Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

Abstract

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar

4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos corrected

References in corpus (5)

• Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Optimal target search on a fast folding polymer chain with volume exchange
• On reaction-subdiffusion equations
• A Random Walk to a Non-Ergodic Equilibrium Concept

Cited by in corpus (46)

• Intermittent search strategies
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Spatio-temporal correlations can drastically change the response of a MAPK pathway
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Non-universal tracer diffusion in crowded media of non-inert obstacles
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Noisy continuous time random walks
• In vivo facilitated diffusion model
• Weakly non-ergodic Statistical Physics
• Chemical continuous time random walks
• Bulk-mediated diffusion on a planar surface: full solution
• Aging dynamics in interacting many-body systems
• Distributional Response to Biases in Deterministic Superdiffusion
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• The subdiffusive target problem: Survival probability
• Single-trajectory spectral analysis of scaled Brownian motion
• Learning physical properties of anomalous random walks using graph neural networks
• First passage statistics for aging diffusion in annealed and quenched disorder
• Universal fluctuations in subdiffusive transport
• Disentangling sources of anomalous diffusion
• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
• Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers
• Subordinated diffusion and CTRW asymptotics
• Strange kinetics of bulk-mediated diffusion on lipid bilayers
• Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion
• Modelling diffusional transport in the interphase cell nucleus
• Duality symmetries and effective dynamics in disordered hopping models
• Continuous Time Random Walk in a velocity field: Role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
• Anomalous Diffusion in a Bench-Scale Pulsed Fluidized Bed
• Motion of a Brownian molecule in the presence of reactive boundaries
• Boundary conditions at a thin membrane for normal diffusion equation which generate subdiffusion
• Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime
• Duality between random trap and barrier models
• Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman-Kac Approach
• The macroscopic effects of microscopic heterogeneity
• Enhanced molecular diffusion near a soft fluctuating membrane
• Subdiffusion in a system with a partially permeable partially absorbing wall
• The importance of crowding in signaling, genetic, and metabolic networks
• Generalized Khinchin Theorem for a Class of Aging Processes