Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics.

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.

Venetoclax, alone and in combination with the BH3 mimetic S63845, depletes HIV-1 latently infected cells and delays rebound in humanized mice.

HIV-1 persists indefinitely in people living with HIV (PLWH) on antiretroviral therapy (ART). If ART is stopped, the virus rapidly rebounds from long-lived latently infected cells. Using a humanized mouse model of HIV-1 infection and CD4+ T cells from PLWH on ART, we investigate whether antagonizing host pro-survival proteins can prime latent cells to die and facilitate HIV-1 clearance. Venetoclax, a pro-apoptotic inhibitor of Bcl-2, depletes total and intact HIV-1 DNA in CD4+ T cells from PLWH ex vivo. This venetoclax-sensitive population is enriched for cells with transcriptionally higher levels of pro-apoptotic BH3-only proteins. Furthermore, venetoclax delays viral rebound in a mouse model of persistent HIV-1 infection, and the combination of venetoclax with the Mcl-1 inhibitor S63845 achieves a longer delay in rebound compared with either intervention alone. Thus, selective inhibition of pro-survival proteins can induce death of HIV-1-infected cells that persist on ART, extending time to viral rebound.

A necroptosis-independent function of RIPK3 promotes immune dysfunction and prevents control of chronic LCMV infection.

Necroptosis is a lytic and inflammatory form of cell death that is highly constrained to mitigate detrimental collateral tissue damage and impaired immunity. These constraints make it difficult to define the relevance of necroptosis in diseases such as chronic and persistent viral infections and within individual organ systems. The role of necroptotic signalling is further complicated because proteins essential to this pathway, such as receptor interacting protein kinase 3 (RIPK3) and mixed lineage kinase domain-like (MLKL), have been implicated in roles outside of necroptotic signalling. We sought to address this issue by individually defining the role of RIPK3 and MLKL in chronic lymphocytic choriomeningitis virus (LCMV) infection. We investigated if necroptosis contributes to the death of LCMV-specific CD8+ T cells or virally infected target cells during infection. We provide evidence showing that necroptosis was redundant in the pathogenesis of acute forms of LCMV (Armstrong strain) and the early stages of chronic (Docile strain) LCMV infection in vivo. The number of immune cells, their specificity and reactivity towards viral antigens and viral loads are not altered in the absence of either MLKL or RIPK3 during acute and during the early stages of chronic LCMV infection. However, we identified that RIPK3 promotes immune dysfunction and prevents control of infection at later stages of chronic LCMV disease. This was not phenocopied by the loss of MLKL indicating that the phenotype was driven by a necroptosis-independent function of RIPK3. We provide evidence that RIPK3 signaling evoked a dysregulated type 1 interferone response which we linked to an impaired antiviral immune response and abrogated clearance of chronic LCMV infection.

Endothelial Caspase-8 prevents fatal necroptotic hemorrhage caused by commensal bacteria.

Caspase-8 transduces signals from death receptor ligands, such as tumor necrosis factor, to drive potent responses including inflammation, cell proliferation or cell death. This is a developmentally essential function because in utero deletion of endothelial Caspase-8 causes systemic circulatory collapse during embryogenesis. Whether endothelial Caspase-8 is also required for cardiovascular patency during adulthood was unknown. To address this question, we used an inducible Cre recombinase system to delete endothelial Casp8 in 6-week-old conditionally gene-targeted mice. Extensive whole body vascular gene targeting was confirmed, yet the dominant phenotype was fatal hemorrhagic lesions exclusively within the small intestine. The emergence of these intestinal lesions was not a maladaptive immune response to endothelial Caspase-8-deficiency, but instead relied upon aberrant Toll-like receptor sensing of microbial commensals and tumor necrosis factor receptor signaling. This lethal phenotype was prevented in compound mutant mice that lacked the necroptotic cell death effector, MLKL. Thus, distinct from its systemic role during embryogenesis, our data show that dysregulated microbial- and death receptor-signaling uniquely culminate in the adult mouse small intestine to unleash MLKL-dependent necroptotic hemorrhage after loss of endothelial Caspase-8. These data support a critical role for Caspase-8 in preserving gut vascular integrity in the face of microbial commensals.

Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models.

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Epigenetic Silencing of RIPK3 in Hepatocytes Prevents MLKL-mediated Necroptosis From Contributing to Liver Pathologies.

BACKGROUND & AIMS: Necroptosis is a highly inflammatory mode of cell death that has been implicated in causing hepatic injury including steatohepatitis/ nonalcoholic steatohepatitis (NASH); however, the evidence supporting these claims has been controversial. A comprehensive, fundamental understanding of cell death pathways involved in liver disease critically underpins rational strategies for therapeutic intervention. We sought to define the role and relevance of necroptosis in liver pathology. METHODS: Several animal models of human liver pathology, including diet-induced steatohepatitis in male mice and diverse infections in both male and female mice, were used to dissect the relevance of necroptosis in liver pathobiology. We applied necroptotic stimuli to primary mouse and human hepatocytes to measure their susceptibility to necroptosis. Paired liver biospecimens from patients with NASH, before and after intervention, were analyzed. DNA methylation sequencing was also performed to investigate the epigenetic regulation of RIPK3 expression in primary human and mouse hepatocytes. RESULTS: Identical infection kinetics and pathologic outcomes were observed in mice deficient in an essential necroptotic effector protein, MLKL, compared with control animals. Mice lacking MLKL were indistinguishable from wild-type mice when fed a high-fat diet to induce NASH. Under all conditions tested, we were unable to induce necroptosis in hepatocytes. We confirmed that a critical activator of necroptosis, RIPK3, was epigenetically silenced in mouse and human primary hepatocytes and rendered them unable to undergo necroptosis. CONCLUSIONS: We have provided compelling evidence that necroptosis is disabled in hepatocytes during homeostasis and in the pathologic conditions tested in this study.

Modeling reveals posttranscriptional regulation of GA metabolism enzymes in response to drought and cold.

The hormone gibberellin (GA) controls plant growth and regulates growth responses to environmental stress. In monocotyledonous leaves, GA controls growth by regulating division-zone size. We used a systems approach to investigate the establishment of the GA distribution in the maize leaf growth zone to understand how drought and cold alter leaf growth. By developing and parameterizing a multiscale computational model that includes cell movement, growth-induced dilution, and metabolic activities, we revealed that the GA distribution is predominantly determined by variations in GA metabolism. Considering wild-type and UBI::GA20-OX-1 leaves, the model predicted the peak in GA concentration, which has been shown to determine division-zone size. Drought and cold modified enzyme transcript levels, although the model revealed that this did not explain the observed GA distributions. Instead, the model predicted that GA distributions are also mediated by posttranscriptional modifications increasing the activity of GA 20-oxidase in drought and of GA 2-oxidase in cold, which we confirmed by enzyme activity measurements. This work provides a mechanistic understanding of the role of GA metabolism in plant growth regulation.

Caspase-8 has dual roles in regulatory T cell homeostasis balancing immunity to infection and collateral inflammatory damage.

Targeting the potent immunosuppressive properties of FOXP3+ regulatory T cells (Tregs) has substantial therapeutic potential for treating autoimmune and inflammatory diseases. Yet, the molecular mechanisms controlling Treg homeostasis, particularly during inflammation, remain unclear. We report that caspase-8 is a central regulator of Treg homeostasis in a context-specific manner that is decisive during immune responses. In mouse genetic models, targeting caspase-8 in Tregs led to accumulation of effector Tregs resistant to apoptotic cell death. Conversely, inflammation induced the MLKL-dependent necroptosis of caspase-8-deficient lymphoid and tissue Tregs, which enhanced immunity to a variety of chronic infections to promote clearance of viral or parasitic pathogens. However, improved immunity came at the risk of lethal inflammation in overwhelming infections. Caspase-8 inhibition using a clinical-stage compound revealed that human Tregs have heightened sensitivity to necroptosis compared with conventional T cells. These findings reveal a fundamental mechanism in Tregs that could be targeted to manipulate the balance between immune tolerance versus response for therapeutic benefit.

Targeting BMI-1 in B cells restores effective humoral immune responses and controls chronic viral infection.

Ineffective antibody-mediated responses are a key characteristic of chronic viral infection. However, our understanding of the intrinsic mechanisms that drive this dysregulation are unclear. Here, we identify that targeting the epigenetic modifier BMI-1 in mice improves humoral responses to chronic lymphocytic choriomeningitis virus. BMI-1 was upregulated by germinal center B cells in chronic viral infection, correlating with changes to the accessible chromatin landscape, compared to acute infection. B cell-intrinsic deletion of Bmi1 accelerated viral clearance, reduced splenomegaly and restored splenic architecture. Deletion of Bmi1 restored c-Myc expression in B cells, concomitant with improved quality of antibody and coupled with reduced antibody-secreting cell numbers. Specifically, BMI-1-deficiency induced antibody with increased neutralizing capacity and enhanced antibody-dependent effector function. Using a small molecule inhibitor to murine BMI-1, we could deplete antibody-secreting cells and prohibit detrimental immune complex formation in vivo. This study defines BMI-1 as a crucial immune modifier that controls antibody-mediated responses in chronic infection.

Gaussian process models of potential energy surfaces with boundary optimization.

A strategy is outlined to reduce the number of training points required to model intermolecular potentials using Gaussian processes, without reducing accuracy. An asymptotic function is used at a long range, and the crossover distance between this model and the Gaussian process is learnt from the training data. The results are presented for different implementations of this procedure, known as boundary optimization, across the following dimer systems: CO-Ne, HF-Ne, HF-Na+, CO2-Ne, and (CO2)2. The technique reduces the number of training points, at fixed accuracy, by up to ∼49%, compared to our previous work based on a sequential learning technique. The approach is readily transferable to other statistical methods of prediction or modeling problems.

Differential requirement for the Polycomb repressor complex 2 in dendritic cell and tissue-resident myeloid cell homeostasis.

Dendritic cells (DCs) and macrophages are at the forefront of immune responses, modifying their transcriptional programs in response to their tissue environment or immunological challenge. Posttranslational modifications of histones, such as histone H3 lysine-27 trimethylation (H3K27me3) by the Polycomb repressive complex 2 (PRC2), are tightly associated with epigenetic regulation of gene expression. To explore whether H3K27me3 is involved in either the establishment or function of the mononuclear phagocyte system, we selectively deleted core components of PRC2, either EZH2 or SUZ12, in CD11c-expressing myeloid cells. Unexpectedly, EZH2 deficiency neither prevented the deposition and maintenance of H3K27me3 in DCs nor hindered DC/macrophage homeostasis. In contrast, SUZ12 deficiency markedly impaired the capacity of DCs and macrophages to maintain H3K27me3. SUZ12 ablation induced a rapid loss of the alveolar macrophage and Langerhans cell networks under both steady state and inflammatory conditions because these cells could no longer proliferate to facilitate their self-renewal. Despite the reduced H3K27me3, DC development and function were unaffected by SUZ12 ablation, suggesting that PRC2-mediated gene repression was dispensable for DC homeostasis. Thus, the role of SUZ12 highlights the fundamentally different homeostatic mechanisms used by tissue-resident myeloid cells versus DCs.

Macrophage and neutrophil death programs differentially confer resistance to tuberculosis.

Apoptosis can potently defend against intracellular pathogens by directly killing microbes and eliminating their replicative niche. However, the reported ability of Mycobacterium tuberculosis to restrict apoptotic pathways in macrophages in vitro has led to apoptosis being dismissed as a host-protective process in tuberculosis despite a lack of in vivo evidence. Here we define crucial in vivo functions of the death receptor-mediated and BCL-2-regulated apoptosis pathways in mediating protection against tuberculosis by eliminating distinct populations of infected macrophages and neutrophils and priming T cell responses. We further show that apoptotic pathways can be targeted therapeutically with clinical-stage compounds that antagonize inhibitor of apoptosis (IAP) proteins to promote clearance of M. tuberculosis in mice. These findings reveal that any inhibition of apoptosis by M. tuberculosis is incomplete in vivo, advancing our understanding of host-protective responses to tuberculosis (TB) and revealing host pathways that may be targetable for treatment of disease.

The role of MKK4 in T-cell development and immunity to viral infections.

The stress-activated protein kinases (SAPKs)/c-Jun-N-terminal-kinases (JNK) are members of the mitogen-activated protein kinase family. These kinases are responsible for transducing cellular signals through a phosphorylation-dependent signaling cascade. JNK activation in immune cells can lead to a range of critical cellular responses that include proliferation, differentiation and apoptosis. MKK4 is a SAPK that can activate both JNK1 and JNK2; however, its role in T-cell development and function has been controversial. Additionally, loss of either JNK1 or JNK2 has opposing effects in the generation of T-cell immunity to viral infection and cancer. We used mice with a conditional loss of MKK4 in T cells to investigate the in vivo role of MKK4 in T-cell development and function during lymphocytic choriomeningitis virus (LCMV) infection. We found no physiologically relevant differences in T-cell responses or immunity to either acute or chronic LCMV in the absence of MKK4.

Mathematical modelling of a microRNA-regulated gene network in Caenorhabditis elegans.

MicroRNAs are known to regulate gene expression either by repressing translation or by directing sequence-specific degradation of target mRNAs, and are therefore considered to be key regulators of gene expression. A gene-regulatory pathway involving heterochronic genes controls the temporal pattern of Caenorhabditis elegans postembryonic cell lineages. Based on experimental data, we propose and analyze a mathematical model of a gene-regulatory module in this nematode involving two heterochronic genes, lin-14 and lin-28, which are both regulated by lin-4, encoding a microRNA. The conditions under which the model experiences bifurcations are investigated. We determine the parameter regimes for which the system exhibits monostability and bistability, the latter associated with a biological switch. We observe in particular that bistability occurs without co-operativity, in keeping with knowledge about the regulatory behaviour of lin-14 and lin-28. The analytical results are confirmed by numerical simulations that illustrate how the microRNA lin-4 plays a crucial role in determining of the qualitative dynamics of the model.

Positioning the Root Elongation Zone Is Saltatory and Receives Input from the Shoot.

In the root, meristem and elongation zone lengths remain stable, despite growth and division of cells. To gain insight into zone stability, we imaged individual Arabidopsis thaliana roots through a horizontal microscope and used image analysis to obtain velocity profiles. For a root, velocity profiles obtained every 5 min over 3 h coincided closely, implying that zonation is regulated tightly. However, the position of the elongation zone saltated, by on average 17 µm every 5 min. Saltation was apparently driven by material elements growing faster and then slower, while moving through the growth zone. When the shoot was excised, after about 90 min, growth zone dynamics resembled those of intact roots, except that the position of the elongation zone moved, on average, rootward, by several hundred microns in 24 h. We hypothesize that mechanisms determining elongation zone position receive input from the shoot.

Parameter inference to motivate asymptotic model reduction: An analysis of the gibberellin biosynthesis pathway.

Developing effective strategies to use models in conjunction with experimental data is essential to understand the dynamics of biological regulatory networks. In this study, we demonstrate how combining parameter estimation with asymptotic analysis can reveal the key features of a network and lead to simplified models that capture the observed network dynamics. Our approach involves fitting the model to experimental data and using the profile likelihood to identify small parameters and cases where model dynamics are insensitive to changing particular individual parameters. Such parameter diagnostics provide understanding of the dominant features of the model and motivate asymptotic model reductions to derive simpler models in terms of identifiable parameter groupings. We focus on the particular example of biosynthesis of the plant hormone gibberellin (GA), which controls plant growth and has been mutated in many current crop varieties. This pathway comprises two parallel series of enzyme-substrate reactions, which have previously been modelled using the law of mass action (Middleton et al., 2012). Considering the GA20ox-mediated steps, we analyse the identifiability of the model parameters using published experimental data; the analysis reveals the ratio between enzyme and GA levels to be small and motivates us to perform a quasi-steady state analysis to derive a reduced model. Fitting the parameters in the reduced model reveals additional features of the pathway and motivates further asymptotic analysis which produces a hierarchy of reduced models. Calculating the Akaike information criterion and parameter confidence intervals enables us to select a parsimonious model with identifiable parameters. As well as demonstrating the benefits of combining parameter estimation and asymptotic analysis, the analysis shows how GA biosynthesis is limited by the final GA20ox-mediated steps in the pathway and generates a simple mathematical description of this part of the GA biosynthesis pathway.

Three-dimensional plant architecture and sunlit-shaded patterns: a stochastic model of light dynamics in canopies.

Background and Aims: Diurnal changes in solar position and intensity combined with the structural complexity of plant architecture result in highly variable and dynamic light patterns within the plant canopy. This affects productivity through the complex ways that photosynthesis responds to changes in light intensity. Current methods to characterize light dynamics, such as ray-tracing, are able to produce data with excellent spatio-temporal resolution but are computationally intensive and the resulting data are complex and high-dimensional. This necessitates development of more economical models for summarizing the data and for simulating realistic light patterns over the course of a day. Methods: High-resolution reconstructions of field-grown plants are assembled in various configurations to form canopies, and a forward ray-tracing algorithm is applied to the canopies to compute light dynamics at high (1 min) temporal resolution. From the ray-tracer output, the sunlit or shaded state for each patch on the plants is determined, and these data are used to develop a novel stochastic model for the sunlit-shaded patterns. The model is designed to be straightforward to fit to data using maximum likelihood estimation, and fast to simulate from. Key Results: For a wide range of contrasting 3-D canopies, the stochastic model is able to summarize, and replicate in simulations, key features of the light dynamics. When light patterns simulated from the stochastic model are used as input to a model of photoinhibition, the predicted reduction in carbon gain is similar to that from calculations based on the (extremely costly) ray-tracer data. Conclusions: The model provides a way to summarize highly complex data in a small number of parameters, and a cost-effective way to simulate realistic light patterns. Simulations from the model will be particularly useful for feeding into larger-scale photosynthesis models for calculating how light dynamics affects the photosynthetic productivity of canopies.

Therapeutic manipulation of host cell death pathways to facilitate clearance of persistent viral infections.

Most persistent viral infections can be controlled, but not cured, by current therapies. Abrogated antiviral immunity and stable latently infected cells represent major barriers to cure. This necessitates life-long suppressive antiviral therapy. Achieving a cure for HIV, hepatitis B virus, Epstein Barr-virus, and others, requires novel approaches to facilitate the clearance of infected cells from the host. One such approach is to target host cell death pathways, rather than the virus itself. Here, we summarize recent findings from studies that have utilized therapeutics to manipulate host cell death pathways as a means to treat and cure persistent viral infections.

Necroptotic signaling is primed in Mycobacterium tuberculosis-infected macrophages, but its pathophysiological consequence in disease is restricted.

Mixed lineage kinase domain-like (MLKL)-dependent necroptosis is thought to be implicated in the death of mycobacteria-infected macrophages, reportedly allowing escape and dissemination of the microorganism. Given the consequent interest in developing inhibitors of necroptosis to treat Mycobacterium tuberculosis (Mtb) infection, we used human pharmacologic and murine genetic models to definitively establish the pathophysiological role of necroptosis in Mtb infection. We observed that Mtb infection of macrophages remodeled the intracellular signaling landscape by upregulating MLKL, TNFR1, and ZBP1, whilst downregulating cIAP1, thereby establishing a strong pro-necroptotic milieu. However, blocking necroptosis either by deleting Mlkl or inhibiting RIPK1 had no effect on the survival of infected human or murine macrophages. Consistent with this, MLKL-deficiency or treatment of humanized mice with the RIPK1 inhibitor Nec-1s did not impact on disease outcomes in vivo, with mice displaying lung histopathology and bacterial burdens indistinguishable from controls. Therefore, although the necroptotic pathway is primed by Mtb infection, macrophage necroptosis is ultimately restricted to mitigate disease pathogenesis. We identified cFLIP upregulation that may promote caspase 8-mediated degradation of CYLD, and other necrosome components, as a possible mechanism abrogating Mtb's capacity to coopt necroptotic signaling. Variability in the capacity of these mechanisms to interfere with necroptosis may influence disease severity and could explain the heterogeneity of Mtb infection and disease.

Transcription Factor IRF4 Promotes CD8+ T Cell Exhaustion and Limits the Development of Memory-like T Cells during Chronic Infection.

During chronic stimulation, CD8+ T cells acquire an exhausted phenotype characterized by expression of inhibitory receptors, down-modulation of effector function, and metabolic impairments. T cell exhaustion protects from excessive immunopathology but limits clearance of virus-infected or tumor cells. We transcriptionally profiled antigen-specific T cells from mice infected with lymphocytic choriomeningitis virus strains that cause acute or chronic disease. T cell exhaustion during chronic infection was driven by high amounts of T cell receptor (TCR)-induced transcription factors IRF4, BATF, and NFATc1. These regulators promoted expression of inhibitory receptors, including PD-1, and mediated impaired cellular metabolism. Furthermore, they repressed the expression of TCF1, a transcription factor required for memory T cell differentiation. Reducing IRF4 expression restored the functional and metabolic properties of antigen-specific T cells and promoted memory-like T cell development. These findings indicate that IRF4 functions as a central node in a TCR-responsive transcriptional circuit that establishes and sustains T cell exhaustion during chronic infection.