DynaCoSys

The DynaCoSys model is a hybrid differential equation model that describes the complement activation of the alternative pathway. The dynamics of the surface bound molecules are described by a set of ordinary equations and the dynamics of the key fluid phase molecules are described by partial differential equations. The non-linear model includes all features of the complement system: activation, opsonization, stabilization, amplification and regulation. The DynaCoSys model is used in our studies for analyzing the complement activation mediated by Factor H and researching the complement immune evasion of candida albicans in the complement immune evasion study.

Complement activation can be divided into five parts: (i) activation, (ii) opsonization, (iii) stabilization, (iv) amplification, and (v) regulation. (A) The model focuses on the dynamics of the central component 𝐶3⁢𝑏: Active 𝐶3⁢𝑏 in the fluid phase, 𝐶3⁢𝑏𝑓, results from cleavage of precursor molecule 𝐶𝑓3. The interaction of the fluid phase molecule 𝐶3⁢𝑏𝑓 with the cell surface is modeled by the interaction with free surface binding sites 𝐵𝑠𝐶3⁢𝑏,𝑓⁡𝑟⁢𝑒⁢𝑒 and binding sites BsC3b that are occupied with molecules 𝐶3⁢𝑏𝑠 on the surface. 𝐶3⁢𝑏𝑓 that does not bind to the cell surface gets inactivated via a Factor H mediated inhibition process, or gets stabilized by water molecules and is no longer able to bind to the cell surface. Surface-bound 𝐶3⁢𝑏𝑠 can form 𝐶3-convertase molecules—𝐶3⁢𝑏𝑠⁢𝐵⁢𝑏 and 𝐶3⁢𝑏𝑠⁢𝐵⁢𝑏⁢𝑃–that cleave 𝐶𝑓3 molecules to 𝐶3⁢𝑏𝑓 molecules in the vicinity of the cell surface. 𝐶3⁢𝑏𝑠 can be inactivated via an inhibition process that is mediated by surface-bound Factor H, whose concentration depends on the concentration of binding sites on the cell surface 𝐵𝑠𝑓⁡𝐻,𝑚⁢𝑎⁢𝑥. (B) The lifetime of active 𝐶3⁢𝑏𝑓 is short such that, depending on the distance from the cell surface, the fraction of molecules that reach the cell surface is small; for example, only 1% at a distance of 196 nm within a simple decay model.