Statistical Metamodeling and Sequential Design of Computer Experiments to Model Glyco-Altered Gating of Sodium Channels in Cardiac Myocytes

Glycan structures account for up to 35% of the mass of cardiac sodium (Na v) channels. To question whether and how reduced sialylation affects Na v activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4^-/-) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in I Na and AP is difficult without performing in silico studies. However, computer model of Na v channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Na v models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Na v channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Na v channels. Notably, ST3Gal4^-/- myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.