/* * Differential Regulation of ER Ca2+ Uptake and Release Rates * Accounts for Multiple Modes of Ca2+-induced Ca2+ Release * * Model Status * * This model is consistently represented within the CellML but * contains sets of algebraic equations that prevent the model * from being solved in currently available software - 03/08. * * ValidateCellML found unit inconsistencies in this model * * Model Structure * * Calcium is an important signalling ion, and changes in Ca2+ * concentration ([Ca2+]) regulate diverse processes in many cellular * compartments. In excitable cells, depolarisation-induced Ca2+ * entry increases [Ca2+]i, leading to secondary changes in [Ca2+] * within organelles such as mitochondria and ER that regulate * specific Ca2+-sensitive targets within these organelles. Although * mitochondria accumulate Ca2+ in response to depolarisation-evoked * [Ca2+]i elevations (see The Colegrove et al Model Of Mitochondrial * Ca2+ Uptake And Release, 2000), the ER is also an important * component in Ca2+ signalling in virtually all non-muscle cells, * and it has been described as either a Ca2+ source or sink. Different * modes of net ER Ca2+ transport are expected to have very different * effects on cytoplasmic and intraluminal Ca2+ signals and on * the processes they regulate (see The Albrecht et al Model Of * Multiple Modes of Ca2+-induced Ca2+ Release in Sympathetic Neurons, * 2001). * * In a follow up study to their 2001 paper, Meredith A. Albrecht, * Stephen L. Colegrove and David D. Friel have examined how differential * regulation of ER Ca2+ uptake and release rates accounts for * multiple modes of Ca2+-induced Ca2+ release. Three different * macroscopic Ca2+ fluxes were modelled: JSERCA, the rate of Ca2+ * uptake via SR Ca-ATPases; JICa, the total cytoplasmic Ca2+ flux * when SR Ca-ATPases are inhibited; and Jpm, the rate of Ca2+ * extrusion across the plasma membrane. One additional flux Jrelease * was calculated from the difference between JICa and Jpm (see * below). This mathematical model has been translated into a CellML * description which can be downloaded in various formats as described * in . * * The complete original paper reference is cited below: * * Differential Regulation of ER Ca2+ Uptake and Release Rates * Accounts for Multiple Modes of Ca2+-induced Ca2+ Release, Meredith * A. Albrecht, Stephen L. Colegrove and David D. Friel, 2002, * The Journal Of General Physiology, 119, 211-233. PubMed ID: * 11865019 * * cell schematic for the model * * [[Image file: albrecht_2002.png]] * * Schematic of the model indicating Ca2+ compartmentation in the * extracellular matrix, cytosol and the ER and pathways for Ca2+ * ion movement between the compartments. */ import nsrunit; // Warning: unit conversion turned off due to unit errors in 3 equation(s) unit conversion off; unit per_second=1 second^(-1); // unit millivolt predefined //Warning: unit millimolar_ renamed from millimolar, as the latter is predefined in JSim with different fundamental units. unit millimolar_=1E-3 meter^(-3)*mole^1; // unit micromolar predefined // unit nanomolar predefined unit nanomolar_per_second=1E-6 meter^(-3)*second^(-1)*mole^1; unit micromolar_per_second=1E-3 meter^(-3)*second^(-1)*mole^1; unit micro_litre=1E-9 meter^3; unit coulomb_per_millimole=1E3 second^1*ampere^1*mole^(-1); unit picoA=1E-12 ampere^1; math main { //Warning: the following variables were set 'extern' or given // an initial value of '0' because the model would otherwise be // underdetermined: Ca_i, Ca_ER, v_ER, k_ER, v_i, k_i, I_Ca realDomain time second; time.min=0; extern time.max; extern time.delta; real Ca_i(time) nanomolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) Ca_i=0; real J_i(time) nanomolar_per_second; real J_ER(time) nanomolar_per_second; real J_pm(time) nanomolar_per_second; real Ca_ER(time) nanomolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) Ca_ER=0; extern real v_ER micro_litre; extern real k_ER dimensionless; real Ca_ER_init(time) nanomolar; extern real v_i micro_litre; extern real k_i dimensionless; real P_ER(time) per_second; real J_SERCA(time) nanomolar_per_second; real J_ICa nanomolar_per_second; real F coulomb_per_millimole; F=96.5; extern real I_Ca picoA; real J_extru(time) nanomolar_per_second; real k_leak_pm per_second; k_leak_pm=0.00000015; real Vmax_extru nanomolar_per_second; Vmax_extru=25.0; real EC50_extru nanomolar; EC50_extru=386.0; real n_extru dimensionless; n_extru=2.4; real Ca_o millimolar_; Ca_o=2.0; real Vmax_SERCA nanomolar_per_second; Vmax_SERCA=2146.0; real EC50_SERCA micromolar; EC50_SERCA=30.3; real n_SERCA dimensionless; n_SERCA=2.5; real P_basal per_second; P_basal=0.009; real Pmax_RyR per_second; Pmax_RyR=0.05; real EC50_RyR nanomolar; EC50_RyR=2641.0; real n_RyR dimensionless; n_RyR=0.96; real J_release(time) nanomolar_per_second; // // Ca_i:time=((-1)*J_i); J_i=(J_pm+J_ER); // Ca_ER:time=(J_ER*(v_i*k_i/(v_ER*k_ER))); Ca_ER_init=(Ca_i+J_SERCA*Ca_i/(P_ER*(Ca_i/v_i))); // J_ICa=(I_Ca/(2*F*v_i*k_i)); // J_pm=(J_extru+J_ICa); J_extru=(k_i^(-1)*(k_leak_pm*(Ca_i-Ca_o)+Vmax_extru/(1+(EC50_extru/Ca_i)^n_extru))); // J_SERCA=(Vmax_SERCA/(k_i*(1+(EC50_SERCA/Ca_i)^n_SERCA))); // J_release=(P_ER*(Ca_i-Ca_ER)/(v_i*k_i)); J_ER=(J_SERCA+J_release); P_ER=(v_i*(P_basal+Pmax_RyR/(1+(EC50_RyR/Ca_i)^n_RyR))); }