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Modeling of the chemotaxis pathway

Schematical overview of the light switch device and the interaction with the chemotaxis pathway. LSP refers to light switch protein, AP to anchor protein and Che to the attacked protein of the chemotaxis pathway.

Background

Schematical overview of the chemotaxis pathway. MCPs refers to the membrane receptor proteins and Che to the intracellular chemotaxis proteins.

The complex chemotaxis pathway in E. coli has been well analyzed in the modeling literature and, as the following published models [1], [2], [3], [4] show, many and different assumptions are necessary in order to answer the investigated questions. In the case of E. lemming, the question regarding the chemotaxis pathway is:

• How does the output species (CheYp bias) react to perturbations of upstream species?

The chemotaxis network represents the main decision factor in bacterial movement and therefore, it received special attention for the optimal experimental design. In order to achieve a more general consensus prediction of the chemotaxis behavior in E. lemming, it was decided to adapt and extend four different models based on published approaches on modeling the chemotaxis pathway [1], [2], [3], [4].

The interface to the light switch model was defined to be the selected Che species, which is linked to one light-sensitive protein (LSP1). Concentration of this species (LSP1-Che) is determined by the light switch model. Evaluation of the model based on this approach was conducted by changing the concentration of the selected Che species according to a series of time steps reflecting light pulses. This assumes total removal of the species. In addition to the selected Che species (CheR, B, Y, Z), possible phosphorylated subspecies were analyzed.

Important for analyzing the chemotaxis network in E. lemming is the concentration of the output species CheYp. Threshold of suitable CheYp concentration is determined, according to predictions of the movement model, regarding an optimization of corresponding tumbling / directed movement frequency. The response of the chemotaxis models was measured by taking the relative amplitude in CheYp concentration between two different light pulses. For CheR and Y, the difference in CheYp concentration drops more than Delta (initial value - threshold), for CheB and Z it increases more than Delta. Manipulation of CheR and Y concentration therefore have an inverse effect on tumbling / directed movement ratio than CheB and Z.

Out of the four models of the chemotaxis pathway that our modeling team implemented, only two of them were further investigated in the combined model of E. lemming: Spiro et al. (1997) [1] and Mello & Tu (2003) [2]. These models were chosen not only because they are representative for modeling the chemotaxis pathway, but also because they differ in a few important aspects, as explained later.

Model based on Spiro et al. (1997) [1]

The model based on Spiro et al. (1997) [1] has been used to identify candidates of the chemotaxis receptor pathway by enabling removal or addition of a species upon light induction. For all Che proteins (CheR, Y, B, Z), the concentrations stay below/above the threshold, until they are added again (LSPs are deactivated with far-red light and dimerization is reversed). In terms of aspartate ligand concentration, the best results were obtained for assuming a high ligand concentration (saturation, the methylation level of the receptors is high). For CheY and Z, the reaction times are much faster than for CheB and CheR.

Che protein species predicted by the model based on Spiro et al. (1997) CheY is coupled to PIF3. PhyB is present in a concentration of 100 μM, anchor in a concentration of 130 μM. Medium asparate levels (10^-6 uM) were chosen. Red light pulses were induced for 0.3s at times 10s, 200s and 390s; far-red light pulses were induced for 10s at times 50s, 250s and 440s.

Total Che protein species predicted by the model based on Spiro et al. (1997) Only the total concentration of CheY is changed by the light switch in this model.

Response of the system. CheYp amplitude is predicted to be high, according to the model based on Spiro et al. (1997).

Model based on Mello & Tu (2003) [2]

The model based on Mello & Tu (2003) differs from the one based on Spiro et al. (1997) in a way, that it is able to reach perfect and near-perfect adaptation. Mello & Tu investigated robustness of the chemotaxis receptor network, covering the effect of attractant binding through the phosphorylation of CheY. Governing ODEs are derived by applying the law of mass action to the known reactions. Five states of methylation and demethylation of the attractant-bound and free receptors are considered.

The published model assumes the binding and unbinding of the ligand to the receptors to be a fast reaction and thus is approximated by a quasi-steady state assumption. Aspartate ligand binding is therefore described by a fraction of total saturation of the chemotaxis receptors. To make it compatible to absolute ligand concentration (as used by the other model), the binding and unbinding reaction rate constants used by Spiro et al. (1997) were used.

Another adaption was made, because the receptors in the publication of Mello & Tu (2003) were defined by an algebraic equation. To solve the resulting differential algebraic equations, they were included as additional states with a stable equilibrium to fulfill the algebraic equations.

The model based on Mello & Tu (2003) shows similar behavior compared to the adapted Spiro et al. (1997) model.

Che protein species predicted by the model based on Mello & Tu (2003) CheY is coupled to PIF3. PhyB is present in a concentration of 100 μM, anchor in a concentration of 130 uM. Medium asparate levels (10^-6 μM) were chosen. Red light pulses were induced for 0.3s at times 10s, 200s and 390s; far-red light pulses were induced for 10s at times 50s, 250s and 440s.

Total Che protein species predicted by the model based on Mello & Tu (2003). The total concentration of CheR is changed in addition to the CheYp concentration in this model.

Response of the system. The model based on Mello & Tu (2003) predicts a much smaller CheYp amplitude than the model based on Spiro et al. (1997).

Download

The chemotaxis models are included within the Matlab Toolbox and can be downloaded there.

References

[1] Spiro et al: A model of excitation and adaptation in bacterial chemotaxis. PNAS 1997 94;14;7263-7268.

[2] Mello & Tu: Perfect and Near-Perfect Adaptation in a Model of Bacterial Chemotaxis. Biophysical Journal 2003 84;5;2943-2956.

[3] Rao et al: Design and Diversity in Bacterial Chemotaxis. PLoS Biol 2004;2;2;239-252.

[4] Barkai & Leibler: Robustness in simple biochemical networks. Nature 1997;387;913-917.