How is Brownian Motion Affected by a Fluctuating Random Surface?
Department of Chemistry, Tokyo Metropolitan University
© The Physical Society of Japan
This article is on
Brownian Motion on a Fluctuating Random Geometry
J. Phys. Soc. Jpn. 89, 074001 (2020).
A researcher has developed a new theory to describe the Brownian motion of a small object that is confined in a fluctuating random surface.
Owing to the recent advances in highprecision imaging techniques, scientists can directly observe the Brownian motion of a protein molecule embedded in a biological membrane. This type of membrane typically consists of a thin lipid bilayer and can be regarded as a twodimensional fluid sheet. Another important characteristic of a lipid membrane is its high flexibility. Thus, the membrane can exhibit large outofplane shape fluctuations, which can be experimentally measured [1].
What is the lateral diffusion behavior of proteins confined in such a highly fluctuating environment? Previous theories have predicted that the effective diffusion coefficient of a particle immersed in a fluctuating membrane is smaller than that in a flat membrane. On a fluctuating random membrane, a moving object needs to travel a larger distance between two points in a threedimensional space because the trajectories are constrained on a rough surface rather than on a flat surface (Fig. 1). This is referred to as “geometrical contribution”.
Fig. 1. Image for Brownian motion of a particle confined in a fluctuating random surface.
Recently, Ohta revisited the problem of lateral diffusion on a random surface using a new theoretical approach [2]. In addition to the geometrical contribution mentioned above, Ohta reported a new “dynamical contribution”, originating from the velocity correlation of the fluctuating surface. The new dynamical contribution increases the effective diffusion coefficient, as opposed to the geometrical contribution.
What is then the overall effect on the lateral diffusion coefficient owing to these two contributions? According to the numerical estimate of the effective diffusion coefficient, its reduction compared to that of a flat surface is diminished. Nevertheless, the net reduction is still 20–30%, which should be considered for an experimental data analysis.
In recent years, numerous studies have been carried out to quantify the nonequilibrium properties of biological systems by measuring the fluctuations at different levels and scales [1]. The study by Ohta shows that the Brownian motion of a particle and surface fluctuations are coupled in a nontrivial specific manner. As the diffusion of molecules on cell membranes has a crucial role for information processing in living cells, this study is of fundamental importance for analyses of biological soft matter.
References
[1] H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.F. Joanny, G. Gompper, and T. Betz, Nat. Phys. 12, 513 (2016).
[2] T. Ohta, J. Phys. Soc. Jpn. 89, 074001 (2020).
Brownian Motion on a Fluctuating Random Geometry
J. Phys. Soc. Jpn. 89, 074001 (2020).
Share this topic
Fields
Related Articles

Unraveling the Unique Properties of Icosahedral Quasicrystals
Magnetic properties in condensed matter
Structure and mechanical and thermal properties in condensed matter
Crossdisciplinary physics and related areas of science and technology
2022628
Scientists review the magnetism, nonFermi liquid behavior, and quantum critical behavior observed in icosahedral quasicrystals (QCs), and compare these properties with that of heavy fermions and approximant crystals.

Tensor Networks Across Physics
Mathematical methods, classical and quantum physics, relativity, gravitation, numerical simulation, computational modeling
Statistical physics and thermodynamics
Magnetic properties in condensed matter
202267
Researchers from Japan provide the first comprehensive review of the historical development of tensor networks from a statistical mechanics viewpoint, with a focus on its theoretical background.

Understanding Relaxor Ferroelectrics with Simple Landau Theory
Dielectric, optical, and other properties in condensed matter
Structure and mechanical and thermal properties in condensed matter
Crossdisciplinary physics and related areas of science and technology
2022523
Thirdorder nonlinear dielectric susceptibility is measured in the paraelectric phase of Pb(Sc_{1/2}Ta_{1/2})O_{3}. The linear and nonlinear dielectric susceptibility results can be consistently explained based on the Landautype freeenergy density.

Violation of FluctuationDissipation Theorem Results in Robustness of Fluctuation Against Localization
Statistical physics and thermodynamics
Electronic transport in condensed matter
Electronic structure and electrical properties of surfaces and nanostructures
2022323
We study equilibrium current fluctuations in systems without timereversal symmetry, violating the fluctuationdissipation theorem. Notably, the offdiagonal fluctuation is insensitive to system imperfections in contrast to other fluctuations and conductivity.

FourDimensional XY Quantum Phase Transition in Superfluid Helium4
Structure and mechanical and thermal properties in condensed matter
2022318
Liquid helium confined in nanopores exhibits a quantum superfluid transition at absolute zero. Investigations have revealed that the quantum nature also dominates the finitetemperature superfluid transition, obeying a simple meanfield theory.