and modeling standards for interoperability and reuse. Finally, we emphasize that given the non-trivial effort required to implement the guidelines, the community moves to automate as many of the guidelines as possible.

Mathematical Modeling and Inference of Epidermal Growth Factor-Induced Mitogen-Activated Protein Kinase Cell Signaling Pathways

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.

Mechanistic modeling of cell viability assays with in silico lineage tracing

Data from cell viability assays, which measure cumulative division and death events in a population and reflect substantial cellular heterogeneity, are widely available. However, interpreting such data with mechanistic computational models is hindered because direct model/data comparison is often muddled. We developed an algorithm that tracks simulated division and death events in mechanistically detailed single-cell lineages to enable such a model/data comparison and suggest causes of cell-cell drug response variability. Using our previously developed model of mammalian single-cell proliferation and death signaling, we simulated drug dose response experiments for four targeted anti-cancer drugs (alpelisib, neratinib, trametinib and palbociclib) and compared them to experimental data. Simulations are consistent with data for strong growth inhibition by trametinib (MEK inhibitor) and overall lack of efficacy for alpelisib (PI-3K inhibitor), but are inconsistent with data for palbociclib (CDK4/6 inhibitor) and neratinib (EGFR inhibitor). Model/data inconsistencies suggest (i) the importance of CDK4/6 for driving the cell cycle may be overestimated, and (ii) that the cellular balance between basal (tonic) and ligand-induced signaling is a critical determinant of receptor inhibitor response. Simulations show subpopulations of rapidly and slowly dividing cells in both control and drug-treated conditions. Variations in mother cells prior to drug treatment all impinging on ERK pathway activity are associated with the rapidly dividing phenotype and trametinib resistance. This work lays a foundation for the application of mechanistic modeling to large-scale cell viability assay datasets and better understanding determinants of cellular heterogeneity in drug response.

Self-consistent signal transduction analysis for modeling context-specific signaling cascades and perturbations

Biological signal transduction networks are central to information processing and regulation of gene expression across all domains of life. Dysregulation is known to cause a wide array of diseases, including cancers. Here I introduce self-consistent signal transduction analysis, which utilizes genome-scale -omics data (specifically transcriptomics and/or proteomics) in order to predict the flow of information through these networks in an individualized manner. I apply the method to the study of endocrine therapy in breast cancer patients, and show that drugs that inhibit estrogen receptor α elicit a wide array of antitumoral effects, and that their most clinically-impactful ones are through the modulation of proliferative signals that control the genes GREB1, HK1, AKT1, MAPK1, AKT2, and NQO1. This method offers researchers a valuable tool in understanding how and why dysregulation occurs, and how perturbations to the network (such as targeted therapies) effect the network itself, and ultimately patient outcomes.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Network-driven cancer cell avatars for combination discovery and biomarker identification for DNA damage response inhibitors

Combination therapy is well established as a key intervention strategy for cancer treatment, with the potential to overcome monotherapy resistance and deliver a more durable efficacy. However, given the scale of unexplored potential target space and the resulting combinatorial explosion, identifying efficacious drug combinations is a critical unmet need that is still evolving. In this paper, we demonstrate a network biology-driven, simulation-based solution, the Simulated Cell™. Integration of omics data with a curated signaling network enables the accurate and interpretable prediction of 66,348 combination-cell line pairs obtained from a large-scale combinatorial drug sensitivity screen of 684 combinations across 97 cancer cell lines (BAC = 0.62, AUC = 0.7). We highlight drug combination pairs that interact with DNA Damage Response pathways and are predicted to be synergistic, and deep network insight to identify biomarkers driving combination synergy. We demonstrate that the cancer cell 'avatars' capture the biological complexity of their in vitro counterparts, enabling the identification of pathway-level mechanisms of combination benefit to guide clinical translatability.

Endothelial cells signaling and patterning under hypoxia: a mechanistic integrative computational model including the Notch-Dll4 pathway

Introduction: Several signaling pathways are activated during hypoxia to promote angiogenesis, leading to endothelial cell patterning, interaction, and downstream signaling. Understanding the mechanistic signaling differences between endothelial cells under normoxia and hypoxia and their response to different stimuli can guide therapies to modulate angiogenesis. We present a novel mechanistic model of interacting endothelial cells, including the main pathways involved in angiogenesis. Methods: We calibrate and fit the model parameters based on well-established modeling techniques that include structural and practical parameter identifiability, uncertainty quantification, and global sensitivity. Results: Our results indicate that the main pathways involved in patterning tip and stalk endothelial cells under hypoxia differ, and the time under hypoxia interferes with how different stimuli affect patterning. Additionally, our simulations indicate that Notch signaling might regulate vascular permeability and establish different Nitric Oxide release patterns for tip/stalk cells. Following simulations with various stimuli, our model suggests that factors such as time under hypoxia and oxygen availability must be considered for EC pattern control. Discussion: This project provides insights into the signaling and patterning of endothelial cells under various oxygen levels and stimulation by VEGFA and is our first integrative approach toward achieving EC control as a method for improving angiogenesis. Overall, our model provides a computational framework that can be built on to test angiogenesis-related therapies by modulation of different pathways, such as the Notch pathway.

Multi-scale models of whole cells: progress and challenges

Whole-cell modeling is "the ultimate goal" of computational systems biology and "a grand challenge for 21st century" (Tomita, Trends in Biotechnology, 2001, 19(6), 205-10). These complex, highly detailed models account for the activity of every molecule in a cell and serve as comprehensive knowledgebases for the modeled system. Their scope and utility far surpass those of other systems models. In fact, whole-cell models (WCMs) are an amalgam of several types of "system" models. The models are simulated using a hybrid modeling method where the appropriate mathematical methods for each biological process are used to simulate their behavior. Given the complexity of the models, the process of developing and curating these models is labor-intensive and to date only a handful of these models have been developed. While whole-cell models provide valuable and novel biological insights, and to date have identified some novel biological phenomena, their most important contribution has been to highlight the discrepancy between available data and observations that are used for the parametrization and validation of complex biological models. Another realization has been that current whole-cell modeling simulators are slow and to run models that mimic more complex (e.g., multi-cellular) biosystems, those need to be executed in an accelerated fashion on high-performance computing platforms. In this manuscript, we review the progress of whole-cell modeling to date and discuss some of the ways that they can be improved.

PI3K signaling through a biochemical systems lens

Following 3 decades of extensive research into PI3K signaling, it is now evidently clear that the underlying network does not equate to a simple ON/OFF switch. This is best illustrated by the multifaceted nature of the many diseases associated with aberrant PI3K signaling, including common cancers, metabolic disease, and rare developmental disorders. However, we are still far from a complete understanding of the fundamental control principles that govern the numerous phenotypic outputs that are elicited by activation of this well-characterized biochemical signaling network, downstream of an equally diverse set of extrinsic inputs. At its core, this is a question on the role of PI3K signaling in cellular information processing and decision making. Here, we review the determinants of accurate encoding and decoding of growth factor signals and discuss outstanding questions in the PI3K signal relay network. We emphasize the importance of quantitative biochemistry, in close integration with advances in single-cell time-resolved signaling measurements and mathematical modeling.

Deep Neural Networks for Predicting Single-Cell Responses and Probability Landscapes

Engineering biology relies on the accurate prediction of cell responses. However, making these predictions is challenging for a variety of reasons, including the stochasticity of biochemical reactions, variability between cells, and incomplete information about underlying biological processes. Machine learning methods, which can model diverse input-output relationships without requiring a priori mechanistic knowledge, are an ideal tool for this task. For example, such approaches can be used to predict gene expression dynamics given time-series data of past expression history. To explore this application, we computationally simulated single-cell responses, incorporating different sources of noise and alternative genetic circuit designs. We showed that deep neural networks trained on these simulated data were able to correctly infer the underlying dynamics of a cell response even in the presence of measurement noise and stochasticity in the biochemical reactions. The training set size and the amount of past data provided as inputs both affected prediction quality, with cascaded genetic circuits that introduce delays requiring more past data. We also tested prediction performance on a bistable auto-activation circuit, finding that our initial method for predicting a single trajectory was fundamentally ill-suited for multimodal dynamics. To address this, we updated the network architecture to predict the entire distribution of future states, showing it could accurately predict bimodal expression distributions. Overall, these methods can be readily applied to the diverse prediction tasks necessary to predict and control a variety of biological circuits, a key aspect of many synthetic biology applications.

MOBILE pipeline enables identification of context-specific networks and regulatory mechanisms

Robust identification of context-specific network features that control cellular phenotypes remains a challenge. We here introduce MOBILE (Multi-Omics Binary Integration via Lasso Ensembles) to nominate molecular features associated with cellular phenotypes and pathways. First, we use MOBILE to nominate mechanisms of interferon-γ (IFNγ) regulated PD-L1 expression. Our analyses suggest that IFNγ-controlled PD-L1 expression involves BST2, CLIC2, FAM83D, ACSL5, and HIST2H2AA3 genes, which were supported by prior literature. We also compare networks activated by related family members transforming growth factor-beta 1 (TGFβ1) and bone morphogenetic protein 2 (BMP2) and find that differences in ligand-induced changes in cell size and clustering properties are related to differences in laminin/collagen pathway activity. Finally, we demonstrate the broad applicability and adaptability of MOBILE by analyzing publicly available molecular datasets to investigate breast cancer subtype specific networks. Given the ever-growing availability of multi-omics datasets, we envision that MOBILE will be broadly useful for identification of context-specific molecular features and pathways.

Predicting anti-cancer drug combination responses with a temporal cell state network model

Cancer chemotherapy combines multiple drugs, but predicting the effects of drug combinations on cancer cell proliferation remains challenging, even for simple in vitro systems. We hypothesized that by combining knowledge of single drug dose responses and cell state transition network dynamics, we could predict how a population of cancer cells will respond to drug combinations. We tested this hypothesis here using three targeted inhibitors of different cell cycle states in two different cell lines in vitro. We formulated a Markov model to capture temporal cell state transitions between different cell cycle phases, with single drug data constraining how drug doses affect transition rates. This model was able to predict the landscape of all three different pairwise drug combinations across all dose ranges for both cell lines with no additional data. While further application to different cell lines, more drugs, additional cell state networks, and more complex co-culture or in vivo systems remain, this work demonstrates how currently available or attainable information could be sufficient for prediction of drug combination response for single cell lines in vitro.

Computational speed-up of large-scale, single-cell model simulations via a fully integrated SBML-based format

Summary

Large-scale and whole-cell modeling has multiple challenges, including scalable model building and module communication bottlenecks (e.g. between metabolism, gene expression, signaling, etc.). We previously developed an open-source, scalable format for a large-scale mechanistic model of proliferation and death signaling dynamics, but communication bottlenecks between gene expression and protein biochemistry modules remained. Here, we developed two solutions to communication bottlenecks that speed-up simulation by ∼4-fold for hybrid stochastic-deterministic simulations and by over 100-fold for fully deterministic simulations. Fully deterministic speed-up facilitates model initialization, parameter estimation and sensitivity analysis tasks.

Availability and implementation

Source code is freely available at https://github.com/birtwistlelab/SPARCED/releases/tag/v1.3.0 implemented in python, and supported on Linux, Windows and MacOS (via Docker).

MEMMAL: A tool for expanding large-scale mechanistic models with machine learned associations and big datasets

Computational models that can explain and predict complex sub-cellular, cellular, and tissue-level drug response mechanisms could speed drug discovery and prioritize patient-specific treatments (i.e., precision medicine). Some models are mechanistic with detailed equations describing known (or supposed) physicochemical processes, while some are statistical or machine learning-based approaches, that explain datasets but have no mechanistic or causal guarantees. These two types of modeling are rarely combined, missing the opportunity to explore possibly causal but data-driven new knowledge while explaining what is already known. Here, we explore combining machine learned associations with mechanistic models to develop computational models that could more fully represent cellular behavior. In this proposed MEMMAL (MEchanistic Modeling with MAchine Learning) framework, machine learning/statistical models built using omics datasets provide predictions for new interactions between genes and proteins where there is physicochemical uncertainty. These interactions are used as a basis for new reactions in mechanistic models. As a test case, we focused on incorporating novel IFNγ/PD-L1 related associations into a large-scale mechanistic model for cell proliferation and death to better recapitulate the recently released NIH LINCS Consortium MCF10A dataset and enable description of the cellular response to checkpoint inhibitor immunotherapies. This work is a template for combining big-data-inferred interactions with mechanistic models, which could be more broadly applicable for building multi-scale precision medicine and whole cell models.