In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption
at a reactive surface, which takes into account stochastic switching of a diffusing particle’s conformational state.
For simplicity, we consider a two-state model in which the probability of surface absorption depends on the
current particle state and the amount of time the particle has spent in a neighborhood of the surface in each state.
The latter is determined by a pair of local times n,t , n = 0, 1, which are Brownian functionals that keep track
of particle-surface encounters over the time interval [0,t]. We proceed by constructing a differential ChapmanKolmogorov equation for a pair of generalized propagators Pn (x,0, 1,t), where Pn is the joint probability
density for the set (Xt, 0,t, 1,t) when Nt = n, where Xt denotes the particle position and Nt is the corresponding
conformational state. Performing a double Laplace transform with respect to 0, 1 yields an effective system of
equations describing diffusion in a bounded domain , in which there is switching between two Robin boundary
conditions on ∂. The corresponding constant reactivities are κj = Dzj and j = 0, 1, where zj is the Laplace
variable corresponding to j and D is the diffusivity. Given the solution for the propagators in Laplace space, we
construct a corresponding probabilistic model for partial absorption, which requires finding the inverse Laplace
transform with respect to z0,z1. We illustrate the theory by considering diffusion of a particle on the half-line
with the boundary at x = 0 effectively switching between a totally reflecting and a partially absorbing state. We
calculate the flux due to absorption and use this to compute the resulting MFPT in the presence of a renewalbased stochastic resetting protocol. The latter resets the position and conformational state of the particle as well
as the corresponding local times. Finally, we indicate how to extend the analysis to higher spatial dimensions
using the spectral theory of Dirichlet-to-Neumann operators.