We perform a spatially resolved simulation study of an AND gate based on DNA strand displacement  . DNA strands are modelled using a coarse-grained dynamic bonding model [ C. URL, Comp. Phys. Comm. 183, 1793 (2012) ] . We simulate the operation of the AND gate using several lengths of the toehold and the adjacent domains. Our simulations exhibit non-ideal behaviour as expected in an experimental implementation of strand displacement operations. We characterize this non-ideal behaviour in detail and characterize how the kinetic operation of the gate depends on the  toehold and adjacent domain lengths. In particular, we observe that, while the final output state is reached with high fidelity when both input strands are present, our simulations exhibit numerous long-lived transition paths from the initial input stateto the final output state .
We perform a spatially resolved simulation study of an AND gate based on DNA strand displacement using several lengths of the toehold and the adjacent domains . DNA strands are modelled using a coarse-grained dynamic bonding model [ C. URL, Comp. Phys. Comm. 183, 1793 (2012) ] . We observe a complex transition path from the initial state to the final state of the AND gate . This path is strongly influenced by non-ideal effects due to transient bubbles revealing undesired toeholds and thermal melting of whole strands. We have also characterized the bound and unbound kinetics of single strands, and in particular the kinetics of the total AND operation and the three distinct distinct DNA transitions that it is based on. We observe a exponential kinetic dependence on the toehold length of the competitive displacement operation, but that the gate operation time is only weakly dependent on both the toehold and adjacent domain length. Our gate displays excellent logical fidelity in three input states, and quite poor fidelity in the fourth input state. This illustrates how non-ideality can have very selective effects on fidelity. Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations .
A
using several lengths of the toehold and the adjacent domains
R
. We simulate the operation
. We observe a complex transition path from the initial state to the final state
R
using several lengths of the toehold and the adjacent domains. Our simulations exhibit
. This path is strongly influenced by
R
behaviour as expected in an experimental implementation of strand displacement operations. We characterize this non-ideal behaviour in detail and characterize how the kinetic operation of the gate depends on
effects due to transient bubbles revealing undesired toeholds and thermal melting of whole strands. We have also characterized the bound and unbound kinetics of single strands, and in particular the kinetics of the total AND operation and
A
three distinct distinct DNA transitions that it is based on. We observe a exponential kinetic dependence on the toehold length of the competitive displacement operation, but that the gate operation time is only weakly dependent on both the
R
lengths. In particular, we observe that, while the final output state is reached with high fidelity when both input strands are present, our simulations exhibit numerous long-lived transition paths from the initial input stateto the final output state
length. Our gate displays excellent logical fidelity in three input states, and quite poor fidelity in the fourth input state. This illustrates how non-ideality can have very selective effects on fidelity. Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations