Steady-State Kinetic Modeling Constrains Cellular Resting States and Dynamic Behavior

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y1 signaling can cause widespread compensatory effects on cellular resting states

Metabolic Dynamics in Skeletal Muscle during Acute Reduction in Blood Flow and Oxygen Supply to Mitochondria: In-Silico Studies Using a Multi-Scale, Top-Down Integrated Model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD+. The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise

Systems Modeling of Calcium Homeostasis and Mobilization in Platelets Mediated by Ip3 and Store-Operated Calcium Entry

Platelet aggregation is one of the body\u27s first responses to vascular damage to prevent blood loss; upon injury to the endothelium platelets react to the exposed extracellular matrix and undergo a host of intracellular biochemical changes enabling them to activate and form a plug at the site of injury. Internally, platelets respond to their environment by exhibiting a sharp rise in cytosolic calcium that triggers a series of chemical and morphological changes which are critical to platelet activation and subsequent clot propagation. This thesis develops a mechanistic, computational model of platelet calcium regulation using coupled sets of ordinary differential equations. This thesis extends previous work modeling calcium release mediated by inositol 1,4,5-trisphosphate (IP3) to engineer what is the first, to date, complete model of store-operated calcium entry (SOCE) integrated into a systems model for calcium signaling. SOCE is a ubiquitous extracellular calcium entry pathway which is activated by calcium store depletion, is seen in many cells types and is yet to be fully understood. Our model for SOCE regulation consists of diffusion-limited dimerization of the calcium sensor STIM1, followed by fast, cytosolic calcium-dependent association of STIM1 dimers with Orai1 channels in the plasma membrane resulting in graded store-operated channel activation. Appropriate model resting states were characterized using a dense Monte Carlo technique on an initial condition sampling space constrained by available data on species concentrations and protein copy numbers. From this set of resting configurations, following application of physiologic IP3 stimuli, we selected for resting states exhibiting calcium dynamics that are in agreement with experimental data. We also selected for states presenting significant SOCE current based on differences in cytosolic calcium between simulations run with and without extracellular calcium. Low resting levels of IP3 are required for system robustness and for simultaneous appropriate dynamic response to physiologic agonists. Platelets require a resting electrical potential across the membrane surrounding the calcium stores of greater than -70 mV in order to exhibit significant agonist-induced calcium release

Resolving the Fast Kinetics of Cooperative Binding: Ca2+ Buffering by Calretinin

Cooperativity is one of the most important properties of molecular interactions in biological systems. It is the ability to influence ligand binding at one site of a macromolecule by previous ligand binding at another site of the same molecule. As a consequence, the affinity of the macromolecule for the ligand is either decreased (negative cooperativity) or increased (positive cooperativity). Over the last 100 years, O2 binding to hemoglobin has served as the paradigm for cooperative ligand binding and allosteric modulation, and four practical models were developed to quantitatively describe the mechanism: the Hill, the Adair-Klotz, the Monod-Wyman-Changeux, and the Koshland-Némethy-Filmer models. The predictions of these models apply under static conditions when the binding reactions are at equilibrium. However, in a physiological setting, e.g., inside a cell, the timing and dynamics of the binding events are essential. Hence, it is necessary to determine the dynamic properties of cooperative binding to fully understand the physiological implications of cooperativity. To date, the Monod-Wyman-Changeux model was applied to determine the kinetics of cooperative binding to biologically active molecules. In this model, cooperativity is established by postulating two allosteric isoforms with different binding properties. However, these studies were limited to special cases, where transition rates between allosteric isoforms are much slower than the binding rates or where binding and unbinding rates could be measured independently. For all other cases, the complex mathematical description precludes straightforward interpretations. Here, we report on calculating for the first time the fast dynamics of a cooperative binding process, the binding of Ca2+ to calretinin. Calretinin is a Ca2+-binding protein with four cooperative binding sites and one independent binding site. The Ca2+ binding to calretinin was assessed by measuring the decay of free Ca2+ using a fast fluorescent Ca2+ indicator following rapid (<50-μs rise time) Ca2+ concentration jumps induced by uncaging Ca2+ from DM-nitrophen. To unravel the kinetics of cooperative binding, we devised several approaches based on known cooperative binding models, resulting in a novel and relatively simple model. This model revealed unexpected and highly specific nonlinear properties of cellular Ca2+ regulation by calretinin. The association rate of Ca2+ with calretinin speeds up as the free Ca2+ concentration increases from cytoplasmic resting conditions (∼100 nM) to approximately 1 μM. As a consequence, the Ca2+ buffering speed of calretinin highly depends on the prevailing Ca2+ concentration prior to a perturbation. In addition to providing a novel mode of action of cellular Ca2+ buffering, our model extends the analysis of cooperativity beyond the static steady-state condition, providing a powerful tool for the investigation of the dynamics and functional significance of cooperative binding in general

Energy metabolism and glutamate-glutamine cycle in the brain: a stoichiometric modeling perspective

Background: The energetics of cerebral activity critically relies on the functional and metabolic interactions between neurons and astrocytes. Important open questions include the relation between neuronal versus astrocytic energy demand, glucose uptake and intercellular lactate transfer, as well as their dependence on the level of activity. Results: We have developed a large-scale, constraint-based network model of the metabolic partnership between astrocytes and glutamatergic neurons that allows for a quantitative appraisal of the extent to which stoichiometry alone drives the energetics of the system. We find that the velocity of the glutamate-glutamine cycle (Vcyc) explains part of the uncoupling between glucose and oxygen utilization at increasing Vcyc levels. Thus, we are able to characterize different activation states in terms of the tissue oxygen-glucose index (OGI). Calculations show that glucose is taken up and metabolized according to cellular energy requirements, and that partitioning of the sugar between different cell types is not significantly affected by Vcyc. Furthermore, both the direction and magnitude of the lactate shuttle between neurons and astrocytes turn out to depend on the relative cell glucose uptake while being roughly independent of Vcyc. Conclusions: These findings suggest that, in absence of ad hoc activity-related constraints on neuronal and astrocytic metabolism, the glutamate-glutamine cycle does not control the relative energy demand of neurons and astrocytes, and hence their glucose uptake and lactate exchange. © 2013 Massucci et al.; licensee BioMed Central Ltd

Biophysical properties of presynaptic short-term plasticity in hippocampal neurons: insights from electrophysiology, imaging and mechanistic models

Hippocampal neurons show different types of short-term plasticity (STP). Some exhibit facilitation of their synaptic responses and others depression. In this review we discuss presynaptic biophysical properties behind heterogeneity in STP in hippocampal neurons such as alterations in vesicle priming and docking, fusion, neurotransmitter filling and vesicle replenishment. We look into what types of information electrophysiology, imaging and mechanistic models have given about the time scales and relative impact of the different properties on STP with an emphasis on the use of mechanistic models as complementary tools to experimental procedures. Taken together this tells us that it is possible for a multitude of different mechanisms to underlie the same STP pattern, even though some are more important in specific cases, and that mechanistic models can be used to integrate the biophysical properties to see which mechanisms are more important in specific cases of STP

STDP in a Bistable Synapse Model Based on CaMKII and Associated Signaling Pathways

The calcium/calmodulin-dependent protein kinase II (CaMKII) plays a key role in the induction of long-term postsynaptic modifications following calcium entry. Experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states. The biochemical network involving CaMKII and its regulating protein signaling cascade has been hypothesized to durably maintain the evoked synaptic state in the form of a bistable switch. However, it is still unclear whether experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such a network. We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentration, and high calcium transients can switch the system from the weakly phosphorylated (DOWN) to the highly phosphorylated (UP) state of the CaMKII (similar to a LTP event). We show here that increased CaMKII dephosphorylation activity at intermediate Ca2+ concentrations can lead to switching from the UP to the DOWN state (similar to a LTD event). This can be achieved if protein phosphatase activity promoting CaMKII dephosphorylation activates at lower Ca2+ levels than kinase activity. Finally, it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes

Modeling and Analysis of the Molecular Basis of Pain in Sensory Neurons

Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies