Calcium (Ca2+) oscillations in hepatocytes have a wide dynamic range. In particular, recent experimental evidence shows that agonist stimulation of the P2Y family of receptors leads to qualitatively diverse Ca2+ oscillations. We present a new model of Ca2+ oscillations in hepatocytes based on these experiments to investigate the mechanisms controlling P2Y-activated Ca2+ oscillations. The model accounts for Ca2+ regulation of the IP3 receptor (IP3R), the positive feedback from Ca2+ on phospholipase C (PLC) and the P2Y receptor phosphorylation by protein kinase C (PKC). Furthermore, PKC is shown to control multiple cellular substrates. Utilising the model, we suggest the activity and intensity of PLC and PKC necessary to explain the qualitatively diverse Ca2+ oscillations in response to P2Y receptor activation.

We discuss how the presence of a slow binding site in molecular motor traffic gives rise to defect-induced "traffic jams" that have properties different from those of the well-studied boundary-induced jams that originate from an imbalance between initiation and termination. To this end we analyze in detail the stationary distribution of a lattice gas model for traffic of molecular motors with a defect. In particular, we obtain analytically the exact spatial distribution of motors, the probability distribution of the random position of the molecular traffic jam and we report unexpected spatial anticorrelations between local molecular motor densities near the defect.

Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.

Transposable elements (TEs) are essential components of the eukaryotic genomes. While mostly deleterious, evidence is mounting that TEs provide the host with beneficial adaptations. How 'selfish' or 'parasitic' DNA persists until it helps species evolution is emerging as a major evolutionary puzzle, especially in asexual taxa where the lack of sex strongly impede the spread of TEs. Since occasional but unchecked TE proliferations would ultimately drive host lineages toward extinction, asexual genomes are typically predicted to be free of TEs, which contrasts with their persistence in asexual taxa. We designed innovative 'Eco-genomic' models that account for both host demography and within-host molecular mechanisms of transposition and silencing to analyze their impact on TE dynamics in asexual genome populations. We unraveled that the spread of TEs can be limited to a stable level by density-dependent purifying selection when TE copies are over-dispersed among lineages and the host demographic turn-over is fast. We also showed that TE silencing can protect host populations in two ways; by preventing TEs with weak effects to accumulate or by favoring the elimination of TEs with large effects. Our predictions may explain TE persistence in known asexual taxa that typically show fast demography and where TE copy number variation between lineages is expected. Such TE persistence in asexual taxa potentially has important implications for their evolvability and the preservation of sexual reproduction.

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment, the so-called stem cell niche, is challenging. Therefore, the details of HSC dynamics and the cellular interactions in the stem cell niche remain elusive. Mutations that lead to a competitive advantage are the cause of clinical challenges when treating HSC-derived malignancies such as acute myeloid leukemia or the myeloproliferative neoplasms (MPNs). To investigate the significance of the interaction between the HSC and the stem cell niche in these malignancies, we propose and analyse a mechanism-based mathematical model of HSC dynamics within the bone-marrow microenvironment. The model is based on the central hypothesis that HSC self-renewal depends on the niche. In the model, the interaction of HSC with specific niches located in the bone marrow are key to the indefinite HSC renewal necessary for long-term maintenance of blood cell production. We formulate a general model of n distinct clones that differ with respect to cell properties. We identify an attractive trapping region and compute and classify all steady states. A concept of HSC fitness naturally arises from the model analysis. HSC fitness is found to determine the asymptotic behaviour of the model, as the HSC clone with the highest fitness is related to the unique locally stable steady state. Based on biological assumptions about HSC, we propose two reduced models of different complexity. A thorough mathematical analysis reveals that both reduced models have the same asymptotic behaviour as the full model. We compare the simpler of the two models, a logistic equation of the disease burden, to clinical data of MPN-patients. The reduced model is found to agree well with data and suggests a simple interpretation and possible prediction of patient prognosis. The proposed mathematical model and the reduced forms have the potential to provide insights into the regulation of HSC dynamics and blood cell formation, and ultimately for future advances in treatment of hematologic malignancies.

Dense innervation of the heart by the sympathetic nervous system (SNS) allows cardiac output to respond appropriately to the needs of the body under varying conditions, but occasionally the abrupt onset of SNS activity can trigger cardiac arrhythmias. Sympathetic activity leads to the release of norepinephrine (NE) onto cardiomyocytes, activating β1-adrenergic receptors (β1-ARs) and leading to the production of the second messenger cyclic AMP (cAMP). Upon sudden activation of β1-ARs in experiments, intracellular cAMP can transiently rise to a high concentration before converging to a steady state level. Although changes to cellular cAMP concentration are important in modulating the overall cardiovascular response to sympathetic tone, the underlying mechanisms of the cAMP transients and the parameters that control their magnitude are unclear. We reduce a detailed computational model of the β1-adrenergic signaling cascade to a system of two differential equations by eliminating extraneous variables and applying quasi-steady state approximation. The structure of the reduced model reveals that the large cAMP transients associated with abrupt β1-AR activation are generated by the interplay of production/degradation of cAMP and desensitization/resensitization of β1-ARs. The reduced model is used to predict how the dynamics of intracellular cAMP depend on the concentrations of norepinephrine (NE), phosphodiesterases 3 and 4 (PDE3,4), G-protein coupled receptor kinase 2 (GRK2), and β1-AR, in healthy conditions and a simple model of early stages of heart failure. The key findings of the study are as follows: 1) Applying a reduced model of the dynamics of cardiac sympathetic signaling we show that the concentrations of two variables, cAMP and non-desensitized β1-AR, capture the overall dynamics of sympathetic signaling; 2) The key factors influencing cAMP production are AC activity and PDE3,4 activity, while those that directly impact β1-AR phosphorylation are GRK2 and PKA1. Thus, disease states that affect sympathetic control of the heart can be thoroughly assessed by studying AC activity, PDE3,4, GRK2 and PKA activity, as these factors directly impact cAMP production/degradation and β1-AR (de) phosphorylation and are therefore predicted to comprise the most effective pharmaceutical targets in diseases affecting cardiac β1-adrenergic signaling.

Acetaminophen (APAP) overdose is one of the predominant causes of drug induced acute liver injury in the U.S and U.K. Clinical studies show that ingestion of alcohol may increase the risk of APAP induced liver injury. Chronic alcoholism may potentiate APAP hepatotoxicity and this increased risk of APAP toxicity is observed when APAP is ingested even shortly after alcohol is cleared from the body. However, clinical reports also suggest that acute alcohol consumption may have a protective effect against hepatotoxicity by inhibiting microsomal acetaminophen oxidation and thereby reducing N-acetyl-p-benzoquinone imine (NAPQI) production. The aim of this study is to model this dual role of alcohol to determine how the timing of alcohol ingestion affects APAP metabolism and resulting liver injury and identify mechanisms of APAP induced liver injury. The mathematical model is developed to capture condition of a patient of single time APAP overdose who may be an acute or chronic alcohol user. The analysis suggests that the risk of APAP-induced hepatotoxicity is increased if APAP is ingested shortly after alcohol is cleared from the body in chronic alcohol users. A protective effect of acute consumption of alcohol is also observed in patients with APAP overdose. For example, simultaneous ingestion of alcohol and APAP overdose or alcohol intake after or before few hours of APAP overdose may result in less APAP-induced hepatotoxicity when compared to a single time APAP overdose. The rate of hepatocyte damage in APAP overdose patients depends on trade-off between induction and inhibition of CYP enzyme.

Among the Hominidae family of primates, Homo is characterized by more economical bipedal walking. Over the course of evolution towards bipedalism, the foot becomes the only organ directly interacting with substrate and likely influence the bipedal walking economy. However, working out the energy expenditure in bipedal walking from the specific aspect of foot morphology is still challenging, which hinders the understanding of the evolution of both hominid feet and economical bipedal walking. Here we present a functional model to quantitatively assess bipedal walking expenditure of energy from hominid foot morphology. According to our results, the feet of Homo are most suited to economical bipedal walking among hominids. However, the genus whose feet possess second best ability for economical bipedal walking is not our closest relative Pan, but is Gorilla. Using phylogenetically informed morphometric analyses, we further infer the evolutionary changes of hominid foot morphology and investigate the corresponding variation of bipedal walking expenditure. Our results reveal the economical bipedal walking benefits from the morphological changes of human foot after descending from the last common ancestor of hominids. Conversely, the foot morphologies of great apes reflect selections for other locomotor modes, at cost of larger energy expenditure in bipedal walking.

It is well-established that extracellular potassium (Ko+) accumulation reduces muscle fiber excitability, however the effects of Ko+ on the excitation-contraction coupling (ECC) pathway are less understood. In vivo and in vitro studies following fatiguing stimulation protocols are limited in their ability to capture the effects of Ko+ on force production in combination with other simultaneously changing factors. To address this, a computational model of ECC for slow and fast twitch muscle is presented to explore the relative contributions of excitability-induced and metabolic-induced changes in force generation in response to increasing [Formula: see text] . The model incorporates mechanisms previously unexplored in modelling studies, including the effects of extracellular calcium on excitability, calcium-dependent inhibition of calcium release, ATP-dependent ionic pumping, and the contribution of ATP hydrolysis to intracellular phosphate accumulation rate. The model was able to capture the frequency-dependent biphasic Force- [Formula: see text] response observed experimentally. Force potentiation for moderately elevated [Formula: see text] was driven by increased action potential duration, myoplasmic calcium potentiation, and phosphate accumulation rate, while attenuation of force at higher [Formula: see text] was due to action potential failure resulting in reduced calcium release. These results suggest that altered calcium release and phosphate accumulation work together with elevated Ko+ to affect force during sustained contractions.

Systems biology aims to understand how holistic systems theory can be used to explain the observable living system characteristics, and mathematical modeling tools have been successful in understanding the intricate relationships underlying cellular functions. Lately, researchers have been interested in understanding molecular mechanisms underlying obesity, which is a major health concern worldwide and has been linked to several diseases. Various mechanisms such as peroxisome proliferator-activated receptors (PPARs) are known to modulate obesity-induced inflammation and its consequences. In this study, we have modeled the PPAR pathway using a Bayesian model and inferred the sub-pathways that are potentially responsible for the activation of the output processes that are associated with high fat diet (HFD)-induced obesity. We examined a previously published dataset from a study that compared gene expression profiles of 40 mice maintained on HFD against 40 mice fed with chow diet (CD). Our simulations have highlighted that GPCR and FATCD36 sub-pathways were aberrantly active in HFD mice and are therefore favorable targets for anti-obesity strategies. We further cross-validated our observations with experimental results from the literature. We believe that mathematical models such as those presented in the present study can help in inferring other pathways and deducing significant biological relationships.

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitness, a measure of reproductive success used in evolutionary graph theory, is related to the life-history of individuals in terms of their birth and death rates. In simple networks, these ecologically motivated dynamics are used to provide new insight into the spread of adaptive mutations, both with and without clonal interference. For example, the star network, which is known to be an amplifier of selection in evolutionary graph theory, can inhibit the spread of adaptive mutations when individuals can die naturally.