Control of DNA Strand Displacement Kinetics using Toehold Exchange Supporting Materials

Validity of QSS Many systems of chemical reactions obey QSSA in all but the initial moments of the reaction [1]. QSSA treats the rates of change of the intermediates’ concentrations ( dt and d[J] dt in our system) as small enough to be approximated as 0. The validity of QSSA is ensured when the timescale of the overall reaction is slower than the timescale at which I and J reach their quasi-steady state values. For all experiments presented in this paper except for those in Fig. 7, the timescale of the overall reaction is at least 15 minutes, while the timescale of intermediate equilibration is estimated to be on the order of 20 seconds: The value of parameter kb was fitted to be 1.0 s −1, so I and J equilibrate with each other on a time scale faster than 1 s. The time constant τ of the initial rise of [I] from 0 to its quasi-steady state value [I]qss is estimated by τ ≈ [I]qss kf [X(m,n)][S] . In time τ , the concentration of [I] rises to [I]qss(1− 1 e ) ≈ 0.6[I]qss. For convenience, define x = kr(βm) and y = kr(γn). In equation (7) in the next section, the expression for [I]qss is seen to be kf (kb+kr(βm))[X(m,n)][S] kr(γn)kr(βm)+kr(γn)kb+kr(βm)kb .