NBCR Team Models Nucleotide Diffusion in the Cardiac Myofilament Lattice at Molecular and Subcellular Scales
An NBCR research team recently published a paper investigating the spatiotemporal diffusion of adenine di- and triphosphate (ADP and ATP) nucleotides through the myofilament lattice in heart muscle. The investigation of diffusion of these biomolecules is important because they regulate cardiac energetics and coupling between cell excitation and contraction.
The newly developed methodology and computational tools provide a novel bridge between atomistic-resolution reconstruction of macromolecular complexes (e.g., troponin, actin, myosin) and subcellular-scale metabolic processes, which may help to better understand the mechanisms regulating excitation-contraction coupling in cardiomyocytes.
These new tools are likely to benefit the study of cardiac function at the tissue and organ level. For example, one of the projects at NBCR focuses on whole-heart contractility models. Such multi-scale models reflect interactions between cellular, tissue, and organ scales. This team’s work will enable integrating molecular and cellular perspectives into such predictive models of whole heart function to increase the models’ accuracy.
Perhaps more unexpectedly, the researchers believe this new methodology can be applied further afield to other biological, and even non-biological, problems that cross multiple scales.
Lead author Peter M. Kekenes-Huskey, a postdoctoral researcher in J. Andrew McCammon’s lab at UCSD, provides some background for the work: “The ability of cardiac cells to contract depends on the displacement of large macromolecular fibers called myofilaments through work done by the myosin motors. ATP provides the critical source of energy for this process, through its hydrolysis by myosin.” This reaction releases stored energy in the muscle to produce work, such as through muscle contraction.
The research team showed that nucleotide diffusion is anisotropic, that is, the diffusion of ATP is faster along myofilament lattice fibers relative to the perpendicular direction, which could influence the energetics of metabolism. Specifically, the team attributed the disparity to molecular details of the periodic hexagonal lattice of the thin (actin) and thick (myosin) filaments. “Our results,” says Kekenes-Huskey, “are consistent with experimental measurements of ATP diffusion but provide more accurate estimates than previous studies using cryo-electromagnetic-resolution models of the thin and thick filaments.”
Similar results of anisotropic Ca2+ diffusion by Shorten and Sneyd (Biophys J 2009) were based on skeletal muscle cells. The NBCR team extended those studies to heart cells, accounting for the different structural properties of the cardiac myofilaments, such as the wider distances between filaments. More importantly, the team based their study on newly available atomic-resolution structural data, acquired by X-ray crystallography, from the Protein Data Bank to refine the estimates of nucleotide diffusion.
The multi-scale approach was made possible through homogenization theory, a mathematical tool to describe the influence of high-resolution structural data on diffusion in considerably larger volumes. This theory yields an effective diffusion constant that can be used to model the transport of small molecules like ATP. This theory describes both molecular- and cellular-length scales by integrating microscopic myofibril geometries with macroscopic, sarcomere-scale models of metabolism. “We used this theory,” says Kekenes-Huskey, “to examine how variations in diffusion coefficients caused by filament overlap, cross-bridge density, and lattice spacing influence the transport of ATP and its partners in the reaction process.”
In summary, their results show considerable anisotropy in nucleotide diffusion due to lattice spacing and myofilament overlap. This finding indicates greater hindrance to diffusion than estimated in previous studies based on lower-resolution geometries.
This work was a complex, multidisciplinary effort. The team adopted some of the computational theory and methodologies developed by Mike Holst, a professor in the UCSD Department of Mathematics, to efficiently solve the more complicated math problems. Yongjie “Jessica” Zhang, an associate professor in the Department of Mechanical Engineering at Carnegie Mellon and an NBCR collaborator, contributed next-generation techniques to convert the experimental structure of the myofilament lattice to a mesh; this was an important starting point for numerical solution of the homogenization model. Andrew K. Gillette, previously a postdoctoral researcher of Holst’s (now an assistant professor at the University of Arizona), worked with Kekenes-Huskey to apply the computational theory to the myofilament model. Tao Liao, a graduate student in Zhang’s group, developed the complicated meshes. Johan E. Hake, a postdoctoral researcher supported through NBCR, provided easily tested, easy-to-use tools to solve the numerical models. NBCR provided the computational platform: a GPU-enabled cluster to run the computations with technical assistance from programmer/analyst Nadya Williams. Scientific advice was provided by Anushka P. Michailova and Andrew D. McCulloch who contributed expertise on the nuances of energy and metabolism in cardiac cells.
"We believe that accurate determination of diffusion,” says Kekenes-Huskey, “depends on more accurately describing the molecular volume through the use of atomistic-resolution data, as done in the published experiment. Further, we found that the high level of accuracy afforded by homogenizing molecular-scale features over a macroscopic region may be a powerful multi-scale tool for a variety of biological processes occurring within cells.”
- Kekenes-Huskey, Peter M., Tao Liao, Andrew K. Gillette, Johan E. Hake, Yongjie Zhang, Anushka P. Michailova, Andrew D. McCulloch, and J. Andrew McCammon, Molecular and Subcellular-scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice, Biophysical Journal, Vol. 105, No. 9, pp. 2130-2140, November 5, 2013, doi:10.1016/j.bpj.2013.09.020.
Researchers: Peter M. Kekenes-Huskey, Tao Liao, Andrew K. Gillette, Johan E. Hake, Yongjie Zhang, Anushka P. Michailova, Andrew D. McCulloch, and J. Andrew McCammon