Biswas Arup, Pal Arnab, Mondal Debasish, Ray Somrita
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India.
Department of Chemistry, Indian Institute of Technology Tirupati, Tirupati 517619, India.
J Chem Phys. 2023 Aug 7;159(5). doi: 10.1063/5.0154210.
"Gating" is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In general, gating is a mechanism that imposes an additional restriction on a transport, as the process ends only when the "gate" is open and continues otherwise. When diffusion occurs in the presence of a constant bias to a gated target, i.e., to a target that switches between an open and a closed state, the dynamics essentially slow down compared to ungated drift-diffusion, resulting in an increase in the mean completion time, ⟨TG⟩ > ⟨T⟩, where T denotes the random time of transport and G indicates gating. In this work, we utilize stochastic resetting as an external protocol to counterbalance the delay due to gating. We consider a particle in the positive semi-infinite space that undergoes drift-diffusion in the presence of a stochastically gated target at the origin and is moreover subjected to rate-limiting resetting dynamics. Calculating the minimal mean completion time ⟨Tr⋆G⟩ rendered by an optimal resetting rate r⋆ for this exactly solvable system, we construct a phase diagram that owns three distinct phases: (i) where resetting can make gated drift-diffusion faster even compared to the original ungated process, ⟨Tr⋆G⟩<⟨T⟩<⟨TG⟩, (ii) where resetting still expedites gated drift-diffusion but not beyond the original ungated process, ⟨T⟩≤⟨Tr⋆G⟩<⟨TG⟩, and (iii) where resetting fails to expedite gated drift-diffusion, ⟨T⟩<⟨TG⟩≤⟨Tr⋆G⟩. We also highlight various non-trivial behaviors of the completion time as the resetting rate, gating parameters, and geometry of the set-up are carefully ramified. Gated drift-diffusion aptly models various stochastic processes such as chemical reactions that exclusively take place in certain activated states of the reactants. Our work predicts the conditions under which stochastic resetting can act as a useful strategy to enhance the rate of such processes without compromising their selectivity.
“门控”是生物化学中一种广泛存在的现象，它描述了离子通道在激活（或开放）状态与失活（或关闭）状态之间的转变，这使得通过该通道的运输具有高度选择性。一般来说，门控是一种对运输施加额外限制的机制，因为只有当“门”打开时过程才会结束，否则过程会持续。当在存在对门控目标的恒定偏置（即目标在开放和关闭状态之间切换）的情况下发生扩散时，与非门控漂移扩散相比，动力学本质上会减慢，导致平均完成时间增加，即⟨TG⟩ > ⟨T⟩，其中T表示随机运输时间，G表示门控。在这项工作中，我们利用随机重置作为一种外部协议来抵消由于门控导致的延迟。我们考虑一个位于正半无限空间中的粒子，它在原点处存在随机门控目标的情况下进行漂移扩散，并且还受到限速重置动力学的影响。通过计算这个精确可解系统的最优重置率r⋆所给出的最小平均完成时间⟨Tr⋆G⟩，我们构建了一个具有三个不同相的相图：（i）重置甚至可以使门控漂移扩散比原始非门控过程更快，即⟨Tr⋆G⟩<⟨T⟩<⟨TG⟩；（ii）重置仍然可以加速门控漂移扩散，但不会超过原始非门控过程，即⟨T⟩≤⟨Tr⋆G⟩<⟨TG⟩；（iii）重置无法加速门控漂移扩散，即⟨T⟩<⟨TG⟩≤⟨Tr⋆G⟩。我们还强调了随着重置率、门控参数和设置几何形状的仔细划分，完成时间的各种非平凡行为。门控漂移扩散恰当地模拟了各种随机过程，例如仅在反应物的某些激活状态下发生的化学反应。我们的工作预测了随机重置可以作为一种有用策略来提高此类过程的速率而不影响其选择性的条件。
