Toward modular biological models: defining analog modules based on referent physiological mechanisms

Utilizing virtual experiments to increase understanding of discrepancies involving in vitro-to-in vivo predictions of hepatic clearance

Predictions of xenobiotic hepatic clearance in humans using in vitro-to-in vivo extrapolation methods are frequently inaccurate and problematic. Multiple strategies are being pursued to disentangle responsible mechanisms. The objective of this work is to evaluate the feasibility of using insights gained from independent virtual experiments on two model systems to begin unraveling responsible mechanisms. The virtual culture is a software analog of hepatocytes in vitro, and the virtual human maps to hepatocytes within a liver within an idealized model human. Mobile objects (virtual compounds) map to amounts of xenobiotics. Earlier versions of the two systems achieved quantitative validation targets for intrinsic clearance (virtual culture) and hepatic clearance (virtual human). The major difference between the two systems is the spatial organization of the virtual hepatocytes. For each pair of experiments (virtual culture, virtual human), hepatocytes are configured the same. Probabilistic rules govern virtual compound movements and interactions with other objects. We focus on highly permeable virtual compounds and fix their extracellular unbound fraction at one of seven values (0.05–1.0). Hepatocytes contain objects that can bind and remove compounds, analogous to metabolism. We require that, for a subset of compound properties, per-hepatocyte compound exposure and removal rates during culture experiments directly predict corresponding measures made during virtual human experiments. That requirement serves as a cross-system validation target; we identify compound properties that enable achieving it. We then change compound properties, ceteris paribus, and provide model mechanism-based explanations for when and why measures made during culture experiments under- (or over-) predict corresponding measures made during virtual human experiments. The results show that, from the perspective of compound removal, the organization of hepatocytes within virtual livers is more efficient than within cultures, and the greater the efficiency difference, the larger the underprediction. That relationship is noteworthy because most in vitro-to-in vivo extrapolation methods abstract away the structural organization of hepatocytes within a liver. More work is needed on multiple fronts, including the study of an expanded variety of virtual compound properties. Nevertheless, the results support the feasibility of the approach and plan.

A mathematical model of in vitro hepatocellular cholesterol and lipoprotein metabolism for hyperlipidemia therapy

Cardiovascular diseases associated with high cholesterol (hypercholesterolemia) and low-density lipoproteins (LDL) levels are significant contributors to total mortality in developing and developed countries. Mathematical modeling of LDL metabolism is an important step in the development of drugs for hypercholesterolemia. The aim of this work was to develop and to analyze an integrated mathematical model of cholesterol metabolism in liver cells and its interaction with two types of drugs, statins and PCSK9 inhibitors. The model consisted of 21 ordinary differential equations (ODE) describing cholesterol biosynthesis and lipoprotein endocytosis in liver cells in vitro. The model was tested for its ability to mimic known biochemical effects of familial hypercholesterolemia, statin therapy, and PCSK9 inhibitors. The model qualitatively reproduced the well-known biology of cholesterol regulation, which confirms its potential for minimizing cellular research in initial testing of new drugs for cardiology.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Propagation of Pericentral Necrosis During Acetaminophen-Induced Liver Injury: Evidence for Early Interhepatocyte Communication and Information Exchange

Acetaminophen (APAP)-induced liver injury is clinically significant, and APAP overdose in mice often serves as a model for drug-induced liver injury in humans. By specifying that APAP metabolism, reactive metabolite formation, glutathione depletion, and mitigation of mitochondrial damage within individual hepatocytes are functions of intralobular location, an earlier virtual model mechanism provided the first concrete multiattribute explanation for how and why early necrosis occurs close to the central vein (CV). However, two characteristic features could not be simulated consistently: necrosis occurring first adjacent to the CV, and subsequent necrosis occurring primarily adjacent to hepatocytes that have already initiated necrosis. We sought parsimonious model mechanism enhancements that would manage spatiotemporal heterogeneity sufficiently to enable meeting two new target attributes and conducted virtual experiments to explore different ideas for model mechanism improvement at intrahepatocyte and multihepatocyte levels. For the latter, evidence supports intercellular communication via exosomes, gap junctions, and connexin hemichannels playing essential roles in the toxic effects of chemicals, including facilitating or counteracting cell death processes. Logic requiring hepatocytes to obtain current information about whether downstream and lateral neighbors have triggered necrosis enabled virtual hepatocytes to achieve both new target attributes. A virtual hepatocyte that is glutathione-depleted uses that information to determine if it will initiate necrosis. When a less-stressed hepatocyte is flanked by at least two neighbors that have triggered necrosis, it too will initiate necrosis. We hypothesize that the resulting intercellular communication-enabled model mechanism is analogous to the actual explanation for APAP-induced hepatotoxicity at comparable levels of granularity.

Deep Reinforcement Learning and Simulation as a Path Toward Precision Medicine

Traditionally, precision medicine involves classifying patients to identify subpopulations that respond favorably to specific therapeutics. We pose precision medicine as a dynamic feedback control problem, where treatment administered to a patient is guided by measurements taken during the course of treatment. We consider sepsis, a life-threatening condition in which dysregulation of the immune system causes tissue damage. We leverage an existing simulation of the innate immune response to infection and apply deep reinforcement learning (DRL) to discover an adaptive personalized treatment policy that specifies effective multicytokine therapy to simulated sepsis patients based on systemic measurements. The learned policy achieves a dramatic reduction in mortality rate over a set of 500 simulated patients relative to standalone antibiotic therapy. Advantages of our approach are threefold: (1) the use of simulation allows exploring therapeutic strategies beyond clinical practice and available data, (2) advances in DRL accommodate learning complex therapeutic strategies for complex biological systems, and (3) optimized treatments respond to a patient's individual disease progression over time, therefore, capturing both differences across patients and the inherent randomness of disease progression within a single patient. We hope that this work motivates both considering adaptive personalized multicytokine mediation therapy for sepsis and exploiting simulation with DRL for precision medicine more broadly.

A Model Mechanism-Based Explanation of an In Vitro-In Vivo Disconnect for Improving Extrapolation and Translation

An improved understanding of in vivo-to-in vitro hepatocyte changes is crucial to interpreting in vitro data correctly and further improving hepatocyte-based in vitro-to-in vivo extrapolations to human targets. We demonstrate using virtual experiments as a means of helping to untangle plausible causes of inaccurate extrapolations. We start with virtual mice that use biomimetic software livers. Previously, using these mice, we discovered model mechanisms that enabled achieving quantitative validation targets while also providing plausible causal explanations for temporal characteristics of acetaminophen hepatotoxicity. We isolated virtual hepatocytes, created a virtual culture, and then conducted dose-response experiments in both culture and mice. We expected to see differences between the two dose-response curves but were somewhat surprised that they crossed because it evidenced that simulated acetaminophen metabolism and toxicity are different for virtual culture and mouse contexts even though individual hepatocyte mechanisms were unchanged. Differences in dose-response curves provide a virtual example of an in vivo-to-in vitro disconnect. We use detailed results of experiments to explain this disconnect. Individual hepatocytes contribute differently to system-level phenomena. In liver, hepatocytes are exposed to acetaminophen sequentially. Relative production of the reactive acetaminophen metabolite is largest (smallest) in pericentral (periportal) hepatocytes. Because that sequential exposure is absent in culture, hepatocytes from different lobular locations do not respond the same. A virtual culture-to-mouse translation can stand as a scientifically challengeable hypothesis explaining an in vivo-to-in vitro disconnect. It provides a framework to develop more reliable interpretations of in vitro observations, which then may be used to improve extrapolations.

Simulation enabled search for explanatory mechanisms of the fracture healing process

A significant portion of bone fractures fail to heal properly, increasing healthcare costs. Advances in fracture management have slowed because translation barriers have limited generation of mechanism-based explanations for the healing process. When uncertainties are numerous, analogical modeling can be an effective strategy for developing plausible explanations of complex phenomena. We demonstrate the feasibility of engineering analogical models in software to facilitate discovery of biomimetic explanations for how fracture healing may progress. Concrete analogical models—Callus Analogs—were created using the MASON simulation toolkit. We designated a Target Region initial state within a characteristic tissue section of mouse tibia fracture at day-7 and posited a corresponding day-10 Target Region final state. The goal was to discover a coarse-grain analog mechanism that would enable the discretized initial state to transform itself into the corresponding Target Region final state, thereby providing an alternative way to study the healing process. One of nine quasi-autonomous Tissue Unit types is assigned to each grid space, which maps to an 80×80 μm region of the tissue section. All Tissue Units have an opportunity each time step to act based on individualized logic, probabilities, and information about adjacent neighbors. Action causes transition from one Tissue Unit type to another, and simulation through several thousand time steps generates a coarse-grain analog—a theory—of the healing process. We prespecified a minimum measure of success: simulated and actual Target Region states achieve ≥ 70% Similarity. We used an iterative refinement protocol to explore many combinations of Tissue Unit logic and action constraints. Workflows progressed through four stages of analog mechanisms. Similarities of 73–90% were achieved for Mechanisms 2–4. The range of Upper-Level similarities increased to 83–94% when we allowed for uncertainty about two Tissue Unit designations. We have demonstrated how Callus Analog experiments provide domain experts with a fresh medium and tools for thinking about and understanding the fracture healing process.

Translation barriers have limited the generation of mechanism-based explanations of fracture healing processes. Those barriers help explain why, to date, biological therapeutics have had only a minor impact on fracture management. Alternative approaches are needed, and we present one that is intended to help develop incrementally better mechanism-based explanations of fracture healing phenomena. We created virtual Callus Analogs to simulate how the histologic appearance of a mouse fracture callus may transition from day-7 to day-10. Callus Analogs use software-based model mechanisms, and simulation experiments enable challenging and improving those model mechanisms. During execution, model mechanism operation provides a coarse-grain explanation (a theory) of a four-day portion of the healing process. Simulated day-10 callus histologic images achieved 73–94% Similarity to a corresponding day-10 fracture callus image, thus demonstrating feasibility. Simulated healing provides an alternative perspective on the actual healing process and an alternative way of thinking about plausible fracture healing mechanisms. Our working hypothesis is that the approach can be extended to cover more of the healing process while making features of simulated and actual fracture healing increasingly analogous. The methods presented are intended to be extensible to other research areas that use histologic analysis to investigate and explain tissue level phenomena.

Competing Mechanistic Hypotheses of Acetaminophen-Induced Hepatotoxicity Challenged by Virtual Experiments

Acetaminophen-induced liver injury in mice is a model for drug-induced liver injury in humans. A precondition for improved strategies to disrupt and/or reverse the damage is a credible explanatory mechanism for how toxicity phenomena emerge and converge to cause hepatic necrosis. The Target Phenomenon in mice is that necrosis begins adjacent to the lobule's central vein (CV) and progresses outward. An explanatory mechanism remains elusive. Evidence supports that location dependent differences in NAPQI (the reactive metabolite) formation within hepatic lobules (NAPQI zonation) are necessary and sufficient prerequisites to account for that phenomenon. We call that the NZ-mechanism hypothesis. Challenging that hypothesis in mice is infeasible because 1) influential variables cannot be controlled, and 2) it would require sequential intracellular measurements at different lobular locations within the same mouse. Virtual hepatocytes use independently configured periportal-to-CV gradients to exhibit lobule-location dependent behaviors. Employing NZ-mechanism achieved quantitative validation targets for acetaminophen clearance and metabolism but failed to achieve the Target Phenomenon. We posited that, in order to do so, at least one additional feature must exhibit zonation by decreasing in the CV direction. We instantiated and explored two alternatives: 1) a glutathione depletion threshold diminishes in the CV direction; and 2) ability to repair mitochondrial damage diminishes in the CV direction. Inclusion of one or the other feature into NZ-mechanism failed to achieve the Target Phenomenon. However, inclusion of both features enabled successfully achieving the Target Phenomenon. The merged mechanism provides a multilevel, multiscale causal explanation of key temporal features of acetaminophen hepatotoxicity in mice. We discovered that variants of the merged mechanism provide plausible quantitative explanations for the considerable variation in 24-hour necrosis scores among 37 genetically diverse mouse strains following a single toxic acetaminophen dose.

STON: exploring biological pathways using the SBGN standard and graph databases

Background

When modeling in Systems Biology and Systems Medicine, the data is often extensive, complex and heterogeneous. Graphs are a natural way of representing biological networks. Graph databases enable efficient storage and processing of the encoded biological relationships. They furthermore support queries on the structure of biological networks.

Results

We present the Java-based framework STON (SBGN TO Neo4j). STON imports and translates metabolic, signalling and gene regulatory pathways represented in the Systems Biology Graphical Notation into a graph-oriented format compatible with the Neo4j graph database.

Conclusion

STON exploits the power of graph databases to store and query complex biological pathways. This advances the possibility of: i) identifying subnetworks in a given pathway; ii) linking networks across different levels of granularity to address difficulties related to incomplete knowledge representation at single level; and iii) identifying common patterns between pathways in the database.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1394-x) contains supplementary material, which is available to authorized users.

Virtual Experiments Enable Exploring and Challenging Explanatory Mechanisms of Immune-Mediated P450 Down-Regulation

Hepatic cytochrome P450 levels are down-regulated during inflammatory disease states, which can cause changes in downstream drug metabolism and hepatotoxicity. Long-term, we seek sufficient new insight into P450-regulating mechanisms to correctly anticipate how an individual’s P450 expressions will respond when health and/or therapeutic interventions change. To date, improving explanatory mechanistic insight relies on knowledge gleaned from in vitro, in vivo, and clinical experiments augmented by case reports. We are working to improve that reality by developing means to undertake scientifically useful virtual experiments. So doing requires translating an accepted theory of immune system influence on P450 regulation into a computational model, and then challenging the model via in silico experiments. We build upon two existing agent-based models—an in silico hepatocyte culture and an in silico liver—capable of exploring and challenging concrete mechanistic hypotheses. We instantiate an in silico version of this hypothesis: in response to lipopolysaccharide, Kupffer cells down-regulate hepatic P450 levels via inflammatory cytokines, thus leading to a reduction in metabolic capacity. We achieve multiple in vitro and in vivo validation targets gathered from five wet-lab experiments, including a lipopolysaccharide-cytokine dose-response curve, time-course P450 down-regulation, and changes in several different measures of drug clearance spanning three drugs: acetaminophen, antipyrine, and chlorzoxazone. Along the way to achieving validation targets, various aspects of each model are falsified and subsequently refined. This iterative process of falsification-refinement-validation leads to biomimetic yet parsimonious mechanisms, which can provide explanatory insight into how, where, and when various features are generated. We argue that as models such as these are incrementally improved through multiple rounds of mechanistic falsification and validation, we will generate virtual systems that embody deeper credible, actionable, explanatory insight into immune system-drug metabolism interactions within individuals.

BrainSignals Revisited: Simplifying a Computational Model of Cerebral Physiology

Multimodal monitoring of brain state is important both for the investigation of healthy cerebral physiology and to inform clinical decision making in conditions of injury and disease. Near-infrared spectroscopy is an instrument modality that allows non-invasive measurement of several physiological variables of clinical interest, notably haemoglobin oxygenation and the redox state of the metabolic enzyme cytochrome c oxidase. Interpreting such measurements requires the integration of multiple signals from different sources to try to understand the physiological states giving rise to them. We have previously published several computational models to assist with such interpretation. Like many models in the realm of Systems Biology, these are complex and dependent on many parameters that can be difficult or impossible to measure precisely. Taking one such model, BrainSignals, as a starting point, we have developed several variant models in which specific regions of complexity are substituted with much simpler linear approximations. We demonstrate that model behaviour can be maintained whilst achieving a significant reduction in complexity, provided that the linearity assumptions hold. The simplified models have been tested for applicability with simulated data and experimental data from healthy adults undergoing a hypercapnia challenge, but relevance to different physiological and pathophysiological conditions will require specific testing. In conditions where the simplified models are applicable, their greater efficiency has potential to allow their use at the bedside to help interpret clinical data in near real-time.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

The Open Physiology workflow: modeling processes over physiology circuitboards of interoperable tissue units

A key challenge for the physiology modeling community is to enable the searching, objective comparison and, ultimately, re-use of models and associated data that are interoperable in terms of their physiological meaning. In this work, we outline the development of a workflow to modularize the simulation of tissue-level processes in physiology. In particular, we show how, via this approach, we can systematically extract, parcellate and annotate tissue histology data to represent component units of tissue function. These functional units are semantically interoperable, in terms of their physiological meaning. In particular, they are interoperable with respect to [i] each other and with respect to [ii] a circuitboard representation of long-range advective routes of fluid flow over which to model long-range molecular exchange between these units. We exemplify this approach through the combination of models for physiology-based pharmacokinetics and pharmacodynamics to quantitatively depict biological mechanisms across multiple scales. Links to the data, models and software components that constitute this workflow are found at http://open-physiology.org/.