Charged, mucoadhesive molecules can penetrate mucin-based hydrogels such as native mucus with similar efficiency as inert, non-mucoadhesive molecules.

Finite stochastic Markov models play a major role in modeling biological systems. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a certain extend arbitrary since it depends on the resolution of accomodating measurements. Here, we present a systematic way to simplify such stochastic descriptions which preserves both the meso-micro and the meso-macro connection. The former is achieved by demanding locality, the latter by considering cycles on the network of states. Our method preserves fluctuations of observables much better than naïve approaches.PACS numbers: 05.70. Ln, 87.18.Tt, 87.10.Mn In recent years non-equilibrium fluctuations have become the center interest of stochastic thermodynamics [1,2]. Rare events in situations far from equilibrium can now be universally described by fluctuation theorems [3][4][5]. Intensive stochastic modelling of biophysical processes has started in the 1960s with Hill's cycle kinetics [6,7] (where the focus lies on averages) and is still a very active field of research, though attention has shifted to the importance of fluctuations, cf. Ref. [8].Although Hill's methods were designed for biological problems, they have lead to general insights in statistical physics [9] and mathematics [10,11]. It was understood that in non-equilibrium situations currents driven by non-trivial forces which are usually called affinities. Assigning these affinities to cycles on the network of states rather then to the states themselves, they have a direct thermodynamic interpretation [5,9]. This hints at possible redundancy in the description and already Hill asked how and when a network reduction would be possible. In statistical physics, such reduction are often summarized under the term of coarse-graining (CG) methods. It was recently shown for a special CG procedure that the ability to capture fluctations depends on the preservation of cycle topology of the network [12].In this Letter we present a new paradigm for coarsegraining of stochastic dynamics which preserves the nonequilibrium steady-state fluctuations of physical currents. Though we focus on biological situations the method can be universally applied to any finite model of stochastic thermodynamics. Our method is based on two requirements: (i) The preservation of the algebraic and topological structure of the cycles of the network and (ii) locality. Further, (iii) the variation of the system's entropy along single trajectories [3] is considered to close the equations. To illustrate our method we consider the molecular motor kinesin which is able to perform directed motion along intracellular filaments called microtubuli [2,[13][14][15]. It has two heads (active sites) where adenosin triphosphate (AT P ) is catalytically split into adenosin diphosphate (ADP ) and inorganic phosphate (P ). During the re-The catalytic cycle at kinesin's active site. In a four-stage process AT P binds to the Empty molecule and is split into Θ = ADP +...

Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulantgenerating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.