From 2010.igem.org

Combined Model

Combined model. Coupled individual models for the simulation of the whole process and their interfaces. The concentration of CheYp determines the movement bias.

Interface

To combine light switch, chemotaxis and movement models, interfaces were defined. The combination was achieved in two steps:

• First, the deterministic light switch and chemotaxis models were combined by assuming a complete removal of a selected Che protein species by the light switch. The interface was defined as the concentration ([LSP-Che]) of this linked device.

• Second, the stochastic movement model was combined with the light switch - chemotaxis model. The link between the two was the dependency CheYp - running probability (or the bias), representing the output of the deterministic coupled model and the input of the probabilistic one. At every time point of the simulation, the next state (running/tumbling) of the bacterium was selected, based on the input bias.

Combined model. Coupled individual models for the simulation of the whole process and their interfaces.

Light switch - Chemotaxis

Schematical overview on the chemotactical pathway. MCPs refers to the membrane receptor proteins and Che are the intracellular chemotactical proteins.

The following assumptions have been made according to the molecular mechanism to link the light switch and chemotaxis models:

Upon red light pulse induction, the two light-sensitive proteins dimerize and thus the coupled Che protein is spatially dislocated. This means,

• CheR is not able to methylate the MCPs anymore,
• CheY can't be phosphorylated and interact with the motor anymore; nevertheless, it still can be dephosphorylated.

Since CheB and CheZ regulate the chemotactic receptor pathway inverse compared to CheR and CheY, they repress tumbling

• CheB is not able to demethylate the MCPs and can't be phosphorylated anymore, but still can be dephosphorylated,
• CheZ can't dephosphorylate CheY anymore (This assumption is very unsteady, since CheY is not strictly located).

All of these assumptions will lead to a decrease of tumbling / directed movement ratio upon red light induction and an increase of corresponding far-red light induction.

Chemotaxis - Movement

The combination of the deterministic and probabilistic models was (first) the biggest challenge and (afterwards) the biggest accomplishment in combining the models. Besides its theoretical complexity, the complete coupling is also conceptually very important. It closes the loop of our modeling and it combines two different types of models: deterministic and probabilistic, under the same global approach.
The two models have different timesteps, the molecular one being much faster than the stochastic one, therefore their combination has been done via Simulink interface. Both models have been independently numerically integrated and the output of the deterministic model was passed as an input to the stochastic one, at every slower time-step.
The main assumption we used in the complete coupling was that the mean run length is a function of the bias, while mean tumbling length is bias - independent.