Random walk of passive tracers among randomly moving obstacles

Abstract

BackgroundThis study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target.MethodBy means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles.ResultsThe relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance.ConclusionsThe results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

Experimental evidence for long-distance electrodynamic intermolecular forces

“…Then, by working at different concentrations (i.e., intermolecular distances) and excitation power of a laser as the light source, we have achieved the following: (i) observation of the activation of collective intramolecular oscillation of the proteins, a necessary prerequisite to activating the physical mechanism pictorially outlined in Fig. 1A; (ii) observation of a distributed-clustering transition dependent on activation of these collective molecular oscillations, as expected after a thorough preparatory work (3,23,24,25); and (iii) the consequent expected change of the frequency of the collective oscillation (26). For this, two experimental techniques were used: terahertz (THz) spectroscopy, mainly composed of two setups using either a THz rectenna or a microwire probe as sensors, respectively (see Materials and Methods for details), and fluorescence correlation spectroscopy (FCS) (Fig.…”

“…Theory predicts that ED dipole-dipole interaction between two molecules results in a shift  of their vibration frequency from the unperturbed frequency  0 , a shift proportional to 1/r 3 with r being the intermolecular distance (12). This law is preserved also for a large number of interacting molecules, that is, the frequency shift is proportional to 1/〈r〉 3 , where 〈r〉 is the average intermolecular distance given by 〈r〉 = 𝒞 −1/3 (see the Supplementary Materials for the theoretical explanation). The unperturbed vibration frequency  0 is operationally measured at very low molecular concentrations.…”

Serotonin in Space: Understanding Single Fibers

“…However, individual serotonergic fibers can be viewed as 1D-like probes that sample the microarchitecture of 3D-brain tissue. The 3D-properties of tissue then can be theoretically inferred from the statistics of individual fiber trajectories, by taking advantage of the sophisticated mathematical machinery of random heterogeneous materials, random walks with obstacles, and self-avoiding random walks …”

Experimental evidence for long-distance electrodynamic intermolecular forces

“…Then, by working at different concentrations (i.e. intermolecular distances) and excitation power of a laser as the light source, we have achieved what follows: i) observation of the activation of collective intramolecular oscillation of the proteins, a necessary pre-requisite to activate the physical mechanism pictorially outlined in Figure 1a; ii) observation of a distributed-clustering transition dependent on activation of these collective molecular oscillations, as expected after a thorough preparatory work [3,23,24,25], and iii) the consequent expected change of the frequency of the collective oscillation [26]. For this, two experimental techniques were used: THz spectroscopy, mainly composed of two setups using either a THz-rectenna or a microwire-probe With respect to the reference frequency at "infinite" dilution, a frequency-shift inversely proportional to the cubic power of the average intermolecular distance is theoretically expected if the proteins interact through ED forces.…”

“…Fundamentally, it is assumed that 2 this network of interactions is dominated by random molecular diffusion throughout the cellular spaces in which, sooner or later, a molecule will encounter its cognate partners. However, free diffusion is considerably slowed down in a highly crowded environment [3] as in the case of the cell interior. Moreover, when diffusion measurements are performed in complex molecular organizations such as those of living cells, most of the biomolecules show anomalous rather than Brownian diffusion [4,5].…”