Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach.

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present a modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding rational strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally determined from experiments, augmented with dynamical network computations involving endpoint objective functions, mutual information, change-point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method, based on the strategies described above. The cybernetic-inspired method is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this innovative framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

Sequestration of histidine kinases by non-cognate response regulators establishes a threshold level of stimulation for bacterial two-component signaling.

Bacterial two-component systems (TCSs) consist of a sensor histidine kinase (HK) that perceives a specific signal, and a cognate response regulator (RR) that modulates the expression of target genes. Positive autoregulation improves TCS sensitivity to stimuli, but may trigger disproportionately large responses to weak signals, compromising bacterial fitness. Here, we combine experiments and mathematical modelling to reveal a general design that prevents such disproportionate responses: phosphorylated HKs (HK~Ps) can be sequestered by non-cognate RRs. We study five TCSs of Mycobacterium tuberculosis and find, for all of them, non-cognate RRs that show higher affinity than cognate RRs for HK~Ps. Indeed, in vitro assays show that HK~Ps preferentially bind higher affinity non-cognate RRs and get sequestered. Mathematical modelling indicates that this sequestration would introduce a 'threshold' stimulus strength for eliciting responses, thereby preventing responses to weak signals. Finally, we construct tunable expression systems in Mycobacterium bovis BCG to show that higher affinity non-cognate RRs suppress responses in vivo.

Leveraging mathematical modeling to analyze nonadherence for hydroxyurea therapy in sickle cell disease.

Nonadherence is common in individuals with sickle cell disease (SCD) on hydroxyurea therapy and can be observed with waning improvements in hematologic parameters or biomarkers like mean cell volume and fetal hemoglobin level over time. We modeled the impact of hydroxyurea nonadherence on longitudinal biomarker profiles. We estimated the potential nonadherent days in individuals exhibiting a drop in biomarker levels by modifying the dosing profile using a probabilistic approach. Incorporating additional nonadherence using our approach besides existing ones in the dosing profile improves the model fits. We also studied how different patterns in adherence give rise to various physiological profiles of biomarkers. The key finding is consecutive days of nonadherence are less favorable than when nonadherence is interspersed. These findings improve our understanding of nonadherence and how appropriate intervention strategies can be applied for individuals with SCD susceptible to the severe impacts of nonadherence.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach.

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present an elegant modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding entirely novel strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally-determined from experiments, augmented with dynamical network computations involving end point objective functions, mutual information, change point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method (CIM), utilizing the strategies described above. The CIM is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this state-of-the-art framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights. STATEMENT OF SIGNIFICANCE: Cellular processes like cell cycle are overly complex, involving multiple players interacting at multiple levels, and explicit modeling of such systems is challenging. The availability of longitudinal RNA measurements provides an opportunity to "reverse-engineer" for novel regulatory models. We develop a novel framework, inspired using goal-oriented cybernetic model, to implicitly model transcriptional regulation by constraining the system using inferred temporal goals. A preliminary causal network based on information-theory is used as a starting point, and our framework is used to distill the network to temporally-based networks containing essential molecular players. The strength of this approach is its ability to dynamically model the RNA temporal measurements. The approach developed paves the way for inferring regulatory processes in many complex cellular processes.

The Extent of Antimicrobial Resistance Due to Efflux Pump Regulation.

A key mechanism driving antimicrobial resistance (AMR) stems from the ability of bacteria to up-regulate efflux pumps upon exposure to drugs. The resistance gained by this up-regulation is pliable because of the tight regulation of efflux pump levels. This leads to temporary enhancement in survivability of bacteria due to higher efflux pump levels in the presence of antibiotics, which can be reversed when the cells are no longer exposed to the drug. Knowledge of the extent of resistance thus gained would inform intervention strategies aimed at mitigating AMR. Here, we combine mathematical modeling and experiments to quantify the maximum extent of resistance that efflux pump up-regulation can confer via phenotypic induction in the presence of drugs and genotypic abrogation of regulation. Our model describes the dynamics of drug transport in and out of cells coupled with the associated regulation of efflux pump levels and predicts the increase in the minimum inhibitory concentration (MIC) of drugs due to such regulation. To test the model, we measured the uptake and efflux as well as the MIC of the compound ethidium bromide (EtBr), a substrate of the efflux pump LfrA, in wild-type Mycobacterium smegmatis mc2155, as well as in two laboratory-generated strains. Our model captured the observed EtBr levels and MIC fold-changes quantitatively. Further, the model identified key parameters associated with the resulting resistance, variations in which could underlie the extent to which such resistance arises across different drug-bacteria combinations, potentially offering tunable handles to optimize interventions aimed at minimizing AMR.

Mathematical Modeling of Hydroxyurea Therapy in Individuals with Sickle Cell Disease.

Sickle cell disease (SCD) is a chronic hemolytic anemia affecting millions worldwide with acute and chronic clinical manifestations and early mortality. While hydroxyurea (HU) and other treatment strategies managed to ameliorate disease severity, high inter-individual variability in clinical response and a lack of an ability to predict those variations need to be addressed to maximize the clinical efficacy of HU. We developed pharmacokinetics (PK) and pharmacodynamics (PD) models to study the dosing, efficacy, toxicity, and clinical response of HU treatment in more than eighty children with SCD. The clinical PK parameters were used to model the HU plasma concentration for a 24 h period, and the estimated daily average HU plasma concentration was used as an input to our PD models with approximately 1 to 9 years of data connecting drug exposure with drug response. We modeled the biomarkers mean cell volume and fetal hemoglobin to study treatment efficacy. For myelosuppression, we modeled red blood cells and absolute neutrophil count. Our models provided excellent fits for individuals with known or correctly inferred adherence. Our models can be used to determine the optimal dosing regimens and study the effect of non-adherence on HU-treated individuals.

Early exposure to broadly neutralizing antibodies may trigger a dynamical switch from progressive disease to lasting control of SHIV infection.

Antiretroviral therapy (ART) for HIV-1 infection is life-long. Stopping therapy typically leads to the reignition of infection and progressive disease. In a major breakthrough, recent studies have shown that early initiation of ART can lead to sustained post-treatment control of viremia, raising hopes of long-term HIV-1 remission. ART, however, elicits post-treatment control in a small fraction of individuals treated. Strikingly, passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 early in infection was found recently to elicit long-term control in a majority of SHIV-infected macaques, suggesting that HIV-1 remission may be more widely achievable. The mechanisms underlying the control elicited by bNAb therapy, however, remain unclear. Untreated infection typically leads to progressive disease. We hypothesized that viremic control represents an alternative but rarely realized outcome of the infection and that early bNAb therapy triggers a dynamical switch to this outcome. To test this hypothesis, we constructed a model of viral dynamics with bNAb therapy and applied it to analyse clinical data. The model fit quantitatively the complex longitudinal viral load data from macaques that achieved lasting control. The model predicted, consistently with our hypothesis, that the underlying system exhibited bistability, indicating two potential outcomes of infection. The first had high viremia, weak cytotoxic effector responses, and high effector exhaustion, marking progressive disease. The second had low viremia, strong effector responses, and low effector exhaustion, indicating lasting viremic control. Further, model predictions suggest that early bNAb therapy elicited lasting control via pleiotropic effects. bNAb therapy lowers viremia, which would also limit immune exhaustion. Simultaneously, it can improve effector stimulation via cross-presentation. Consequently, viremia may resurge post-therapy, but would encounter a primed effector population and eventually get controlled. ART suppresses viremia but does not enhance effector stimulation, explaining its limited ability to elicit post-treatment control relative to bNAb therapy.

Mutational pathway maps and founder effects define the within-host spectrum of hepatitis C virus mutants resistant to drugs.

Knowledge of the within-host frequencies of resistance-associated amino acid variants (RAVs) is important to the identification of optimal drug combinations for the treatment of hepatitis C virus (HCV) infection. Multiple RAVs may exist in infected individuals, often below detection limits, at any resistance locus, defining the diversity of accessible resistance pathways. We developed a multiscale mathematical model to estimate the pre-treatment frequencies of the entire spectrum of mutants at chosen loci. Using a codon-level description of amino acids, we performed stochastic simulations of intracellular dynamics with every possible nucleotide variant as the infecting strain and estimated the relative infectivity of each variant and the resulting distribution of variants produced. We employed these quantities in a deterministic multi-strain model of extracellular dynamics and estimated mutant frequencies. Our predictions captured database frequencies of the RAV R155K, resistant to NS3/4A protease inhibitors, presenting a successful test of our formalism. We found that mutational pathway maps, interconnecting all viable mutants, and strong founder effects determined the mutant spectrum. The spectra were vastly different for HCV genotypes 1a and 1b, underlying their differential responses to drugs. Using a fitness landscape determined recently, we estimated that 13 amino acid variants, encoded by 44 codons, exist at the residue 93 of the NS5A protein, illustrating the massive diversity of accessible resistance pathways at specific loci. Accounting for this diversity, which our model enables, would help optimize drug combinations. Our model may be applied to describe the within-host evolution of other flaviviruses and inform vaccine design strategies.

Towards multiscale modeling of the CD8+ T cell response to viral infections.

The CD8+ T cell response is critical to the control of viral infections. Yet, defining the CD8+ T cell response to viral infections quantitatively has been a challenge. Following antigen recognition, which triggers an intracellular signaling cascade, CD8+ T cells can differentiate into effector cells, which proliferate rapidly and destroy infected cells. When the infection is cleared, they leave behind memory cells for quick recall following a second challenge. If the infection persists, the cells may become exhausted, retaining minimal control of the infection while preventing severe immunopathology. These activation, proliferation and differentiation processes as well as the mounting of the effector response are intrinsically multiscale and collective phenomena. Remarkable experimental advances in the recent years, especially at the single cell level, have enabled a quantitative characterization of several underlying processes. Simultaneously, sophisticated mathematical models have begun to be constructed that describe these multiscale phenomena, bringing us closer to a comprehensive description of the CD8+ T cell response to viral infections. Here, we review the advances made and summarize the challenges and opportunities ahead. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Fates Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models.

Interferon at the cellular, individual, and population level in hepatitis C virus infection: Its role in the interferon-free treatment era.

The advent of powerful direct-acting antiviral agents (DAAs) has revolutionized the treatment of hepatitis C. DAAs cure nearly all patients with short duration, oral treatments. Significant efforts are now underway to optimize DAA-based treatments. We discuss the potential role of interferon in this optimization. Clinical studies present compelling evidence that DAAs perform better in treatment-naive individuals than in individuals who previously failed treatment with interferon, a surprising correlation because interferon and DAAs are thought to act independently. Recent mathematical models explore a mechanistic hypothesis underlying this correlation. The hypothesis invokes the action of interferon at the cellular, individual, and population levels. Strong interferon responses prevent the productive infection of cells, reduce viral replication, and impede the development of resistance to DAAs in infected individuals and improve cure rates elicited by DAAs in treated populations. The models develop descriptions of these processes, integrate them into a comprehensive framework, and capture clinical data quantitatively, providing a successful test of the hypothesis. Individuals with strong endogenous interferon responses thus present a promising subpopulation for reducing DAA treatment durations. This review discusses the conceptual advances made by the models, highlights the new insights they unravel, and examines their applicability to optimize DAA-based treatments.

Modelling how responsiveness to interferon improves interferon-free treatment of hepatitis C virus infection.

Direct-acting antiviral agents (DAAs) for hepatitis C treatment tend to fare better in individuals who are also likely to respond well to interferon-alpha (IFN), a surprising correlation given that DAAs target specific viral proteins whereas IFN triggers a generic antiviral immune response. Here, we posit a causal relationship between IFN-responsiveness and DAA treatment outcome. IFN-responsiveness restricts viral replication, which would prevent the growth of viral variants resistant to DAAs and improve treatment outcome. To test this hypothesis, we developed a multiscale mathematical model integrating IFN-responsiveness at the cellular level, viral kinetics and evolution leading to drug resistance at the individual level, and treatment outcome at the population level. Model predictions quantitatively captured data from over 50 clinical trials demonstrating poorer response to DAAs in previous non-responders to IFN than treatment-naïve individuals, presenting strong evidence supporting the hypothesis. Model predictions additionally described several unexplained clinical observations, viz., the percentages of infected individuals who 1) spontaneously clear HCV, 2) get chronically infected but respond to IFN-based therapy, and 3) fail IFN-based therapy but respond to DAA-based therapy, resulting in a comprehensive understanding of HCV infection and treatment. An implication of the causal relationship is that failure of DAA-based treatments may be averted by adding IFN, a strategy of potential use in settings with limited access to DAAs. A second, wider implication is that individuals with greater IFN-responsiveness would require shorter DAA-based treatment durations, presenting a basis and a promising population for response-guided therapy.