Yasmin L. Hashambhoy

Neural Correlates of Reach Errors

Reach errors may be broadly classified into errors arising from unpredictable changes in target location, called target errors, and errors arising from miscalibration of internal models (e.g., when prisms alter visual feedback or a force field alters limb dynamics), called execution errors. Execution errors may be caused by miscalibration of dynamics (e.g., when a force field alters limb dynamics) or by miscalibration of kinematics (e.g., when prisms alter visual feedback). Although all types of errors lead to similar on-line corrections, we found that the motor system showed strong trial-by-trial adaptation in response to random execution errors but not in response to random target errors. We used functional magnetic resonance imaging and a compatible robot to study brain regions involved in processing each kind of error. Both kinematic and dynamic execution errors activated regions along the central and the postcentral sulci and in lobules V, VI, and VIII of the cerebellum, making these areas possible sites of plastic changes in internal models for reaching. Only activity related to kinematic errors extended into parietal area 5. These results are inconsistent with the idea that kinematics and dynamics of reaching are computed in separate neural entities. In contrast, only target errors caused increased activity in the striatum and the posterior superior parietal lobule. The cerebellum and motor cortex were as strongly activated as with execution errors. These findings indicate a neural and behavioral dissociation between errors that lead to switching of behavioral goals and errors that lead to adaptation of internal models of limb dynamics and kinematics.

CaMKII-Induced Shift in Modal Gating Explains L-Type Ca2+ Current Facilitation: A Modeling Study

Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) plays an important role in L-type Ca(2+) channel (LCC) facilitation: the Ca(2+)-dependent augmentation of Ca(2+) current (I(CaL)) exhibited during rapid repeated depolarization. Multiple mechanisms may underlie facilitation, including an increased rate of recovery from Ca(2+)-dependent inactivation and a shift in modal gating distribution from mode 1, the dominant mode of LCC gating, to mode 2, a mode in which openings are prolonged. We hypothesized that the primary mechanism underlying facilitation is the shift in modal gating distribution resulting from CaMKII-mediated LCC phosphorylation. We developed a stochastic model describing the dynamic interactions among CaMKII, LCCs, and phosphatases as a function of dyadic Ca(2+) and calmodulin levels, and we incorporated it into an integrative model of the canine ventricular myocyte. The model reproduces behaviors at physiologic protein levels and allows for dynamic transition between modes, depending on the LCC phosphorylation state. Simulations showed that a CaMKII-dependent shift in LCC distribution toward mode 2 accounted for the I(CaL) positive staircase. Moreover, simulations demonstrated that experimentally observed changes in LCC inactivation and recovery kinetics may arise from modal gating shifts, rather than from changes in intrinsic inactivation properties. The model therefore serves as a powerful tool for interpreting I(CaL) experiments.

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50‐year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage‐gated ion channels, mitochondrial energy production, ATP‐dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392–413 DOI: 10.1002/wsbm.122

Recursive Identification of Switched ARX Models with Unknown Number of Models and Unknown Orders

We consider the problem of recursively identifying the parameters of a switched ARX (SARX) model from input/output data under the assumption that the number of models, the model orders and the switching sequence are unknown. Our approach exploits the fact that applying a polynomial embedding to the input/output data leads to a lifted ARX model whose dynamics are linear on the so-called hybrid model parameters and independent of the switching sequence. In principle, one can use a standard recursive algorithm to identify such hybrid parameters. However, when the number of models and the model orders are unknown the embedded regressors may not be persistently exciting, hence the estimates of the hybrid parameters may not converge exponentially to a constant vector. Nevertheless, we show that these estimates still converge to a vector that depends continuously on the initial condition. By identifying the hybrid model parameters starting from two different initial conditions, we show that one can build two homogeneous polynomials whose derivatives at a regressor give an estimate of the parameters of the ARX model generating that regressor. After properly enforcing some of the entries of the hybrid model parameters to be zero, such estimates are shown to converge exponentially to the true ARX model parameters under suitable persistence of excitation conditions on the input/output data. Although our algorithm is designed for the case of perfect input/output data, our experiments also show its performance with noisy data.

Cardiac Resynchronization Therapy Improves Altered Na Channel Gating in Canine Model of Dyssynchronous Heart Failure

Background—Slowed Na+ current (INa) decay and enhanced late INa (INa-L) prolong the action potential duration (APD) and contribute to early afterdepolarizations. Cardiac resynchronization therapy (CRT) shortens APD compared with dyssynchronous heart failure (DHF); however, the role of altered Na+ channel gating in CRT remains unexplored. Methods and Results—Adult dogs underwent left-bundle branch ablation and right atrial pacing (200 beats/min) for 6 weeks (DHF) or 3 weeks followed by 3 weeks of biventricular pacing at the same rate (CRT). INa and INa-L were measured in left ventricular myocytes from nonfailing, DHF, and CRT dogs. DHF shifted voltage-dependence of INa availability by −3 mV compared with nonfailing, enhanced intermediate inactivation, and slowed recovery from inactivation. CRT reversed the DHF-induced voltage shift of availability, partially reversed enhanced intermediate inactivation but did not affect DHF-induced slowed recovery. DHF markedly increased INa-L compared with nonfailing. CRT dramatically reduced DHF-induced enhanced INa-L, abbreviated the APD, and suppressed early afterdepolarizations. CRT was associated with a global reduction in phosphorylated Ca2+/Calmodulin protein kinase II, which has distinct effects on inactivation of cardiac Na+ channels. In a canine AP model, alterations of INa-L are sufficient to reproduce the effects on APD observed in DHF and CRT myocytes. Conclusions—CRT improves DHF-induced alterations of Na+ channel function, especially suppression of INa-L, thus, abbreviating the APD and reducing the frequency of early afterdepolarizations. Changes in the levels of phosphorylated Ca2+/Calmodulin protein kinase II suggest a molecular pathway for regulation of INa by biventricular pacing of the failing heart.

CaMKII-dependent activation of late I Na contributes to cellular arrhythmia in a model of the cardiac myocyte

Cardiac voltage-gated Na⁺ channels underlie membrane depolarization during the upstroke of the action potential (AP). These channels also exhibit a late, slowly-inactivating component of current (late I<inf>Na</inf>) that may be enhanced under pathological conditions such as heart failure, and may therefore promote AP prolongation and increase the likelihood of arrhythmia. Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) functionally modifies Na⁺ channels, however it remains unclear if the CaMKII-dependent changes in late I<inf>Na</inf> are a major contributor to cellular arrhythmias such as early after depolarizations (EADs). In this study we develop a model of I<inf>Na</inf>, including CaMKII-dependent effects, based on experimental measurements. The Na⁺ channel model is incorporated into a computational model of the whole myocyte which describes excitation-contraction coupling via stochastic simulation of individual Ca²⁺ release sites. Simulations suggest that relatively small augmentation of late I<inf>Na</inf> is sufficient to significantly prolong APs and lead to the appearance of EADs.

Simulations Predict that Competing Gradients of VEGF and sFlt1 Alter VEGF Receptor Activation

We have created an experimentally-based computational model describing spatial transport of vascular endothelial growth factor (VEGF) and its receptors to quantitatively understand how guidance cues may modulate blood vessel sprout growth. VEGF binds to endothelial cells and initiates angiogenesis. Both VEGF concentration and VEGF gradients may control sprout formation. Soluble VEGF receptor 1 (sFlt1) can bind and sequester VEGF. Based on observations in developing vasculature, we hypothesize that a local reduction in sFlt1 expression can increase locally available VEGF and thus control angiogenesis. However, the complex VEGF interaction network makes it difficult to isolate how individual proteins contribute to the spatial distribution of the growth factor using experiments alone. Our computational model represents the local environment of a single blood vessel and nearby tissue and directly incorporates the network of VEGF interactions. In the model, parenchymal cells secrete VEGF, which diffuses through interstitial space and binds extracellular matrix (ECM) and sFlt1. VEGF binds endothelial cells via membrane-bound receptors Flt1 and Flk1, and endothelial cells secrete sFlt1. Additionally, the model accounts for degradation of VEGF and sFlt1 as well as internalization of receptor-bound ligands. Using partial differential equations, we simulate this system, which is constrained by experimentally-derived parameters. Our simulations show that when a sprout-leading tip cell secretes less sFlt1 than neighboring cells, there is decreased local sFlt1 sequestration of VEGF, thus resulting in augmented VEGF-Flk1 levels on the surface of the low-sFlt1 secreting tip cell. This could lead to sprout generation. We also show how variations in sFlt1 secretion and tip cell configuration may affect the gradients of guidance cues and directionality of sprout growth.