Chapter 6
Ratchet Dimer Brownian Motor with
Hydrodynamic Interactions
Keywords Hydrodynamic interactions · Motor proteins · Molecular dynamics ·
Brownian dynamics · Fluctuation phenomena · Random processes · Noise ·
Brownian motion
We use the Brownian dynamics with hydrodynamic interactions simulation in order
to describe the movement of an elastically coupled dimer Brownian motor in
a ratchet potential. The only external forces considered in our system were the
load, the random thermal noise and an unbiased thermal fluctuation. We observe
differences in the dynamic behaviour if hydrodynamic interactions are considered
as compared to the case without them.
6.1 Introduction
Brownian motors are small physical micro- or even nano-machines that operate
far from thermal equilibrium by extracting the energy from both, thermal and
non-equilibrium fluctuations in order to generate work against external loads.
They present the physical analogue of bio-molecular motors that also work out
of equilibrium to direct intracellular transport and to control motion in cells.
In such bio-molecular motors, proteins such as kinesins, myosins and dyneins,
move unidirectionally on one-dimensional “tracks” while hydrolysing adenosine
triphosphate (ATP). These molecular motors are powered by a ratchet mechanism,
[1], they convert the nonequilibrium fluctuation into directed flow of Brownian
particles in an asymmetrical periodic potential (ratchet) without any net external
force or bias. Several authors have studied theoretically the transport of two
coupled particles modeling the two heads of a motor protein [2–13]. Nonequilibrium
fluctuations, whether generated or by a chemical reaction far from equilibrium, can
bias the Brownian motion of a particle in an anisotropic medium without thermal
gradients, a net force such as gravity, or a macroscopic electric field. Fluctuationdriven transport is one mechanism by which chemical energy can directly drive the
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_6
81
Ratchet Dimer Brownian Motor with
Hydrodynamic Interactions
Keywords Hydrodynamic interactions · Motor proteins · Molecular dynamics ·
Brownian dynamics · Fluctuation phenomena · Random processes · Noise ·
Brownian motion
We use the Brownian dynamics with hydrodynamic interactions simulation in order
to describe the movement of an elastically coupled dimer Brownian motor in
a ratchet potential. The only external forces considered in our system were the
load, the random thermal noise and an unbiased thermal fluctuation. We observe
differences in the dynamic behaviour if hydrodynamic interactions are considered
as compared to the case without them.
6.1 Introduction
Brownian motors are small physical micro- or even nano-machines that operate
far from thermal equilibrium by extracting the energy from both, thermal and
non-equilibrium fluctuations in order to generate work against external loads.
They present the physical analogue of bio-molecular motors that also work out
of equilibrium to direct intracellular transport and to control motion in cells.
In such bio-molecular motors, proteins such as kinesins, myosins and dyneins,
move unidirectionally on one-dimensional “tracks” while hydrolysing adenosine
triphosphate (ATP). These molecular motors are powered by a ratchet mechanism,
[1], they convert the nonequilibrium fluctuation into directed flow of Brownian
particles in an asymmetrical periodic potential (ratchet) without any net external
force or bias. Several authors have studied theoretically the transport of two
coupled particles modeling the two heads of a motor protein [2–13]. Nonequilibrium
fluctuations, whether generated or by a chemical reaction far from equilibrium, can
bias the Brownian motion of a particle in an anisotropic medium without thermal
gradients, a net force such as gravity, or a macroscopic electric field. Fluctuationdriven transport is one mechanism by which chemical energy can directly drive the
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_6
81