Compartment calcium model of frog skeletal muscle during activation Weifan Liu, Sarah D. Olson n Department of Mathematical Sciences, Worcester Polytechnic Institute,100 Institute Rd, Worcester, MA 01609, USA HIGHLIGHTS  Developed a voltage dependent calcium dynamics model in frog skeletal muscle fibers.  An electrical model was developed to describe voltage at the surface membrane.  Calcium in the myofibrillar space is examined for twitch and tetanus.  Force generation in tetanus changes due to variations in parameters. article info Article history: Received 27 January 2014 Received in revised form 26 August 2014 Accepted 28 August 2014 Available online 16 September 2014 Keywords: Calcium dynamics Sarcoplasmic reticulum Excitation contraction Hodgkin Huxley equations abstract Skeletal muscle contraction is triggered by a rise in calcium (Ca 2 þ ) concentration in the myofibrillar space. The objective of this study was to develop a voltage dependent compartment model of Ca 2 þ dynamics in frog skeletal muscle fibers. The compartment model corresponds to the myofibrillar space (MS) and a calcium store, the sarcoplasmic reticulum (SR). Ca 2 þ is released from the SR to the MS based on the voltage and is able to bind to several proteins in the MS. We use a detailed model to account for voltage dependent Ca 2 þ release and inactivation. With this model, we are able to match previous experimental data for Ca 2 þ release and binding to proteins for an applied (fixed) voltage. We explore the sensitivity of parameters in the model and illustrate the importance of inactivation of the SR; during a long depolarization, the SR must be inactivated in order to achieve realistic Ca 2 þ concentrations in the MS. A Hodgkin Huxley type model was also developed to describe voltage at the surface membrane using electrophysiological data from previous experiments. This voltage model was then used as the time dependent voltage to determine Ca 2 þ release from the SR. With this fully coupled model, we were able to match previous experimental results for Ca 2 þ concentrations for a given applied current. Additionally, we examined simulated Ca 2 þ concentrations in the case of twitch and tetanus, correspond- ing to different applied currents. The developed model is robust and reproduces many aspects of voltage dependent calcium signaling in frog skeletal muscle fibers. This modeling framework provides a platform for future studies of excitation contraction coupling in skeletal muscle fibers. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction In skeletal muscles, muscular force production is primarily con- trolled by changes in the intracellular calcium (Ca 2 þ ) concentration. In general, when Ca 2þ rises, the muscles contract, and when calcium decreases, the muscles relax (Berchtold et al., 2000). Normal activation of a skeletal muscle fiber involves a motor neuron receiving a signal from the central nervous system. This signal causes a depolarization corresponding to an action potential at the level of the sarcolemma, the cell membrane of the skeletal muscle fiber. The change in voltage causes Ca 2þ to be released from the sarcoplasmic reticulum (SR) (Posterino et al., 2000). This Ca 2 þ release allows the muscle to contract. In frog muscle fibers, Ca 2 þ release channels are located near the Z lines of the sarcomeres. The sarcomere is composed of many myofilaments and the Z line corresponds to the region where adjacent sarcomeres come together (thin dark line when viewed with a microscope, Peachey, 1965). The Ca 2 þ is released from the SR into the myofibrillar space (MS). This is accomplished via voltage dependent conformational changes in receptors and activation of other receptors. A single depolarization or signal from the motor neuron is a twitch. When there are multiple depolarizations within a short period of time, this will result in a sustained increase in Ca 2 þ in the MS, which will cause a sustained muscle contraction and generation of force, corresponding to tetanus (Berchtold et al., 2000; Posterino et al., 2000). Modeling and understanding Ca 2 þ concentrations in the SR and the MS will lead to an understanding of normal and mutant skeletal muscles. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology http://dx.doi.org/10.1016/j.jtbi.2014.08.050 0022-5193/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: weifan.liu@duke.edu (W. Liu), sdolson@wpi.edu (S.D. Olson). Journal of Theoretical Biology 364 (2015) 139–153