Towards a multiscale model of colorectal cancer

Figure 3 Example of a simple kinetic model. The proteins A and B undergo normal protein turnover (s = synthesis rates, d = degradation rates) and associate to form a protein complex, AB (k₊ = assembly rate, k_- = dissociation rate). The behaviour of the system is captured by the following system of ordinary differential equations: d [A]/dt = s_A - k₊ [A] [B] + k_- [AB] - d_A [A]; d [B]/dt = s_B - k₊ [A] [B] + k_- [AB] - d_B [B]; d [AB]/dt = k₊ [A] [B] - k_- [AB]; with initial conditions [A] (0) = A₀, [B] (0) = B₀ and [AB] (0) = 0. It can be shown that, eventually, the components stabilise at levels given by: [A] = s_A/d_A; [B] = s_B/d_B, and [AB] = s_A s_B/(d_A d_B K), with K = k_-/k₊ the dissociation constant.