VeVaPy, a Python Platform for Efficient Verification and Validation of Systems Biology Models with Demonstrations Using Hypothalamic-Pituitary-Adrenal Axis Models.

In order for mathematical models to make credible contributions, it is essential for them to be verified and validated. Currently, verification and validation (V&V) of these models does not meet the expectations of the system biology and systems pharmacology communities. Partially as a result of this shortfall, systemic V&V of existing models currently requires a lot of time and effort. In order to facilitate systemic V&V of chosen hypothalamic-pituitary-adrenal (HPA) axis models, we have developed a computational framework named VeVaPy-taking care to follow the recommended best practices regarding the development of mathematical models. VeVaPy includes four functional modules coded in Python, and the source code is publicly available. We demonstrate that VeVaPy can help us efficiently verify and validate the five HPA axis models we have chosen. Supplied with new and independent data, VeVaPy outputs objective V&V benchmarks for each model. We believe that VeVaPy will help future researchers with basic modeling and programming experience to efficiently verify and validate mathematical models from the fields of systems biology and systems pharmacology.

SWAP, SWITCH, and STABILIZE: Mechanisms of Kinetochore-Microtubule Error Correction.

For correct chromosome segregation in mitosis, eukaryotic cells must establish chromosome biorientation where sister kinetochores attach to microtubules extending from opposite spindle poles. To establish biorientation, any aberrant kinetochore-microtubule interactions must be resolved in the process called error correction. For resolution of the aberrant interactions in error correction, kinetochore-microtubule interactions must be exchanged until biorientation is formed (the SWAP process). At initiation of biorientation, the state of weak kinetochore-microtubule interactions should be converted to the state of stable interactions (the SWITCH process)-the conundrum of this conversion is called the initiation problem of biorientation. Once biorientation is established, tension is applied on kinetochore-microtubule interactions, which stabilizes the interactions (the STABILIZE process). Aurora B kinase plays central roles in promoting error correction, and Mps1 kinase and Stu2 microtubule polymerase also play important roles. In this article, we review mechanisms of error correction by considering the SWAP, SWITCH, and STABILIZE processes. We mainly focus on mechanisms found in budding yeast, where only one microtubule attaches to a single kinetochore at biorientation, making the error correction mechanisms relatively simpler.

Two heads are better than one: current landscape of integrating QSP and machine learning : An ISoP QSP SIG white paper by the working group on the integration of quantitative systems pharmacology and machine learning.

Quantitative systems pharmacology (QSP) modeling is applied to address essential questions in drug development, such as the mechanism of action of a therapeutic agent and the progression of disease. Meanwhile, machine learning (ML) approaches also contribute to answering these questions via the analysis of multi-layer 'omics' data such as gene expression, proteomics, metabolomics, and high-throughput imaging. Furthermore, ML approaches can also be applied to aspects of QSP modeling. Both approaches are powerful tools and there is considerable interest in integrating QSP modeling and ML. So far, a few successful implementations have been carried out from which we have learned about how each approach can overcome unique limitations of the other. The QSP + ML working group of the International Society of Pharmacometrics QSP Special Interest Group was convened in September, 2019 to identify and begin realizing new opportunities in QSP and ML integration. The working group, which comprises 21 members representing 18 academic and industry organizations, has identified four categories of current research activity which will be described herein together with case studies of applications to drug development decision making. The working group also concluded that the integration of QSP and ML is still in its early stages of moving from evaluating available technical tools to building case studies. This paper reports on this fast-moving field and serves as a foundation for future codification of best practices.

Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling.

Individual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of 'patients' with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients' heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic-pituitary-adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system's behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

A Modeling and Machine Learning Pipeline to Rationally Design Treatments to Restore Neuroendocrine Disorders in Heterogeneous Individuals.

Heterogeneity among individual patients presents a fundamental challenge to effective treatment, since a treatment protocol working for a portion of the population often fails in others. We hypothesize that a computational pipeline integrating mathematical modeling and machine learning could be used to address this fundamental challenge and facilitate the optimization of individualized treatment protocols. We tested our hypothesis with the neuroendocrine systems controlled by the hypothalamic-pituitary-adrenal (HPA) axis. With a synergistic combination of mathematical modeling and machine learning (ML), this integrated computational pipeline could indeed efficiently reveal optimal treatment targets that significantly contribute to the effective treatment of heterogeneous individuals. What is more, the integrated pipeline also suggested quantitative information on how these key targets should be perturbed. Based on such ML revealed hints, mathematical modeling could be used to rationally design novel protocols and test their performances. We believe that this integrated computational pipeline, properly applied in combination with other computational, experimental and clinical research tools, can be used to design novel and improved treatment against a broad range of complex diseases.

Extracting Insights From Temporal Data by Integrating Dynamic Modeling and Machine Learning.

Biological processes are dynamic. As a result, temporal analyses are necessary to fully understand the complex interactions that occurs within these systems. One example of a multifaceted biological process is restitution: the initial step in complex wound repair. Restitution is a dynamic process that depends on an elegant orchestration between damaged cells and their intact neighbors. Such orchestration enables the quick repair of the damaged area, which is essential to preserve epithelial integrity and prevent further injury. High quality dynamic data of the cellular and molecular events that make up the gastric restitution process has been documented. However, comprehensive dynamic models that connect all relevant molecular interactions to cellular behaviors are challenging to construct and experimentally validate. In order to efficiently provide feedback to ongoing experimental work, we have integrated dynamical modeling and machine learning to efficiently extract data-driven insights without incorporating detailed mechanisms. Dynamical models convert time course data into a set of static features, which are then subjected to machine learning analysis. The integrated analysis provides data-driven insights into how repair might be regulated in individual gastric organoids. We have provided a "proof of concept" of how such an analysis pipeline can be used to analyze any temporal dataset and provide timely data-driven insights.

Designing combination therapies with modeling chaperoned machine learning.

Chemotherapy resistance is a major challenge to the effective treatment of cancer. Thus, a systematic pipeline for the efficient identification of effective combination treatments could bring huge biomedical benefit. In order to facilitate rational design of combination therapies, we developed a comprehensive computational model that incorporates the available biological knowledge and relevant experimental data on the life-and-death response of individual cancer cells to cisplatin or cisplatin combined with the TNF-related apoptosis-inducing ligand (TRAIL). The model's predictions, that a combination treatment of cisplatin and TRAIL would enhance cancer cell death and exhibit a "two-wave killing" temporal pattern, was validated by measuring the dynamics of p53 accumulation, cell fate, and cell death in single cells. The validated model was then subjected to a systematic analysis with an ensemble of diverse machine learning methods. Though each method is characterized by a different algorithm, they collectively identified several molecular players that can sensitize tumor cells to cisplatin-induced apoptosis (sensitizers). The identified sensitizers are consistent with previous experimental observations. Overall, we have illustrated that machine learning analysis of an experimentally validated mechanistic model can convert our available knowledge into the identity of biologically meaningful sensitizers. This knowledge can then be leveraged to design treatment strategies that could improve the efficacy of chemotherapy.

Correction to: A quantitative systems pharmacology (QSP) model for Pneumocystis treatment in mice.

It was highlighted that the original article [1] contained errors in the figures and their legends and by extension the in-text figure citations. This Corrections article shows the correct figures and correct figure legends.

Constitutive STAT5 activation regulates Paneth and Paneth-like cells to control Clostridium difficile colitis.

Clostridium difficile impairs Paneth cells, driving intestinal inflammation that exaggerates colitis. Besides secreting bactericidal products to restrain C. difficile, Paneth cells act as guardians that constitute a niche for intestinal epithelial stem cell (IESC) regeneration. However, how IESCs are sustained to specify Paneth-like cells as their niche remains unclear. Cytokine-JAK-STATs are required for IESC regeneration. We investigated how constitutive STAT5 activation (Ca-pYSTAT5) restricts IESC differentiation towards niche cells to restrain C. difficile infection. We generated inducible transgenic mice and organoids to determine the effects of Ca-pYSTAT5-induced IESC lineages on C. difficile colitis. We found that STAT5 absence reduced Paneth cells and predisposed mice to C. difficile ileocolitis. In contrast, Ca-pYSTAT5 enhanced Paneth cell lineage tracing and restricted Lgr5 IESC differentiation towards pYSTAT5+Lgr5-CD24+Lyso+ or cKit+ niche cells, which imprinted Lgr5hiKi67+ IESCs. Mechanistically, pYSTAT5 activated Wnt/ß-catenin signaling to determine Paneth cell fate. In conclusion, Ca-pYSTAT5 gradients control niche differentiation. Lack of pYSTAT5 reduces the niche cells to sustain IESC regeneration and induces C. difficile ileocolitis. STAT5 may be a transcription factor that regulates Paneth cells to maintain niche regeneration.

Trefoil factor 2 activation of CXCR4 requires calcium mobilization to drive epithelial repair in gastric organoids.

KEY POINTS: Determining the signalling cascade of epithelial repair, using murine gastric organoids, allows definition of regulatory processes intrinsic to epithelial cells, at the same time as validating and dissecting the signalling cascade with more precision than is possible in vivo Following single cell damage, intracellular calcium selectively increases within cells adjacent to the damage site and is essential for promoting repair. Trefoil factor 2 (TFF2) acts via chemokine C-X-C receptor 4 and epidermal growth factor receptor signalling, including extracellular signal-regulated kinase activation, to drive calcium mobilization and promote gastric repair. Sodium hydrogen exchanger 2, although essential for repair, acts downstream of TFF2 and calcium mobilization. ABSTRACT: The gastric mucosa of the stomach is continually exposed to environmental and physiological stress factors that can cause local epithelial damage. Although much is known about the complex nature of gastric wound repair, the stepwise process that characterizes epithelial restitution remains poorly defined. The present study aimed to determine the effectors that drive gastric epithelial repair using a reductionist culture model. To determine the role of trefoil factor 2 (TFF2) and intracellular calcium (Ca2+ ) mobilization in gastric restitution, gastric organoids were derived from TFF2 knockout (KO) mice and yellow Cameleon-Nano15 (fluorescent calcium reporter) transgenic mice, respectively. Inhibitors and recombinant protein were used to determine the upstream and downstream effectors of gastric restitution following photodamage (PD) to single cells within the gastric organoids. Single cell PD resulted in parallel events of dead cell exfoliation and migration of intact neighbouring cells to restore a continuous epithelium in the damage site. Under normal conditions following PD, Ca2+ levels increased within neighbour migrating cells, peaking at ∼1 min, suggesting localized Ca2+ mobilization at the site of cell protrusion/migration. TFF2 KO organoids exhibit delayed repair; however, this delay can be rescued by the addition of exogenous TFF2. Inhibition of epidermal growth factor receptor (EGFR), extracellular signal-regulated kinase (ERK)1/2 or a TFF2 receptor, chemokine C-X-C receptor 4 (CXCR4), resulted in significant delay and dampened Ca2+ mobilization. Inhibition of sodium hydrogen exchanger 2 (NHE2) caused significant delay but did not affect Ca2+ mobilization. A similar delay was observed in NHE2 KO organoids. In TFF2 KO gastric organoids, the addition of exogenous TFF2 in the presence of EGFR or CXCR4 inhibition was unable to rescue repair. The present study demonstrates that intracellular Ca2+ mobilization occurs within gastric epithelial cells adjacent to the damage site to promote repair by mechanisms that involve TFF2 signalling via CXCR4, as well as activation of EGFR and ERK1/2. Furthermore NHE2 is shown to be important for efficient repair and to operate via a mechanism either downstream or independent of calcium mobilization.

Unraveling the Control of Cell Cycle Periods during Intestinal Stem Cell Differentiation.

During differentiation, intestinal stem cells (ISCs), a prototypical adult stem cell pool, become either secretory transit-amplifying cells, which give rise to all secretory cell types, or absorptive transit-amplifying cells, which give rise to enterocytes. These cells exhibit distinct cell cycle dynamics: ISCs cycle with a period of 24 h and absorptive transit-amplifying cells cycle with a period of ∼12 h, whereas secretory transit-amplifying cells arrest their cycle. The cell cycle dynamics of ISCs and their progeny are a systems-level property that emerges from interactions between the cell cycle control machinery and multiple regulatory pathways. Although many mathematical models have been developed to study the details of the cell cycle and related regulatory pathways, few models have been constructed to unravel the dynamic consequences of their interactions. To fill this gap, we present a simplified model focusing on the interaction between four key regulatory pathways (STAT, Wnt, Notch, and MAPK) and cell cycle control. After experimentally validating a model prediction, which showed that the Notch pathway can fine-tune the cell cycle period, we perform further model analysis that reveals that the change of cell cycle period accompanying ISC differentiation may be controlled by a design principle that has been well studied in dynamical systems theory-a saddle node on invariant circle bifurcation. Given that the mechanisms that control the cell cycle are conserved in most eukaryotic cell types, this general principle potentially controls the interplay between proliferation and differentiation for a broad range of stem cells.

Cell injury triggers actin polymerization to initiate epithelial restitution.

The role of the actin cytoskeleton in the sequence of physiological epithelial repair in the intact epithelium has yet to be elucidated. Here, we explore the role of actin in gastric repair in vivo and in vitro gastric organoids (gastroids). In response to two-photon-induced cellular damage of either an in vivo gastric or in vitro gastroid epithelium, actin redistribution specifically occurred in the lateral membranes of cells neighboring the damaged cell. This was followed by their migration inward to close the gap at the basal pole of the dead cell, in parallel with exfoliation of the dead cell into the lumen. The repair and focal increase of actin was significantly blocked by treatment with EDTA or the inhibition of actin polymerization. Treatment with inhibitors of myosin light chain kinase, myosin II, trefoil factor 2 signaling or phospholipase C slowed both the initial actin redistribution and the repair. While Rac1 inhibition facilitated repair, inhibition of RhoA/Rho-associated protein kinase inhibited it. Inhibitors of focal adhesion kinase and Cdc42 had negligible effects. Hence, initial actin polymerization occurs in the lateral membrane, and is primarily important to initiate dead cell exfoliation and cell migration to close the gap.

A quantitative systems pharmacology (QSP) model for Pneumocystis treatment in mice.

BACKGROUND: The yeast-like fungi Pneumocystis, resides in lung alveoli and can cause a lethal infection known as Pneumocystis pneumonia (PCP) in hosts with impaired immune systems. Current therapies for PCP, such as trimethoprim-sulfamethoxazole (TMP-SMX), suffer from significant treatment failures and a multitude of serious side effects. Novel therapeutic approaches (i.e. newly developed drugs or novel combinations of available drugs) are needed to treat this potentially lethal opportunistic infection. Quantitative Systems Pharmacological (QSP) models promise to aid in the development of novel therapies by integrating available pharmacokinetic (PK) and pharmacodynamic (PD) knowledge to predict the effects of new treatment regimens. RESULTS: In this work, we constructed and independently validated PK modules of a number of drugs with available pharmacokinetic data. Characterized by simple structures and well constrained parameters, these PK modules could serve as a convenient tool to summarize and predict pharmacokinetic profiles. With the currently accepted hypotheses on the life stages of Pneumocystis, we also constructed a PD module to describe the proliferation, transformation, and death of Pneumocystis. By integrating the PK module and the PD module, the QSP model was constrained with observed levels of asci and trophic forms following treatments with multiple drugs. Furthermore, the temporal dynamics of the QSP model were validated with corresponding data. CONCLUSIONS: We developed and validated a QSP model that integrates available data and promises to facilitate the design of future therapies against PCP.

Multiscale positive feedbacks contribute to unidirectional gastric disease progression induced by helicobacter pylori infection.

BACKGROUND: Helicobacter Pylori (HP) is the most common risk factor for gastric cancer. Nearly half the world's population is infected with HP, but only a small percentage of those develop significant pathology. The bacteria itself does not directly cause cancer; rather it promotes an environment that is conducive to tumor formation. Upon infection, HP induces transcriptional changes in the host, leading to enhanced proliferation and host immune response. In addition, HP causes direct damage to gastric epithelial cells. RESULTS: We present a multiscale mechanistic model of HP induced changes. The model includes four modules representing the host transcriptional changes in response to infection, gastric atrophy, the Hedgehog pathway response, and the restriction point that controls cell cycle. This model was able to recapture a number of literature reported observations and was used as an "in silico" representation of the biological system for further analysis. Dynamical analysis of the model revealed that HP might induce the activation of multiple interplayed positive feedbacks, which in turn might result in a "ratchet ladder" system that promotes a unidirectional progression of gastric disease. CONCLUSIONS: The current multiscale model is able to recapitulate the observed experimental features of HP host interactions and provides dynamic insights on the epidemiologically observed heterogeneity in disease progression. This model provides a solid framework that can be further expanded and validated to include additional experimental evidence, to understand the complex multi-pathway interactions characterizing HP infection, and to design novel treatment protocols for HP induced diseases.

A dynamical framework for complex fractional killing.

When chemotherapy drugs are applied to tumor cells with the same or similar genotypes, some cells are killed, while others survive. This fractional killing contributes to drug resistance in cancer. Through an incoherent feedforward loop, chemotherapy drugs not only activate p53 to induce cell death, but also promote the expression of apoptosis inhibitors which inhibit cell death. Consequently, cells in which p53 is activated early undergo apoptosis while cells in which p53 is activated late survive. The incoherent feedforward loop and the essential role of p53 activation timing makes fractional killing a complex dynamical challenge, which is hard to understand with intuition alone. To better understand this process, we have constructed a representative model by integrating the control of apoptosis with the relevant signaling pathways. After the model was trained to recapture the observed properties of fractional killing, it was analyzed with nonlinear dynamical tools. The analysis suggested a simple dynamical framework for fractional killing, which predicts that cell fate can be altered in three possible ways: alteration of bifurcation geometry, alteration of cell trajectories, or both. These predicted categories can explain existing strategies known to combat fractional killing and facilitate the design of novel strategies.

Solving a class of generalized fractional programming problems using the feasibility of linear programs.

This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

A mathematical model of a recombinant humanized anti-cocaine monoclonal antibody's effects on cocaine pharmacokinetics in mice.

AIMS: A recombinant humanized anti-cocaine monoclonal antibody (mAb), h2E2, is at an advanced stage of pre-clinical development as an immunotherapy for cocaine abuse. It is hypothesized that h2E2 binds to and sequesters cocaine in the blood. MAIN METHODS: A three-compartment model of the effects of h2E2 on cocaine's distribution was constructed. The model assumes that h2E2 binds to cocaine and that the h2E2-cocaine complex does not enter the brain but distributes between the central and peripheral compartments. Free cocaine is eliminated from both the central and peripheral compartments, and h2E2 and the h2E2-cocaine complex are eliminated from the central compartment only. This model was tested against a new dataset measuring cocaine concentrations in the brain and plasma over 1h in the presence and absence of h2E2. KEY FINDINGS: The mAb significantly increased plasma cocaine concentrations with a concomitant significant decrease in brain concentration. Plasma concentrations declined over the 1-hour sampling period in both groups. With a set of parameters within reasonable physiological ranges, the three-compartment model was able to qualitatively and quantitatively simulate the increased plasma concentration in the presence of the antibody and the decreased peak brain concentration in the presence of antibody. Importantly, the model explained the decline in plasma concentrations over time as distribution of the cocaine-h2E2 complex into a peripheral compartment. SIGNIFICANCE: This model will facilitate the targeting of ideal mAb PK/PD properties thus accelerating the identification of lead candidate anti-drug mAbs.

Intercellular Coupling of the Cell Cycle and Circadian Clock in Adult Stem Cell Culture.

Circadian clock-gated cell division cycles are observed from cyanobacteria to mammals via intracellular molecular connections between these two oscillators. Here we demonstrate WNT-mediated intercellular coupling between the cell cycle and circadian clock in 3D murine intestinal organoids (enteroids). The circadian clock gates a population of cells with heterogeneous cell-cycle times that emerge as 12-hr synchronized cell division cycles. Remarkably, we observe reduced-amplitude oscillations of circadian rhythms in intestinal stem cells and progenitor cells, indicating an intercellular signal arising from differentiated cells governing circadian clock-dependent synchronized cell division cycles. Stochastic simulations and experimental validations reveal Paneth cell-secreted WNT as the key intercellular coupling component linking the circadian clock and cell cycle in enteroids.

Time to move on: Modeling transcription dynamics during an embryonic transition away from maternal control.

In a recent study, we investigated the regulation of hunchback (hb) transcription dynamics in Drosophila embryos. Our results suggest that shutdown of hb transcription at early nuclear cycle (nc) 14 is an event associated with the global changes taking place during the mid-blastula transition (MBT). Here we have developed a simple model of hb transcription dynamics during this transition time. With kinetic parameters estimated from our published experimental data, the model describes the dynamical processes of hb gene transcription and hb mRNA accumulation. With two steps, transcription onset upon exiting the previous mitosis followed by a sudden impact that blocks gene activation, the model recapitulates the observed dynamics of hb transcription during the nc14 interphase. The timing of gene inactivation is essential, as its alterations lead to changes in both hb transcription dynamics and hb mRNA levels. Our model provides a clear dynamical picture of hb transcription regulation as one of the many, actively regulated events concurrently taking place during the MBT.