Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

Multiscale computational modeling of the effects of 2'-deoxy-ATP on cardiac muscle calcium handling

2'-Deoxy-ATP (dATP), a naturally occurring near analog of ATP, is a well-documented myosin activator that has been shown to increase contractile force, improve pump function, and enhance lusitropy in the heart. Calcium transients in cardiomyocytes with elevated levels of dATP show faster calcium decay compared with cardiomyocytes with basal levels of dATP, but the mechanisms behind this are unknown. Here, we design and utilize a multiscale computational modeling framework to test the hypothesis that dATP acts on the sarcoendoplasmic reticulum calcium-ATPase (SERCA) pump to accelerate calcium re-uptake into the sarcoplasmic reticulum during cardiac relaxation. Gaussian accelerated molecular dynamics simulations of human cardiac SERCA2A in the E1 apo, ATP-bound and dATP-bound states showed that dATP forms more stable contacts in the nucleotide binding pocket of SERCA and leads to increased closure of cytosolic domains. These structural changes ultimately lead to changes in calcium binding, which we assessed using Brownian dynamics simulations. We found that dATP increases calcium association rate constants to SERCA and that dATP binds to apo SERCA more rapidly than ATP. Using a compartmental ordinary differential equation model of human cardiomyocyte excitation-contraction coupling, we found that these increased association rate constants contributed to the accelerated rates of calcium transient decay observed experimentally. This study provides clear mechanistic evidence of enhancements in cardiac SERCA2A pump function due to interactions with dATP.

Nanoscale organization of ryanodine receptor distribution and phosphorylation pattern determines the dynamics of calcium sparks

Super-resolution imaging techniques have provided a better understanding of the relationship between the nanoscale organization and function of ryanodine receptors (RyRs) in cardiomyocytes. Recent data have indicated that this relationship is disrupted in heart failure (HF), as RyRs are dispersed into smaller and more numerous clusters. However, RyRs are also hyperphosphorylated in this condition, and this is reported to occur preferentially within the cluster centre. Thus, the combined impact of RyR relocalization and sensitization on Ca²⁺ spark generation in failing cardiomyocytes is likely complex and these observations suggest that both the nanoscale organization of RyRs and the pattern of phosphorylated RyRs within clusters could be critical determinants of Ca²⁺ spark dynamics. To test this hypothesis, we used computational modeling to quantify the relationships between RyR cluster geometry, phosphorylation patterns, and sarcoplasmic reticulum (SR) Ca²⁺ release. We found that RyR cluster disruption results in a decrease in spark fidelity and longer sparks with a lower amplitude. Phosphorylation of some RyRs within the cluster can play a compensatory role, recovering healthy spark dynamics. Interestingly, our model predicts that such compensation is critically dependent on the phosphorylation pattern, as phosphorylation localized within the cluster center resulted in longer Ca²⁺ sparks and higher spark fidelity compared to a uniformly distributed phosphorylation pattern. Our results strongly suggest that both the phosphorylation pattern and nanoscale RyR reorganization are critical determinants of Ca²⁺ dynamics in HF.

Ryanodine receptors (RyRs) are ion channels located on the membrane of the sarcoplasmic reticulum that are responsible for an increase in cytosolic Ca²⁺ during cell excitation. Here, we investigate how the geometry of RyR clusters combined with spatial phosphorylation patterns impacts on Ca²⁺ spark generation and kinetics. The findings from our study show that phosphorylation pattern and both RyR cluster shape and dispersion have implications on Ca²⁺ spark activity and provide insights into altered Ca²⁺ dynamics during HF.

Computational modeling approaches to cAMP/PKA signaling in cardiomyocytes

The cAMP/PKA pathway is a fundamental regulator of excitation-contraction coupling in cardiomyocytes. Activation of cAMP has a variety of downstream effects on cardiac function including enhanced contraction, accelerated relaxation, adaptive stress response, mitochondrial regulation, and gene transcription. Experimental advances have shed light on the compartmentation of cAMP and PKA, which allow for control over the varied targets of these second messengers and is disrupted in heart failure conditions. Computational modeling is an important tool for understanding the spatial and temporal complexities of this system. In this review article, we outline the advances in computational modeling that have allowed for deeper understanding of cAMP/PKA dynamics in the cardiomyocyte in health and disease, and explore new modeling frameworks that may bring us closer to a more complete understanding of this system. We outline various compartmental and spatial signaling models that have been used to understand how β-adrenergic signaling pathways function in a variety of simulation conditions. We also discuss newer subcellular models of cardiovascular function that may be used as templates for the next phase of computational study of cAMP and PKA in the heart, and outline open challenges which are important to consider in future models.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Multiscale Models of Cardiac Muscle Biophysics and Tissue Remodeling in Hypertrophic Cardiomyopathies

Myocardial hypertrophy is the result of sustained perturbations to the mechanical and/or neurohormonal homeostasis of cardiac cells and is driven by integrated, multiscale biophysical and biochemical processes that are currently not well defined. In this brief review, we highlight recent computational and experimental models of cardiac hypertrophy that span mechanisms from the molecular level to the tissue level. Specifically, we focus on: (i) molecular-level models of the structural dynamics of sarcomere proteins in hypertrophic hearts, (ii) cellular-level models of excitation-contraction coupling and mechanosensitive signaling in disease-state myocytes, and (iii) organ-level models of myocardial growth kinematics and predictors thereof. Finally, we discuss how spanning these scales and combining multiple experimental/computational models will provide new information about the processes governing hypertrophy and potential methods to prevent or reverse them.

A Stochastic Multiscale Model of Cardiac Thin Filament Activation Using Brownian-Langevin Dynamics

We use Brownian-Langevin dynamics principles to derive a coarse-graining multiscale myofilament model that can describe the thin-filament activation process during contraction. The model links atomistic molecular simulations of protein-protein interactions in the thin-filament regulatory unit to sarcomere-level activation dynamics. We first calculate the molecular interaction energy between tropomyosin and actin surface using Brownian dynamics simulations. This energy profile is then generalized to account for the observed tropomyosin transitions between its regulatory stable states. The generalized energy landscape then served as a basis for developing a filament-scale model using Langevin dynamics. This integrated analysis, spanning molecular to thin-filament scales, is capable of tracking the events of the tropomyosin conformational changes as it moves over the actin surface. The tropomyosin coil with flexible overlap regions between adjacent tropomyosins is represented in the model as a system of coupled stochastic ordinary differential equations. The proposed multiscale approach provides a more detailed molecular connection between tropomyosin dynamics, the trompomyosin-actin interaction-energy landscape, and the generated force by the sarcomere.

Cardiac myosin activation with 2-deoxy-ATP via increased electrostatic interactions with actin

The naturally occurring nucleotide 2-deoxy-adenosine 5'-triphosphate (dATP) can be used by cardiac muscle as an alternative energy substrate for myosin chemomechanical activity. We and others have previously shown that dATP increases contractile force in normal hearts and models of depressed systolic function, but the structural basis of these effects has remained unresolved. In this work, we combine multiple techniques to provide structural and functional information at the angstrom-nanometer and millisecond time scales, demonstrating the ability to make both structural measurements and quantitative kinetic estimates of weak actin-myosin interactions that underpin sarcomere dynamics. Exploiting dATP as a molecular probe, we assess how small changes in myosin structure translate to electrostatic-based changes in sarcomere function to augment contractility in cardiac muscle. Through Brownian dynamics simulation and computational structural analysis, we found that deoxy-hydrolysis products [2-deoxy-adenosine 5'-diphosphate (dADP) and inorganic phosphate (Pi)] bound to prepowerstroke myosin induce an allosteric restructuring of the actin-binding surface on myosin to increase the rate of cross-bridge formation. We then show experimentally that this predicted effect translates into increased electrostatic interactions between actin and cardiac myosin in vitro. Finally, using small-angle X-ray diffraction analysis of sarcomere structure, we demonstrate that the proposed increased electrostatic affinity of myosin for actin causes a disruption of the resting conformation of myosin motors, resulting in their repositioning toward the thin filament before activation. The dATP-mediated structural alterations in myosin reported here may provide insight into an improved criterion for the design or selection of small molecules to be developed as therapeutic agents to treat systolic dysfunction.

Insights and Challenges of Multi-Scale Modeling of Sarcomere Mechanics in cTn and Tm DCM Mutants-Genotype to Cellular Phenotype

Dilated Cardiomyopathy (DCM) is a leading cause of sudden cardiac death characterized by impaired pump function and dilatation of cardiac ventricles. In this review we discuss various in silico approaches to elucidating the mechanisms of genetic mutations leading to DCM. The approaches covered in this review focus on bridging the spatial and temporal gaps that exist between molecular and cellular processes. Mutations in sarcomeric regulatory thin filament proteins such as the troponin complex (cTn) and Tropomyosin (Tm) have been associated with DCM. Despite the experimentally-observed myofilament measures of contractility in the case of these mutations, the mechanisms by which the underlying molecular changes and protein interactions scale up to organ failure by these mutations remains elusive. The review highlights multi-scale modeling approaches and their applicability to study the effects of sarcomeric gene mutations in-silico. We discuss some of the insights that can be gained from computational models of cardiac biomechanics when scaling from molecular states to cellular level.

Contributions of Ca2+-Independent Thin Filament Activation to Cardiac Muscle Function

Although Ca2+ is the principal regulator of contraction in striated muscle, in vitro evidence suggests that some actin-myosin interaction is still possible even in its absence. Whether this Ca2+-independent activation (CIA) occurs under physiological conditions remains unclear, as does its potential impact on the function of intact cardiac muscle. The purpose of this study was to investigate CIA using computational analysis. We added a structurally motivated representation of this phenomenon to an existing myofilament model, which allowed predictions of CIA-dependent muscle behavior. We found that a certain amount of CIA was essential for the model to reproduce reported effects of nonfunctional troponin C on myofilament force generation. Consequently, those data enabled estimation of ΔGCIA, the energy barrier for activating a thin filament regulatory unit in the absence of Ca2+. Using this estimate of ΔGCIA as a point of reference (∼7 kJ mol(-1)), we examined its impact on various aspects of muscle function through additional simulations. CIA decreased the Hill coefficient of steady-state force while increasing myofilament Ca2+ sensitivity. At the same time, CIA had minimal effect on the rate of force redevelopment after slack/restretch. Simulations of twitch tension show that the presence of CIA increases peak tension while profoundly delaying relaxation. We tested the model's ability to represent perturbations to the Ca2+ regulatory mechanism by analyzing twitch records measured in transgenic mice expressing a cardiac troponin I mutation (R145G). The effects of the mutation on twitch dynamics were fully reproduced by a single parameter change, namely lowering ΔGCIA by 2.3 kJ mol(-1) relative to its wild-type value. Our analyses suggest that CIA is present in cardiac muscle under normal conditions and that its modulation by gene mutations or other factors can alter both systolic and diastolic function.

Molecular Effects of cTnC DCM Mutations on Calcium Sensitivity and Myofilament Activation-An Integrated Multiscale Modeling Study

Mutations in cardiac troponin C (D75Y, E59D, and G159D), a key regulatory protein of myofilament contraction, have been associated with dilated cardiomyopathy (DCM). Despite reports of altered myofilament function in these mutants, the underlying molecular alterations caused by these mutations remain elusive. Here we investigate in silico the intramolecular mechanisms by which these mutations affect myofilament contraction. On the basis of the location of cardiac troponin C (cTnC) mutations, we tested the hypothesis that intramolecular effects can explain the altered myofilament calcium sensitivity of force development for D75Y and E59D cTnC, whereas altered cardiac troponin C-troponin I (cTnC-cTnI) interaction contributes to the reported contractile effects of the G159D mutation. We employed a multiscale approach combining molecular dynamics (MD) and Brownian dynamics (BD) simulations to estimate cTnC calcium association and hydrophobic patch opening. We then integrated these parameters into a Markov model of myofilament activation to compute the steady-state force-pCa relationship. The analysis showed that myofilament calcium sensitivity with D75Y and E59D can be explained by changes in calcium binding affinity of cTnC and the rate of hydrophobic patch opening, if a partial cTnC interhelical opening angle (110°) is sufficient for cTnI switch peptide association to cTnC. In contrast, interactions between cTnC and cTnI within the cardiac troponin complex must also be accounted for to explain contractile alterations due to G159D. In conclusion, this is the first multiscale in silico study to elucidate how direct molecular effects of genetic mutations in cTnC translate to altered myofilament contractile function.