Important Considerations for Reaction Rates¶
When a molecule has multiple interfaces, such as A(a,b), and can bind to itself using distinct interfaces (e.g., A(a) + A(b) <-> A(a!1).A(b!1)), the ka3D values are read such that KD = kb / ka3D, with no automatic re-scaling. This is suitable for molecules like Actin, which bind to themselves using two distinct interfaces (e.g., A(barbed end) + A(pointed end) ->). However, for models like clathrin, where the distinction between an a site and a b site is purely a label to distinguish their coordinates in space, and all interactions are possible (e.g., A(a) + A(a) ->, A(a) + A(b) ->, A(b) + A(b) ->), users should input rates multiplied by two for these specific cases. For example:
A(a) + A(a) <-> A(a!1).A(a!1) with onRate3Dka = 1
A(a) + A(b) <-> A(a!1).A(b!1) with onRate3Dka = 2
The rate for the true self-interaction (i.e., onRate3Dka = 1 in the example above) corresponds to the KD given all identical sites. If this adjustment is not made, and the same rates are used for A(a) + A(a) binding as for A(a) + A(b) binding, the equilibrium will not match the thermodynamic expectations. This is also discussed in Ref. 2 and applies to all rule-based, rate-based reactions (noted in NFSim, where self-rates are automatically divided by 2). The goal is to have 2 * A(a!).A(a!) = A(a!).A(b!) = A(a!).A(c!), ensuring that each product/complex type has the same number of a sites bound, due to having the same binding free energy. This result emerges from the combinatorics of choosing two of the same molecules from Atot = N0, versus one molecule A from Atot = N0 and one molecule B from Btot = N0. They produce an identical equilibrium with the same number of A in bound states when Aeqself(KD) = Aeqdistinct(KD/2) = Beqdistinct(KD/2).
As described in the NERDSS paper, the reaction rates are input by the user as the 3D values, ka3D, and the code will convert them to the values needed for the appropriate reaction kinetics. We always have that KD = kb / ka3D = koff / kon3D, based on the user-input rates. For information on the rates needed to give to the Green’s function to recover appropriate reaction kinetics, see Ref. 2, SI.