Quantitative systems pharmacology model of erythropoiesis to simulate therapies targeting anemia due to chronic kidney disease.

Anemia induced by chronic kidney disease (CKD) has multiple underlying mechanistic causes and generally worsens as CKD progresses. Erythropoietin (EPO) is a key endogenous protein which increases the number of erythrocyte progenitors that mature into red blood cells that carry hemoglobin (Hb). Recombinant human erythropoietin (rHuEPO) in its native and re-engineered forms is used as a therapeutic to alleviate CKD-induced anemia by stimulating erythropoiesis. However, due to safety risks associated with erythropoiesis-stimulating agents (ESAs), a new class of drugs, prolyl hydroxylase inhibitors (PHIs), has been developed. Instead of administering exogenous EPO, PHIs facilitate the accumulation of HIF-α, which results in the increased production of endogenous EPO. Clinical trials for ESAs and PHIs generally involve balancing decisions related to safety and efficacy by carefully evaluating the criteria for patient selection and adaptive trial design. To enable such decisions, we developed a quantitative systems pharmacology (QSP) model of erythropoiesis which captures key aspects of physiology and its disruption in CKD. Furthermore, CKD virtual populations of varying severities were developed, calibrated, and validated against public data. Such a model can be used to simulate alternative trial protocols while designing phase 3 clinical trials, as well as an asset for reverse translation in understanding emerging clinical data.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFß-SMAD Signaling Pathway.

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFß/SMAD signaling pathway.

Country-specific optimization strategy for testing through contact tracing can help maintain a low reproduction number ([Formula: see text]) during unlock.

In response to the COVID19 pandemic, many countries have implemented lockdowns in multiple phases to ensure social distancing and quarantining of the infected subjects. Subsequent unlocks to reopen the economies started next waves of infection and imposed an extra burden on quarantine to keep the reproduction number ([Formula: see text]) < 1. However, most countries could not effectively contain the infection spread, suggesting identification of the potential sources weakening the effect of lockdowns could help design better informed lockdown-unlock cycles in the future. Here, through building quantitative epidemic models and analyzing the metadata of 50 countries from across the continents we first found that the estimated value of [Formula: see text], adjusted w.r.t the distribution of medical facilities and virus clades correlates strongly with the testing rates in a country. Since the testing capacity of a country is limited by its medical resources, we investigated if a cost-benefit trade-off can be designed connecting testing rate and extent of unlocking. We present a strategy to optimize this trade-off in a country specific manner by providing a quantitative estimate of testing and quarantine rates required to allow different extents of unlocks while aiming to maintain [Formula: see text]. We further show that a small fraction of superspreaders can dramatically increase the number of infected individuals even during strict lockdowns by strengthening the positive feedback loop driving infection spread. Harnessing the benefit of optimized country-specific testing rates would critically require minimizing the movement of these superspreaders via strict social distancing norms, such that the positive feedback driven switch-like exponential spread phase of infection can be avoided/delayed.

Interdependencies between Toll-like receptors in Leishmania infection.

Multiple pathogen-associated molecular patterns (PAMPs) on a pathogen's surface imply their simultaneous recognition by the host cell membrane-located multiple PAMP-specific Toll-like receptors (TLRs). The TLRs on endosomes recognize internalized pathogen-derived nucleic acids and trigger anti-pathogen immune responses aimed at eliminating the intracellular pathogen. Whether the TLRs influence each other's expression and effector responses-termed TLR interdependency-remains unknown. Herein, we first probed the existence of TLR interdependencies and next determined how targeting TLR interdependencies might determine the outcome of Leishmania infection. We observed that TLRs selectively altered expression of their own and of other TLRs revealing novel TLR interdependencies. Leishmania major-an intra-macrophage parasite inflicting the disease cutaneous leishmaniasis in 88 countries-altered this TLR interdependency unfolding a unique immune evasion mechanism. We targeted this TLR interdependency by selective silencing of rationally chosen TLRs and by stimulation with selective TLR ligands working out a novel phase-specific treatment regimen. Targeting the TLR interdependency elicited a host-protective anti-leishmanial immune response and reduced parasite burden. To test whether this observation could be used as a scientific rationale for treating a potentially fatal L. donovani infection, which causes visceral leishmaniasis, we targeted the inter-TLR dependency adopting the same treatment regimen. We observed reduced splenic Leishman-Donovan units accompanied by host-protective immune response in susceptible BALB/c mice. The TLR interdependency optimizes TLR-induced immune response by a novel immunoregulatory framework and scientifically rationalizes targeting TLRs in tandem and in sequence for redirecting immune responses against an intracellular pathogen.

Residue-Specific Message Encoding in CD40-Ligand.

CD40-Ligand (CD40L)-CD40 interaction regulates immune responses against pathogens, autoantigens, and tumor and transplantation antigens. Single amino acid mutations within the 115-155 amino acids stretch, which is responsible for CD40L functions, result in XIgM syndrome. We hypothesize that each of these amino acids of CD40L encodes specific message that, when decoded by CD40 signaling, induces a specific profile of functions. We observed that every single substitution in the XIgM-related amino acids in the 115-155 41-mer peptide in CD40L selectively altered CD40 signaling and effector functions-cytokine productions, HMGCoA reductase, ceramide synthase, inducible nitric oxide synthase and arginase expression, survival of B cells, and control of Leishmania infection and anti-leishmanial T cell response-suggesting residue-specific encoding of a distinct set of messages that collectively define CD40L pleiotropy, serve as a target for engineering the ligand to generate superagonists as immunotherapeutic, and implicate the evolutionary diversification of functions among the ligands in a protein superfamily.

Sharing of Phosphatases Promotes Response Plasticity in Phosphorylation Cascades.

Sharing of positive or negative regulators between multiple targets is frequently observed in cellular signaling cascades. For instance, phosphatase sharing between multiple kinases is ubiquitous within the MAPK pathway. Here we investigate how such phosphatase sharing could shape robustness and evolvability of the phosphorylation cascade. Through modeling and evolutionary simulations, we demonstrate that 1) phosphatase sharing dramatically increases robustness of a bistable MAPK response, and 2) phosphatase-sharing cascades evolve faster than nonsharing cascades. This faster evolution is particularly pronounced when evolving from a monostable toward a bistable phenotype, whereas the transition speed of a population from a bistable to monostable response is not affected by phosphatase sharing. This property may enable the phosphatase-sharing design to adapt better in a changing environment. Analysis of the respective mutational landscapes reveal that phosphatase sharing reduces the number of limiting mutations required for transition from monostable to bistable responses, hence facilitating a faster transition to such response types. Taken together, using MAPK cascade as an example, our study offers a general theoretical framework to explore robustness and evolutionary plasticity of signal transduction cascades.

Cell-specific responses to the cytokine TGFß are determined by variability in protein levels.

The cytokine TGFß provides important information during embryonic development, adult tissue homeostasis, and regeneration. Alterations in the cellular response to TGFß are involved in severe human diseases. To understand how cells encode the extracellular input and transmit its information to elicit appropriate responses, we acquired quantitative time-resolved measurements of pathway activation at the single-cell level. We established dynamic time warping to quantitatively compare signaling dynamics of thousands of individual cells and described heterogeneous single-cell responses by mathematical modeling. Our combined experimental and theoretical study revealed that the response to a given dose of TGFß is determined cell specifically by the levels of defined signaling proteins. This heterogeneity in signaling protein expression leads to decomposition of cells into classes with qualitatively distinct signaling dynamics and phenotypic outcome. Negative feedback regulators promote heterogeneous signaling, as a SMAD7 knock-out specifically affected the signal duration in a subpopulation of cells. Taken together, we propose a quantitative framework that allows predicting and testing sources of cellular signaling heterogeneity.

Comprehensive logic based analyses of Toll-like receptor 4 signal transduction pathway.

Among the 13 TLRs in the vertebrate systems, only TLR4 utilizes both Myeloid differentiation factor 88 (MyD88) and Toll/Interleukin-1 receptor (TIR)-domain-containing adapter interferon-ß-inducing Factor (TRIF) adaptors to transduce signals triggering host-protective immune responses. Earlier studies on the pathway combined various experimental data in the form of one comprehensive map of TLR signaling. But in the absence of adequate kinetic parameters quantitative mathematical models that reveal emerging systems level properties and dynamic inter-regulation among the kinases/phosphatases of the TLR4 network are not yet available. So, here we used reaction stoichiometry-based and parameter independent logical modeling formalism to build the TLR4 signaling network model that captured the feedback regulations, interdependencies between signaling kinases and phosphatases and the outcome of simulated infections. The analyses of the TLR4 signaling network revealed 360 feedback loops, 157 negative and 203 positive; of which, 334 loops had the phosphatase PP1 as an essential component. The network elements' interdependency (positive or negative dependencies) in perturbation conditions such as the phosphatase knockout conditions revealed interdependencies between the dual-specific phosphatases MKP-1 and MKP-3 and the kinases in MAPK modules and the role of PP2A in the auto-regulation of Calmodulin kinase-II. Our simulations under the specific kinase or phosphatase gene-deficiency or inhibition conditions corroborated with several previously reported experimental data. The simulations to mimic Yersinia pestis and E. coli infections identified the key perturbation in the network and potential drug targets. Thus, our analyses of TLR4 signaling highlights the role of phosphatases as key regulatory factors in determining the global interdependencies among the network elements; uncovers novel signaling connections; identifies potential drug targets for infections.

Branched motifs enable long-range interactions in signaling networks through retrograde propagation.

Branched structures arise in the intra-cellular signaling network when a molecule is involved in multiple enzyme-substrate reaction cascades. Such branched motifs are involved in key biological processes, e.g., immune response activated by T-cell and B-cell receptors. In this paper, we demonstrate long-range communication through retrograde propagation between branches of signaling pathways whose molecules do not directly interact. Our numerical simulations and experiments on a system comprising branches with JNK and p38MAPK as terminal molecules respectively that share a common MAP3K enzyme MEKK3/4 show that perturbing an enzyme in one branch can result in a series of changes in the activity levels of molecules "upstream" to the enzyme that eventually reaches the branch-point and affects other branches. In the absence of any evidence for explicit feedback regulation between the functionally distinct JNK and p38MAPK pathways, the experimentally observed modulation of phosphorylation amplitudes in the two pathways when a terminal kinase is inhibited implies the existence of long-range coordination through retrograde information propagation previously demonstrated in single linear reaction pathways. An important aspect of retrograde propagation in branched pathways that is distinct from previous work on retroactivity focusing exclusively on single chains is that varying the type of perturbation, e.g., between pharmaceutical agent mediated inhibition of phosphorylation or suppression of protein expression, can result in opposing responses in the other branches. This can have potential significance in designing drugs targeting key molecules which regulate multiple pathways implicated in systems-level diseases such as cancer and diabetes.

A mathematical model for dynamics of CD40 clustering.

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand-receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.

Modeling and experimental analyses reveals signaling plasticity in a bi-modular assembly of CD40 receptor activated kinases.

Depending on the strength of signal dose, CD40 receptor (CD40) controls ERK-1/2 and p38MAPK activation. At low signal dose, ERK-1/2 is maximally phosphorylated but p38MAPK is minimally phosphorylated; as the signal dose increases, ERK-1/2 phosphorylation is reduced whereas p38MAPK phosphorylation is reciprocally enhanced. The mechanism of reciprocal activation of these two MAPKs remains un-elucidated. Here, our computational model, coupled to experimental perturbations, shows that the observed reciprocity is a system-level behavior of an assembly of kinases arranged in two modules. Experimental perturbations with kinase inhibitors suggest that a minimum of two trans-modular negative feedback loops are required to reproduce the experimentally observed reciprocity. The bi-modular architecture of the signaling pathways endows the system with an inherent plasticity which is further expressed in the skewing of the CD40-induced productions of IL-10 and IL-12, the respective anti-inflammatory and pro-inflammatory cytokines. Targeting the plasticity of CD40 signaling significantly reduces Leishmania major infection in a susceptible mouse strain. Thus, for the first time, using CD40 signaling as a model, we show how a bi-modular assembly of kinases imposes reciprocity to a receptor signaling. The findings unravel that the signalling plasticity is inherent to a reciprocal system and that the principle can be used for designing a therapy.

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade.

BACKGROUND: The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal. RESULTS: We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases. CONCLUSIONS: Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design.

Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops.

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.