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Stochastic Noise and Synchronisation during Dictyostelium Aggregation Make cAMP Oscillations Robust

Figure 1

Dictyostelium cAMP Oscillations

(A) The model of [5] for the network underlying cAMP oscillations in Dictyostelium. The nominal parameter values for the model are taken from [6,9] and are given by: k₁ = 2.0 min⁻¹, k₂ = 0.9 μM⁻¹ min⁻¹, k₃ = 2.5 min⁻¹, k₄ = 1.5 min⁻¹, k₅ = 0.6 min⁻¹, k₆ = 0.8 μM⁻¹ min⁻¹, k₇ = 1.0 μM min⁻¹, k₈ = 1.3 μM⁻¹ min⁻¹ , k₉ = 0.3 min⁻¹, k₁₀ = 0.8 μM⁻¹ min⁻¹, k₁₁ = 0.7 min⁻¹, k₁₂ = 4.9 min⁻¹, k₁₃ = 23.0 min⁻¹, and k₁₄ = 4.5 min⁻¹. A perturbation of magnitude 2% in the model parameters which causes the oscillations to cease is given by [10]: k₁ = 1.9600, k₂ = 0.8820, k₃ = 2.5500, k₄ = 1.5300, k₅ = 0.5880, k₆ = 0.8160, k₇ = 1.0200, k₈ = 1.2740, k₉ = 0.3060, k₁₀ = 0.8160, k₁₁ = 0.6860, k₁₂ = 4.9980, k₁₃ = 22.5400, and k₁₄ = 4.5900.

(B) With the above perturbation in the parameter values, the deterministic model stops oscillating. The stochastic model, on the other hand, continues to exhibit stable and robust oscillations.

doi: https://doi.org/10.1371/journal.pcbi.0030218.g001