Модель «Внутриклеточные колебания кальция»

$$ \left\{ \begin{aligned} \frac{dS_1}{dt} &= v_0 - v_2 - v_4 + v_5 + v_6 \\ \frac{dS_2}{dt} &= v_4 - v_5 - v_6 \\ v_0 &= v_1 + v_3 \end{aligned} \right. \left\{ \begin{aligned} \frac{dS_1}{dt} &= v_0 - k_2 S_1 - k_4 S_1 + \frac{k_5 S_2 S_1^n}{K_{05}^n + S_1^n} + k_6 S_2 \\ \frac{dS_2}{dt} &= k_4 S_1 - \frac{k_5 S_2 S_1^n}{K_{05}^n + S_1^n} - k_6 S_2 \end{aligned} \right. $$

Счёт: Запускать по щелчку Редактировать модель

S₁= S₂=

independent: {
    t: 0
},
dependent: {
      S_1: [5],
      S_2: [5]
},
parameters: {
    v_0: {
        min: 0.1,
        max: 5,
        value: 3
    },
    k_2: {
        min: 0.5,
        max: 2,
        value: 1
    },
    k_4: {
        min: 1,
        max: 3,
        value: 2
    },
    k_5: {
        min: 0,
        max: 10,
        value: 1
    },
    k_6: {
        min: 0.01,
        max: 1,
        value: 0.01
    },
    n: {
        min: 0.2,
        max: 4,
        value: 4
    },
    K_05: {
        min: 0.1,
        max: 7,
        value: 3.1
    }
},
derivatives: {
    dS_1_dt: 'v_0 - k_2 * S_1-k_4*S_1+(k_5*S_2*Math.pow(S_1,n))/(Math.pow(K_05,n)+Math.pow(S_1,n))+k_6*S_2',
    dS_2_dt: 'k_4 * S_1 - (k_5*S_2*Math.pow(S_1,n))/(Math.pow(K_05,n)+Math.pow(S_1,n))-k_6*S_2'
},

param_charts: [  
  
],

solver: {
    step: 0.1,
    accuracy: 0.01,
    autostop: 50,
},
plot_options: {
    'S_1':  { min: 1, max: 8,},
	'S_2':  { min: 0, max: 30,}
},
init_hook: function() {
    var S1_=calc.sys_state['v_0']/calc.sys_state['k_2']
    var drob=calc.sys_state['k_5']/(Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])+Math.pow(S1_,calc.sys_state['n']))
    var S2_=calc.sys_state['v_0']*calc.sys_state['k_4']/calc.sys_state['k_2']/((calc.sys_state['k_6']+(calc.sys_state['k_5']*Math.pow(calc.sys_state['v_0'],calc.sys_state['n']))/(Math.pow(calc.sys_state['v_0'],calc.sys_state['n'])+Math.pow((calc.sys_state['k_2']*calc.sys_state['K_05']),calc.sys_state['n']))))
    var a = -calc.sys_state['k_2']-calc.sys_state['k_4']+Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])*calc.sys_state['k_5']*S2_*calc.sys_state['n']*Math.pow(S1_,(calc.sys_state['n']-1))/Math.pow((Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])+Math.pow(S1_,calc.sys_state['n'])),2);
    var b = calc.sys_state['k_6']+calc.sys_state['k_5']*(Math.pow(S1_,calc.sys_state['n']))/(Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])+Math.pow(S1_,calc.sys_state['n']));
    var c = calc.sys_state['k_4']-calc.sys_state['n']*calc.sys_state['k_5']*S2_*Math.pow(S1_,(calc.sys_state['n']-1))*Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])/(Math.pow((Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])+Math.pow(S1_,calc.sys_state['n'])),2));
    var d = -calc.sys_state['k_6']-calc.sys_state['k_5']*(Math.pow(S1_,calc.sys_state['n']))/(Math.pow(calc.sys_state['K_05'],calc.sys_state['n'])+Math.pow(S1_,calc.sys_state['n']));
    var V = calc.sys_state['v_0'];
    var s_2 = (a+d)/2;
    var sig = (a+d);
    var delta = a*d-b*c;
    var s2_4 = s_2*s_2;
    if (s2_4 >= delta) {
       var l1 = '' + (s_2 - Math.sqrt(s2_4-delta)).toPrecision(3);
        var l2 = '' + (s_2 + Math.sqrt(s2_4-delta)).toPrecision(3);
    } else {
        var l1 = '' + s_2.toPrecision(3) + '+ ' + Math.sqrt(delta-s2_4).toPrecision(3) + ' \\cdot i';
        var l2 = '' + s_2.toPrecision(3) + '- ' + Math.sqrt(delta-s2_4).toPrecision(3) + ' \\cdot i';
    }
    $('trax_controller_postfix').innerHTML = '$$ \\begin{aligned}  \\bar{S_1} &= {'+S1_.toPrecision(4)+'} \\;\\;\\; \\bar{S_2} = {'+S2_.toPrecision(5)+'} \\\\ \\sigma &={'+sig.toPrecision(3)+'} \\; \\; \\; \\Delta ={'+delta.toPrecision(3)+'} \\\\ \\lambda_1 &= {'+l1+'} \\\\ \\lambda_2 &= {'+l2+'}  \\end{aligned} $$';
    MathJax.Hub.Queue(["Typeset",MathJax.Hub,"trax_controller_postfix"]);
},