Narrow escape time to a structured target located on the boundary of a microdomain

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

Trapping of diffusing particles by short absorbing spikes periodically protruding from reflecting base

We study trapping of diffusing particles by a periodic non-uniform boundary formed by absorbing spikes protruding from a reflecting flat base. It is argued that such a boundary can be replaced by a flat uniform partially absorbing boundary with a properly chosen effective trapping rate. Assuming that the spikes are short compared to the inter-spike distance, we propose an approximate expression which gives the trapping rate in terms of geometric parameters of the boundary and the particle diffusivity. To validate this result, we compare some theoretical predictions based on the expression for the effective trapping rate with corresponding quantities obtained from Brownian dynamics simulations.

Encounter dynamics of a small target by a polymer diffusing in a confined domain

We study the first passage time for a polymer, that we call the narrow encounter time (NETP), to reach a small target located on the surface of a microdomain. The polymer is modeled as a freely joint chain (beads connected by springs with a resting non zero length) and we use Brownian simulations to study two cases: when (i) any of the monomer or (ii) only one can be absorbed at the target window. Interestingly, we find that in the first case, the NETP is an increasing function of the polymer length until a critical length, after which it decreases. Moreover, in the long polymer regime, we identified an exponential scaling law for the NETP as a function of the polymer length. In the second case, the position of the absorbed monomer along the polymer chain strongly influences the NETP. Our analysis can be applied to estimate the mean first time of a DNA fragment to a small target in the chromatin structure or for mRNA to find a small target.

Estimating the synaptic current in a multiconductance AMPA receptor model

Synaptic transmission starts after the presynaptic neuron has released diffusing neurotransmitters, leading to postsynaptic receptor activation and a postsynaptic current, mostly mediated by glutamatergic (AMPARs) receptors for excitatory neurons. Despite intense experimental and theoretical research, it is still unclear how factors such as the synaptic cleft geometry, the organization, the number and the multiconductance state of receptors, the geometry of postsynaptic density (PSD), and the neurotransmitter release location, shape the mean and the variance of the postsynaptic current and its plastic changes. To estimate the synaptic current amplitude and to account for the stochastic nature of synaptic transmission, we develop a semianalytical method in which we obtain a general expression for the coefficient of variation. The method uses the experimental data about the multiconductance channels. We find that PSD morphological changes can significantly modulate the synaptic current, which is maximally reliable (the coefficient of variation is minimal) for an optimal size of the PSD, that depends on the vesicular release active zone. We show that this optimal PSD size is due to nonlinear phenomena involving the receptor multibinding cooperativity. We conclude that changes in the PSD geometry can sustain a form of synaptic plasticity, independent of a change in the number of receptors.

A pore-cavity-pore device to trap and investigate single nanoparticles and DNA molecules in a femtoliter compartment: confined diffusion and narrow escape

Spatial confinement from the nano- to the microscale is ubiquitous in nature. Striving to understand the behavior of nanoscale objects in confined domains we present a nanofluidic silicon device which consists of two stacked nanopores forming the in/outlets to a pyramidal cavity of micrometer dimensions (10 fL volume). Being electrically addressable, charged objects can be actively loaded into, trapped inside, and unloaded from the "pore-cavity-pore" (PCP) device. When operated passively, confined Brownian motion and the entropy barriers of the nanopores govern the behavior of nano-objects within the PCP device. We present measurements with single fluorescent nanoparticles as well as particle-ensembles and analyze their trajectories and residence times. Experimental data are compared to random walk simulations and analytical theories on confined diffusion and the Brownian escape of nano-objects across entropy barriers. Single particle data corroborate analytical solutions of the narrow escape problem, but ensemble measurements indicate crowding effects even at low particle concentrations. The utilization of the device to trap biomolecules is demonstrated for single λ-DNA molecules.

Extended narrow escape problem: boundary homogenization-based analysis

Diffusion of particles in confined domains with absorbing spots on the otherwise reflecting boundaries is ubiquitous in nature and technology. Because of nonuniform boundary conditions, the problem of finding the mean first passage time (MFPT) of the particle to one of the spots is extremely complicated. We show how the difficulties can be overcome by means of boundary homogenization when the domain is a circular disk whose boundary contains n nonoverlapping identical absorbing arcs, which may occupy an arbitrary fraction of the boundary. We find the MFPT as a function of the fraction of the boundary occupied by the arcs (i) for n evenly spaced arcs and (ii) for two arcs arbitrarily located on the boundary. As the arc length tends to zero, our approximate solution reduces to the known asymptotic formula for the MFPT rigorously derived in studies devoted of the narrow escape problem.

Narrow escape for a stochastically gated Brownian ligand

Molecular activation in cellular microdomains is usually characterized by a forward binding rate, which is the reciprocal of the arrival time of a ligand to a key target. Upon chemical interactions or conformational changes, a Brownian ligand may randomly switch between different states, and when target activation is possible in a specific state only, switching can significantly alter the activation process. The main goal of this paper is to study the mean time for a switching ligand to activate a small substrate, modelled as the time to exit a microdomain through a small absorbing window on the surface. We present the equations for the mean sojourn times the ligand spends in each state, and study the escape process with switching between two states in dimension one and three. When the ligand can exit in only one of the two states, we find that switching always decreases its sojourn time in the state where it can exit. Moreover, the fastest exit is obtained when the ligand diffuses most of the time in the state with the maximal diffusion coefficient, although this may imply that it spends most of the time 'hidden' in the state where it cannot exit. We discuss the physical mechanisms responsible for this apparent paradox. In dimension three we confirm our results with Brownian simulations. Finally, we suggest possible applications in cellular biology.

Gated narrow escape time for molecular signaling

The mean time for a diffusing ligand to activate a target protein located on the surface of a microdomain can regulate cellular signaling. When the ligand switches between various states induced by chemical interactions or conformational changes, while target activation occurs in only one state, this activation time is affected. We investigate this dynamics using new equations for the sojourn times spent in each state. For two states, we obtain exact solutions in dimension one, and asymptotic ones confirmed by Brownian simulations in dimension 3. We find that the activation time is quite sensitive to changes of the switching rates, which can be used to modulate signaling. Interestingly, our analysis reveals that activation can be fast although the ligand spends most of the time "hidden" in the nonactivating state. Finally, we obtain a new formula for the narrow escape time in the presence of switching.