Artificial Intelligence for Quantitative Modeling in Drug Discovery and Development: An Innovation and Quality Consortium Perspective on Use Cases and Best Practices.

Recent breakthroughs in artificial intelligence (AI) and machine learning (ML) have ushered in a new era of possibilities across various scientific domains. One area where these advancements hold significant promise is model-informed drug discovery and development (MID3). To foster a wider adoption and acceptance of these advanced algorithms, the Innovation and Quality (IQ) Consortium initiated the AI/ML working group in 2021 with the aim of promoting their acceptance among the broader scientific community as well as by regulatory agencies. By drawing insights from workshops organized by the working group and attended by key stakeholders across the biopharma industry, academia, and regulatory agencies, this white paper provides a perspective from the IQ Consortium. The range of applications covered in this white paper encompass the following thematic topics: (i) AI/ML-enabled Analytics for Pharmacometrics and Quantitative Systems Pharmacology (QSP) Workflows; (ii) Explainable Artificial Intelligence and its Applications in Disease Progression Modeling; (iii) Natural Language Processing (NLP) in Quantitative Pharmacology Modeling; and (iv) AI/ML Utilization in Drug Discovery. Additionally, the paper offers a set of best practices to ensure an effective and responsible use of AI, including considering the context of use, explainability and generalizability of models, and having human-in-the-loop. We believe that embracing the transformative power of AI in quantitative modeling while adopting a set of good practices can unlock new opportunities for innovation, increase efficiency, and ultimately bring benefits to patients.

Population pharmacokinetics of molnupiravir in adults with COVID-19: Lack of clinically important exposure variation across individuals.

Effective antiviral treatments for coronavirus disease 2019 (COVID-19) are needed to reduce the morbidity and mortality associated with severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) infection, particularly in patients with risk factors for severe disease. Molnupiravir (MK-4482, EIDD-2801) is an orally administered, ribonucleoside prodrug of ß-D-N4-hydroxycytidine (NHC) with submicromolar potency against SARS-CoV-2. A population pharmacokinetic (PopPK) analysis for molnupiravir exposure was conducted using 4202 NHC plasma concentrations collected in 1207 individuals from a phase I trial in healthy participants, a phase IIa trial in non-hospitalized participants with COVID-19, a phase II trial in hospitalized participants with COVID-19, and a phase II/III trial in non-hospitalized participants with COVID-19. Molnupiravir pharmacokinetics (PK) was best described by a two-compartment model with a transit-compartment absorption model and linear elimination. Molnupiravir apparent elimination clearance increased with body weight less-than-proportionally (power 0.412) and was estimated as 70.6 L/h in 80-kg individuals with a moderate interindividual variability (43.4% coefficient of variation). Additionally, effects of sex and body mass index on apparent central volume and food status and formulation on the absorption mean transit time were identified as statistically significant descriptors of variability in these PK parameters. However, none of the identified covariate effects caused clinically relevant changes in the area under the NHC concentration versus time curve between doses, the exposure metric most closely related to clinical response. Overall, the PopPK model indicates that molnupiravir can be administered in adults without dose adjustment based on age, sex, body size, food, and mild-to-moderate renal or mild hepatic impairment.

Factors Influencing COVID-19 Risk: Insights From Molnupiravir Exposure-Response Modeling of Clinical Outcomes.

Molnupiravir (MOV) is an oral antiviral for the treatment of coronavirus disease 2019 (COVID-19) in outpatient settings. This analysis investigated the relationship between ß-D-N4-hydroxycytidine (NHC) pharmacokinetics and clinical outcomes in patients with mild to moderate COVID-19 in the phase III part of the randomized, double-blind, placebo-controlled MOVe-OUT trial. Logistic regression models of the dependency of outcomes on exposures and covariates were constructed using a multistep process. Influential covariates were identified first using placebo arm data, followed by assessment of exposure-dependency in drug effect using data from both the placebo and MOV arms. The exposure-response (E-R) analysis included 1,313 participants; 630 received MOV and 683 received placebo. Baseline viral load, baseline disease severity, age, weight, viral clade, active cancer, and diabetes were identified as significant determinants of response using placebo data. Absolute measures of viral load on days 5 and 10 were strong on-treatment predictors of hospitalization. An additive area under the curve (AUC)-based maximum effect (Emax ) model with a fixed Hill coefficient of 1 best represented the exposure-dependency in drug effect and the AUC50 was estimated to be 19,900 nM hour. Patients at 800 mg achieved near maximal response, which was larger than for 200 or 400 mg. The final E-R model was externally validated and predicted that the relative reduction in hospitalization with MOV treatment would vary with patient characteristics and factors in the population. In conclusion, the E-R results support the MOV dose of 800 mg twice daily to treat COVID-19. Many patient characteristics and factors impacted outcomes beyond drug exposures.

Safety and Pharmacokinetics of Islatravir in Individuals with Severe Renal Insufficiency.

Islatravir (MK-8591) is a high-potency reverse transcriptase translocation inhibitor in development for the treatment of HIV-1 infection. Data from preclinical and clinical studies suggest that ~30% to 60% of islatravir is excreted renally and that islatravir is not a substrate of renal transporters. To assess the impact of renal impairment on the pharmacokinetics of islatravir, an open-label phase 1 trial was conducted with individuals with severe renal insufficiency (RI). A single dose of islatravir 60 mg was administered orally to individuals with severe RI (estimated glomerular filtration rate [eGFR] <30 mL/min/1.73 m2) and to healthy individuals without renal impairment (matched control group; eGFR ≥90 mL/min/1.73 m2). Safety and tolerability were assessed, and blood samples were collected to measure the pharmacokinetics of islatravir and its major metabolite 4'-ethynyl-2-fluoro-2'deoxyinosine (M4) in plasma, as well as active islatravir-triphosphate (TP) in peripheral blood mononuclear cells (PBMCs). Plasma islatravir and M4 area under the concentration-time curve from zero to infinity (AUC0-∞) were ~2-fold and ~5-fold higher, respectively, in participants with severe RI relative to controls, whereas islatravir-TP AUC0-∞ was ~1.5-fold higher in the RI group than in the control group. The half-lives of islatravir in plasma and islatravir-TP in PBMCs were longer in participants with severe RI than in controls. These findings are consistent with renal excretion playing a major role in islatravir elimination. A single oral dose of islatravir 60 mg was generally well tolerated. These data provide guidance regarding administration of islatravir in individuals with impaired renal function. (This study has been registered at ClinicalTrials.gov under registration no. NCT04303156.).

Mechanistic Modeling of a Novel Oncolytic Virus, V937, to Describe Viral Kinetic and Dynamic Processes Following Intratumoral and Intravenous Administration.

V937 is an investigational novel oncolytic non-genetically modified Kuykendall strain of Coxsackievirus A21 which is in clinical development for the treatment of advanced solid tumor malignancies. V937 infects and lyses tumor cells expressing the intercellular adhesion molecule I (ICAM-I) receptor. We integrated in vitro and in vivo data from six different preclinical studies to build a mechanistic model that allowed a quantitative analysis of the biological processes of V937 viral kinetics and dynamics, viral distribution to tumor, and anti-tumor response elicited by V937 in human xenograft models in immunodeficient mice following intratumoral and intravenous administration. Estimates of viral infection and replication which were calculated from in vitro experiments were successfully used to describe the tumor response in vivo under various experimental conditions. Despite the predicted high clearance rate of V937 in systemic circulation (t1/2 = 4.3 min), high viral replication was observed in immunodeficient mice which resulted in tumor shrinkage with both intratumoral and intravenous administration. The described framework represents a step towards the quantitative characterization of viral distribution, replication, and oncolytic effect of a novel oncolytic virus following intratumoral and intravenous administrations in the absence of an immune response. This model may further be expanded to integrate the role of the immune system on viral and tumor dynamics to support the clinical development of oncolytic viruses.

Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality.

Feed-forward loops (FFLs) are among the most ubiquitously found motifs of reaction networks in nature. However, little is known about their stochastic behavior and the variety of network phenotypes they can exhibit. In this study, we provide full characterizations of the properties of stochastic multimodality of FFLs, and how switching between different network phenotypes are controlled. We have computed the exact steady-state probability landscapes of all eight types of coherent and incoherent FFLs using the finite-butter Accurate Chemical Master Equation (ACME) algorithm, and quantified the exact topological features of their high-dimensional probability landscapes using persistent homology. Through analysis of the degree of multimodality for each of a set of 10,812 probability landscapes, where each landscape resides over 105-106 microstates, we have constructed comprehensive phase diagrams of all relevant behavior of FFL multimodality over broad ranges of input and regulation intensities, as well as different regimes of promoter binding dynamics. In addition, we have quantified the topological sensitivity of the multimodality of the landscapes to regulation intensities. Our results show that with slow binding and unbinding dynamics of transcription factor to promoter, FFLs exhibit strong stochastic behavior that is very different from what would be inferred from deterministic models. In addition, input intensity play major roles in the phenotypes of FFLs: At weak input intensity, FFL exhibit monomodality, but strong input intensity may result in up to 6 stable phenotypes. Furthermore, we found that gene duplication can enlarge stable regions of specific multimodalities and enrich the phenotypic diversity of FFL networks, providing means for cells toward better adaptation to changing environment. Our results are directly applicable to analysis of behavior of FFLs in biological processes such as stem cell differentiation and for design of synthetic networks when certain phenotypic behavior is desired.

Immune-viral dynamics modeling for SARS-CoV-2 drug development.

Coronavirus disease 2019 (COVID-19) global pandemic is caused by severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) viral infection, which can lead to pneumonia, lung injury, and death in susceptible populations. Understanding viral dynamics of SARS-CoV-2 is critical for development of effective treatments. An Immune-Viral Dynamics Model (IVDM) is developed to describe SARS-CoV-2 viral dynamics and COVID-19 disease progression. A dataset of 60 individual patients with COVID-19 with clinical viral load (VL) and reported disease severity were assembled from literature. Viral infection and replication mechanisms of SARS-CoV-2, viral-induced cell death, and time-dependent immune response are incorporated in the model to describe the dynamics of viruses and immune response. Disease severity are tested as a covariate to model parameters. The IVDM was fitted to the data and parameters were estimated using the nonlinear mixed-effect model. The model can adequately describe individual viral dynamics profiles, with disease severity identified as a covariate on infected cell death rate. The modeling suggested that it takes about 32.6 days to reach 50% of maximum cell-based immunity. Simulations based on virtual populations suggested a typical mild case reaches VL limit of detection (LOD) by 13 days with no treatment, a moderate case by 17 days, and a severe case by 41 days. Simulations were used to explore hypothetical treatments with different initiation time, disease severity, and drug effects to demonstrate the usefulness of such modeling in informing decisions. Overall, the IVDM modeling and simulation platform enables simulations for viral dynamics and treatment efficacy and can be used to aid in clinical pharmacokinetic/pharmacodynamic (PK/PD) and dose-efficacy response analysis for COVID-19 drug development.

Mechanistic basis of post-treatment control of SIV after anti-α4ß7 antibody therapy.

Treating macaques with an anti-α4ß7 antibody under the umbrella of combination antiretroviral therapy (cART) during early SIV infection can lead to viral remission, with viral loads maintained at < 50 SIV RNA copies/ml after removal of all treatment in a subset of animals. Depletion of CD8+ lymphocytes in controllers resulted in transient recrudescence of viremia, suggesting that the combination of cART and anti-α4ß7 antibody treatment led to a state where ongoing immune responses kept the virus undetectable in the absence of treatment. A previous mathematical model of HIV infection and cART incorporates immune effector cell responses and exhibits the property of two different viral load set-points. While the lower set-point could correspond to the attainment of long-term viral remission, attaining the higher set-point may be the result of viral rebound. Here we expand that model to include possible mechanisms of action of an anti-α4ß7 antibody operating in these treated animals. We show that the model can fit the longitudinal viral load data from both IgG control and anti-α4ß7 antibody treated macaques, suggesting explanations for the viral control associated with cART and an anti-α4ß7 antibody treatment. This effective perturbation to the virus-host interaction can also explain observations in other nonhuman primate experiments in which cART and immunotherapy have led to post-treatment control or resetting of the viral load set-point. Interestingly, because the viral kinetics in the various treated animals differed-some animals exhibited large fluctuations in viral load after cART cessation-the model suggests that anti-α4ß7 treatment could act by different primary mechanisms in different animals and still lead to post-treatment viral control. This outcome is nonetheless in accordance with a model with two stable viral load set-points, in which therapy can perturb the system from one set-point to a lower one through different biological mechanisms.

Multivariate analysis reveals effect of glutathione-enriched inactive dry yeast on amino acids and volatile components of kiwi wine.

Principal component analysis (PCA) and partial least squares (PLS) regression were applied to investigate the effect of glutathione-enriched inactive dry yeast (g-IDY) on the amino acids and volatile components of kiwi wine. Results indicated that the addition of g-IDY had positive effect on most amino acids of kiwi wine, especially glutamine and glycine. In case of pure juice fermentation, the concentrations of ethyl decanoate, 2-methylbutyric acid, trans-2-nonenal and hexyl butyrate had notably positive correlation with the addition of g-IDY. PLS regression indicated that the amino acids were highly interrelated to the volatile compositions, and glycine had the strongest positive impact on the concentrations of esters and total volatile components. This might explain the similar effect of g-IDY on the amino acids and volatile components of kiwi wine. Besides, PLS regression showed that E-nose was a good method to predict volatile compositions of kiwi wine, especially esters.

Transcriptomic and metabolomic analyses reveal antibacterial mechanism of astringent persimmon tannin against Methicillin-resistant Staphylococcus aureus isolated from pork.

Persimmon tannin (PT) exhibits antibacterial activity against methicillin-resistant Staphylococcus aureus (MRSA) isolated from retail pork. The involved molecular mechanisms were investigated for the first time using transcriptome and metabolome in this study. Results showed that subinhibitory concentration of PT (0.5 mg/ml) induced significant changes in MRSA at both transcriptional and metabolic levels, as 370 genes and 19 metabolites were differentially expressed. Bioinformatic analysis revealed that the varying genes and metabolites were mainly involved in pathways of membrane transport, amino acids, carbohydrate, and energy metabolism. The highlighted changes were those related to osmotic regulation, intracellular pH regulation, amino acid synthesis and metabolism, glycolysis, TCA cycle and iron metabolism, suggesting the multifaceted effects including cell membrane damage, amino acids limitation, energy metabolism disorder and iron deprivation induced by PT. The results provided insight into the anti-MRSA mechanism of PT, which is useful for PT's development and application in food safety.

Sensitivities of Regulation Intensities in Feed-Forward Loops with Multistability.

Gene regulatory networks depict the interactions among genes, proteins, and other components of the cell. These interactions are stochastic when large differences in reaction rates and small copy number of molecules are involved. Discrete Chemical Master Equation (dCME) provides a general framework for understanding the stochastic nature of these networks. Here we used the Accurate Chemical Master Equation method to directly compute the exact steady state probability landscape of the feed-forward loop motif (FFL). FFL is one of the most abundant gene regulatory networks motifs where the regulation is carried out from the top nodes to the bottom ones. We examine the behavior of stochastic FFLs under different conditions of various regulation intensities. Under the conditions with slow promoter binding, we show how FFL can exhibit different multistabilities in their landscapes. We also study the sensitivities of regulations of FFLs and introduce a new definition of stochastic sensitivity to characterize how FFLs respond in their probability distributions at the steady state to perturbations of system parameters. We show how change in gene expression under FFL regulations are sensitive to system parameters, including the state of multistability in FFLs.

Probabilistic control of HIV latency and transactivation by the Tat gene circuit.

The reservoir of HIV latently infected cells is the major obstacle for eradication of HIV infection. The "shock-and-kill" strategy proposed earlier aims to reduce the reservoir by activating cells out of latency. While the intracellular HIV Tat gene circuit is known to play important roles in controlling latency and its transactivation in HIV-infected cells, the detailed control mechanisms are not well understood. Here we study the mechanism of probabilistic control of the latent and the transactivated cell phenotypes of HIV-infected cells. We reconstructed the probability landscape, which is the probability distribution of the Tat gene circuit states, by directly computing the exact solution of the underlying chemical master equation. Results show that the Tat circuit exhibits a clear bimodal probability landscape (i.e., there are two distinct probability peaks, one associated with the latent cell phenotype and the other with the transactivated cell phenotype). We explore potential modifications to reactions in the Tat gene circuit for more effective transactivation of latent cells (i.e., the shock-and-kill strategy). Our results suggest that enhancing Tat acetylation can dramatically increase Tat and viral production, while increasing the Tat-transactivation response binding affinity can transactivate latent cells more rapidly than other manipulations. Our results further explored the "block and lock" strategy toward a functional cure for HIV. Overall, our study demonstrates a general approach toward discovery of effective therapeutic strategies and druggable targets by examining control mechanisms of cell phenotype switching via exactly computed probability landscapes of reaction networks.

CD8+ lymphocyte control of SIV infection during antiretroviral therapy.

CD8+ lymphocytes play an important role in suppressing in vivo viral replication in HIV infection. However, both the extent to which and the mechanisms by which CD8+ lymphocytes contribute to viral control are not completely understood. A recent experiment depleted CD8+ lymphocytes in simian immunodeficiency virus (SIV)-infected rhesus macaques (RMs) on antiretroviral treatment (ART) to study the role of CD8+ lymphocytes. CD8+ lymphocytes depletion resulted in temporary plasma viremia in all studied RMs. Viral control was restored when CD8+ lymphocytes repopulated. We developed a viral dynamic model to fit the viral load (VL) data from the CD8 depletion experiment. We explicitly modeled the dynamics of the latent reservoir and the SIV-specific effector cell population including their exhaustion and their potential cytolytic and noncytolytic functions. We found that the latent reservoir significantly contributes to the size of the peak VL after CD8 depletion, while drug efficacy plays a lesser role. Our model suggests that the overall CD8+ lymphocyte cytolytic killing rate is dynamically changing depending on the levels of antigen-induced effector cell activation and exhaustion. Based on estimated parameters, our model suggests that before ART or without ART the overall CD8 cytolytic killing rate is small due to exhaustion. However, after the start of ART, the overall CD8 cytolytic killing rate increases due to an expansion of SIV-specific CD8 effector cells. Further, we estimate that the cytolytic killing rate can be significantly larger than the cytopathic death rate in some animals during the second phase of ART-induced viral decay. Lastly, our model provides a new explanation for the puzzling findings by Klatt et al. and Wong et al. that CD8 depletion done immediately before ART has no noticeable effect on the first phase viral decay slope seen after ART initiation Overall, by incorporating effector cells and their exhaustion, our model can explain the effects of CD8 depletion on VL during ART, reveals a detailed dynamic role of CD8+ lymphocytes in controlling viral infection, and provides a unified explanation for CD8 depletion experimental data.

Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean.

Fundamental to biological decision-making is the ability to generate bimodal expression patterns where 2 alternate expression states simultaneously exist. Here, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV's fate decision between active replication and viral latency. We find that the HIV transactivator of transcription (Tat) protein manipulates the intrinsic toggling of HIV's promoter, the long terminal repeat (LTR), to generate bimodal ON-OFF expression and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit's noncooperative "nonlatching" feedback architecture is optimized to slow the promoter's toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that nonlatching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV's decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

HIV persistence in tissue macrophages of humanized myeloid-only mice during antiretroviral therapy.

Despite years of fully suppressive antiretroviral therapy (ART), HIV persists in its hosts and is never eradicated. One major barrier to eradication is that the virus infects multiple cell types that may individually contribute to HIV persistence. Tissue macrophages are critical contributors to HIV pathogenesis; however, their specific role in HIV persistence during long-term suppressive ART has not been established. Using humanized myeloid-only mice (MoM), we demonstrate that HIV infection of tissue macrophages is rapidly suppressed by ART, as reflected by a rapid drop in plasma viral load and a dramatic decrease in the levels of cell-associated viral RNA and DNA. No viral rebound was observed in the plasma of 67% of the ART-treated animals at 7 weeks after ART interruption, and no replication-competent virus was rescued from the tissue macrophages obtained from these animals. In contrast, in a subset of animals (∼33%), a delayed viral rebound was observed that is consistent with the establishment of persistent infection in tissue macrophages. These observations represent the first direct evidence, to our knowledge, of HIV persistence in tissue macrophages in vivo.

Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization.

Computational modelling of cells can reveal insight into the mechanisms of the important processes of tissue development. However, current cell models have limitations and are challenged to model detailed changes in cellular shapes and physical mechanics when thousands of migrating and interacting cells need to be modelled. Here we describe a novel dynamic cellular finite-element model (DyCelFEM), which accounts for changes in cellular shapes and mechanics. It also models the full range of cell motion, from movements of individual cells to collective cell migrations. The transmission of mechanical forces regulated by intercellular adhesions and their ruptures are also accounted for. Intra-cellular protein signalling networks controlling cell behaviours are embedded in individual cells. We employ DyCelFEM to examine specific effects of biochemical and mechanical cues in regulating cell migration and proliferation, and in controlling tissue patterning using a simplified re-epithelialization model of wound tissue. Our results suggest that biochemical cues are better at guiding cell migration with improved directionality and persistence, while mechanical cues are better at coordinating collective cell migration. Overall, DyCelFEM can be used to study developmental processes when a large population of migrating cells under mechanical and biochemical controls experience complex changes in cell shapes and mechanics.

Chicoric Acid Ameliorates Lipopolysaccharide-Induced Oxidative Stress via Promoting the Keap1/Nrf2 Transcriptional Signaling Pathway in BV-2 Microglial Cells and Mouse Brain.

As a major nutraceutical component of a typical Mediterranean vegetable chicory, chicoric acid (CA) has been well-documented due to its excellent antioxidant and antiobesity bioactivities. In the current study, the effects of CA on lipopolysaccharide (LPS)-stimulated oxidative stress in BV-2 microglia and C57BL/6J mice and the underlying molecular mechanisms were investigated. Results demonstrated that CA significantly reversed LPS-elicited cell viability decrease, mitochondrial dysfunction, activation of NFκB and MAPK stress pathways, and inflammation responses via balancing cellular redox status. Furthermore, molecular modeling study demonstrated that CA could insert into the pocket of Keap1 and up-regulated Nrf2 signaling and, thus, transcriptionally regulate downstream expressions of antioxidant enzymes including HO-1 and NQO-1 in both microglial cells and ip injection of LPS-treated mouse brain. These results suggested that CA attenuated LPS-induced oxidative stress via mediating Keap1/Nrf2 transcriptional pathways and downstream enzyme expressions, which indicated that CA has great potential as a nutritional preventive strategy in oxidative stress-related neuroinflammation.

ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS.

The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks.

Gß promotes pheromone receptor polarization and yeast chemotropism by inhibiting receptor phosphorylation.

Gradient-directed cell migration (chemotaxis) and growth (chemotropism) are processes that are essential to the development and life cycles of all species. Cells use surface receptors to sense the shallow chemical gradients that elicit chemotaxis and chemotropism. Slight asymmetries in receptor activation are amplified by downstream signaling systems, which ultimately induce dynamic reorganization of the cytoskeleton. During the mating response of budding yeast, a model chemotropic system, the pheromone receptors on the plasma membrane polarize to the side of the cell closest to the stimulus. Although receptor polarization occurs before and independently of actin cable-dependent delivery of vesicles to the plasma membrane (directed secretion), it requires receptor internalization. Phosphorylation of pheromone receptors by yeast casein kinase 1 or 2 (Yck1/2) stimulates their internalization. We showed that the pheromone-responsive Gßγ dimer promotes the polarization of the pheromone receptor by interacting with Yck1/2 and locally inhibiting receptor phosphorylation. We also found that receptor phosphorylation is essential for chemotropism, independently of its role in inducing receptor internalization. A mathematical model supports the idea that the interaction between Gßγ and Yck1/2 results in differential phosphorylation and internalization of the pheromone receptor and accounts for its polarization before the initiation of directed secretion.

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation.

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.