Options for Steady State Analysis

Use Newton

This parameter is a boolean value to determine whether to use the damped Newton method on the non-linear algebraic equations defining the steady-state. The initial concentrations set by the user are taken as guesses for the solution. A value of '1' (the default) indicates that COPASI shall use the damped Newton method.

The damped Newton method is a variant of the famous Newton method for the solution of systems of non-linear equations. The solution is obtained from an iterative procedure that refines an initial guess until the residual error is smaller than required. If a limit number of iterations is reached without an acceptable solution, the method halts without a solution.

The iteration of the plain Newton method is:

Equation 7.1. 

In the damped method if has a larger residual error than one looks at

Equation 7.2. 

and accepts the first such value that has a smaller residual error than . If none is found, the procedure halts without a solution (because it is at a local minimum).

Use Integration

This parameter is a boolean value to determine whether to use the ODE solver (LSODA) to follow the time course defined by the differential equations until a steady state is reached. If at units of time no steady state has been reached the method halts with no solution. If Use Newton is '1' an attempt to find the steady-state via the damped Newton method is made at each intermediate time point. A value of '1' (the default) indicates that COPASI shall use integration.

Use Back Integration

This parameter is a boolean value to determine whether to use the ODE solver (LSODA) to reverse the time course (going backwards in time) defined by the differential equations until a steady state is reached. If at units of time no steady state has been reached the method halts with no solution. If Use Newton is '1' an attempt to find the steady-state via the damped Newton method is made at each intermediate time point. A value of '1' (the default) indicates that COPASI shall use back integration.

Accept Negative Concentrations

This parameter is a boolean value to determine whether to accept a steady-state, which contains negative concentrations. A value of '1' indicates that negative concentrations are acceptable whereas a value of '0' (the default) indicates that such states are discarded.

Iteration Limit

This parameter is a positive integer to determine the maximum number of iterations the damped Newton method shall perform before it fails. The default is '50'.

Derivation Factor

This is a numeric value to determine the step size used to calculate . The default is '0.001'.

Resolution

This is a positive numeric value to determine the resolution used to decide whether the current state is acceptable as a steady-state. If the absolute change of each state variable is smaller than the resolutions the state is accepted. The default is . Note that this value is interpreted as a concentration value, even though the calculation internally uses particle numbers. The reason for that is purely heuristic: In many cases the modeler will choose the units in a way that concentration values are neither extremely large nor extremely small numerically so that the default value for this parameter leads to useful results. However generally it is not save to just keep the default value without checking.