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MATMyoSim

Ramp 2 demonstration

This demo shows how to run a simulation of a single sarcomere subjected to a ramp, hold, and then release protocol.

This demo is very similar to ramp_1 except that it simulates an exponential passive component.

Instructions

  • Launch MATLAB.
  • Change directory to the MATMyoSim\code\demos\ramps\ramp_2 folder in MATLAB.
  • Open demo_ramp_2.m.
  • Press F5 to run the demo.

Code 

function demo_ramp_2
% Function illustrates how to run a simulation of a single-half-sarcomere
% with an exponential passive elastic component and no cycling cross-bridges

% Variables
protocol_file_string = 'ramp_2_protocol.txt';
model_parameters_json_file_string = 'ramp_2_parameters.json';
options_file_string = 'ramp_2_options.json';
model_output_file_string = '..\..\temp\ramp_2_output.myo';

% Make sure the path allows us to find the right files
addpath(genpath('..\..\..\..\code'));

% Run a simulation
sim_output = simulation_driver( ...
    'simulation_protocol_file_string', protocol_file_string, ...
    'model_json_file_string', model_parameters_json_file_string, ...
    'options_json_file_string', options_file_string, ...
    'output_file_string', model_output_file_string);

% Load it back up and display to show how that can be done
sim = load(model_output_file_string,'-mat')
sim_output = sim.sim_output

figure(2);
clf;
subplot(2,1,1);
plot(sim_output.time_s,sim_output.muscle_force,'b-');
ylabel('Force (N m^{-2})');
subplot(2,1,2);
plot(sim_output.time_s,sim_output.hs_length,'b-');
ylabel('Half-sarcomere length (nm)');
xlabel('Time (s)');

Model

The model is defined in repo\code\demos\ramps\ramp_2\ramp_2_parameters.json.

{
    "MyoSim_model":
    {
        "muscle_props":
        {
            "no_of_half_sarcomeres": 1,
            "series_k_linear": 0
        },
        "hs_props":
        {
            "kinetic_scheme": "3state_with_SRX",
            "hs_length": 1300,
            "myofilaments":
            {
                "bin_min": -10,
                "bin_max": 10,
                "bin_width": 0.5,
                "thick_filament_length": 815,
                "thin_filament_length": 1120,
                "bare_zone_length": 80,
                "k_falloff": 0
            },
            "parameters":
            {
                "k_1": 1000,
                "k_force": 0.0,
                "k_2": 0.1,
                "k_3": 0,
                "k_4_0": 20,
                "k_4_1": 0.1,
                "k_cb": 0.001,
                "x_ps": 0,
                "k_on": 6e7,
                "k_off": 200,
                "k_coop": 10,
                "passive_force_mode": "exponential",
                "passive_sigma": 100,
                "passive_hsl_slack": 1250,
                "passive_L": 25,
                "compliance_factor": 0.5,
                "cb_number_density": 6.9e16,
                "k_boltzmann": 1.38e-23,
                "temperature": 288,
                "max_rate": 5000
            }
        }
    }
}

Output

Simulation output

Simulation output

Replotted from output file Replotted output

Comments

If you look at the json model structure, you will see that the two most important points about this model are

  • no cross-bridges attach to the thin filament
  • the parallel elastic component is exponential with
    • passive_sigma = 100 N m-2
    • passive_hsl_slack = 1250 nm
    • passive_L = 25 nm

Since no cross-bridges attach to the thin filament, the stress in the half-sarcomere at length x is F = passive_sigma * exp((x - passive_hsl_slack) / passive_L)

Thus force changes exponentially with length.