A biophysical model of spatiotemporal ATP buffering in a skeletal muscle sarcomere

Muscle sarcomeres contract when calcium flows from the sarcoplasmic reticulum (SR) into the cytoplasm and binds to actin filaments at troponin C (TnC). The cyclic process of contraction and subsequent relaxation is driven by a non-equilibrium ATP/ADP ratio in the cytosol maintained by spatially distributed (creatine kinase (CK) and adenylate kinase (AK)) and stratified (mitochondria and glycolysis) ATP synthetic pathways in the sarcomere cell. Here, the functional significance of the known spatial organization of sites of ATP utilization versus production in the skeletal muscle sarcomere was studied by computer modeling and simulation of ATP metabolism in time and cell space (2D; radial coordinates). Specifically, the question was revisited whether facilitated ADP diffusion is sufficient to activate mitochondrial ATP synthesis during contraction [1]. The 3D spatiotemporal computational model was based on previous work by Groenendaal et al [2] and captured the following biochemical and physicochemical processes: (i) calcium release and reuptake by SR calcium pumps (SERCA), (ii) diffusion, (iii) calcium and magnesium buffering by ATP, TnC and parvalbumin, (iv) ATP turnover by contractile and SERCA ATPase, and (v) CK and AK ATP buffering. At this stage, mitochondrial ATP synthesis was not included. The model was implemented in COMSOL multiphysics 4.1 (COMSOL, Sweden) and contained 37 state variables and 249 parameters. The set of partial differential equations (PDE) were parameterized using literature as well as original experimental data, and solved using a finite element method. The model was verified against in vivo data of ATP metabolism in muscle. To test the hypothesis that facilitated ADP diffusion is sufficient to activate mitochondrial ATP synthesis and maintain energy balance during muscle contraction, diffusion of PCr and Cr and the spatial distribution of CK buffering activity within the sarcomere were varied. CK activity in the actomyosin overlap domain was set at zero. Contraction was simulated at a stimulation frequency of 5Hz. The model predicted an elevated average cytosolic ADP concentration and an elevated cytosolic ADP concentration on the boundary between the cytosol and the mitochondrion for disabled diffusion of PCr and Cr. Variation of CK activity localization resulted in similar average cytosolic ADP concentrations over time, however, the spatial distribution of ADP in the cytosol was altered. These results confirm a crucial role of facilitated ADP diffusion by CK reactants in muscle energy balance. [1]. Meyer, RA, Sweeney, HL and Kushmerick, MJ. 1984. Am J Physiol., Vol. 246, pp. 365-77. [2]. Groenendaal W, et al. 2008. IET Syst Biol 2(6): 411-422.