# Doing a Brownian Dynamics Simulations using Lammps - Enquiry

بسم الله الرحمن الرحيم

Hello,

I am a graduate student and I am working on my thesis which is in Biophysics and the title of it is “Brownian Dynamics simulations for Complexation of DNA with Nano-Cationic Dendrimers.”.

I have read on the Lammps documentations that to do a BD simulation I must use fix langevin with fix nve, so I have some questions on this subject.

My questions are:

1. Is this method in Lammps doing a BD as illustrated in Wikipedia ?
url: https://en.wikipedia.org/wiki/Brownian_dynamics

2. fix nve means microcanonical ensemble in statistical mechanics, and as illustrated in Wikipedia:
url: https://en.wikipedia.org/wiki/Langevin_dynamics

" Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble. "

Does you mean that for LD I must use fix langevin only which mean by default fix nvt and for BD I must use fix langevin along with fix nve?

1. can I run a simulation with no periodic BC and without any limit on the space in Lammps?

Thank you

‘Alaa’ Murrar

I would suggest reading more than Wikipedia… what are you planning to achieve without a box?! Just think: how will you define pressure if there is no box?

Hello Alaa
responses below...

بسم الله الرحمن الرحيم
My questions are:
1.

See below

2. " Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble. "
Does you mean that for LD I must use fix langevin only which mean by default fix nvt and for BD I must use fix langevin along with fix nve?

No. If you are using LAMMPS, then use both "fix langevin" and "fix
nve" together. (Do not add "fix nvt")

3. can I run a simulation with no periodic BC and without any limit on the space in Lammps?

Yes

Keep in mind that if you are using "s" ("shrink wrapped") boundary
conditions and the distance between particles grows to be large,
LAMMPS may run out of memory when it attempts to build neighbor-lists,
due to the large box necessary to enclose your system.. If you are
simulating a single molecule (polymer) and you don't have any freely
diffusing objects in your simulation, then this should not be an
issue. If it is an issue, you can use the "neighbor" command to
increase the bin size and reduce memory usage.
LAMMPS Molecular Dynamics Simulator
(My chromosome folding simulations I use:
neighbor 30.0 bin
30.0 is much larger than the pairwise force cutoff distance I normally use)

1. Is this method in Lammps doing a BD as illustrated in Wikipedia ?
url: Brownian dynamics - Wikipedia

No.
"fix langevin" + "fix nve" together implement Langevin dynamics, not
Brownian dynamics.

Brownian dynamics is Langevin dynamics in the limit that the mass -> 0
(or, equivalently when the friction->infinity). As far as I am aware,
Brownian dynamics is not implemented in LAMMPS. (And for good reason,
in my opinion. See rant below.) Brownian dynamics is considered
reasonably accurate if you are interested in looking at the high
frequency (small timescale dynamics), because the frictional
coefficient of damping for water is so large that it can be
approximated as infinite (compared to the time it takes for anything
interesting to happen in the simulation).

However if you don't care about the high frequency dynamics of the
system... If you are only interested in events that occur on longer
timescales (for example, the time it takes for a protein to fold),
then it is much much more efficient to use Langevin dynamics (compared
to Brownian dynamics). The use of Brownian dynamics

If you are curious, there is a nice paper describing the effect of the
frictional damping rate on the dynamics of protein folding here:

If I remember correctly, they find that you can reduce the frictional
coefficient by a factor of 50 before it even starts to effect the
dynamics of protein folding. If you use run the simulation with 50x
less friction, this effectively increases the efficiency of your
simulation by a factor of 50 (because the rate of movement due to
diffusion is inversely proportional to the the friction). (Again,
increasing mass is equivalent to reducing friction in Langevin
dynamics. To make matters more confusing, this is equivalent to
-increasing- the "damp" parameter used with the fix langevin command
in LAMMPS, which corresponds to damping -time-, not rate.) As an
extreme example, I simulate chromosome folding, which takes vastly
longer more time than most proteins take to fold. To make this
process tractable, I reduce the friction so that the damping time is
on the order of (approximately) 1/10th of the time it takes for the
chromosome to fold (which is vastly, vastly smaller than the friction
of real water, but yet high enough that the DNA polymer still moves
diffusively at the long time scales I care about). Without doing
this, my simulations would never finish.

I remember wrote a simulation program which used true Brownian
dynamics. It was extremely slow and numerically unstable. Particles
moving in the zero-mass limit contain much more high frequency noise
in their movement than particles moving according to Langevin
dynamics, and the sudden jumps that occurred caused particles to bump
too far into each other and the simulation would explode (often).
running your simulations using Langevin dynamics with a large mass
value (small friction coefficient).

Hope this helps

Andrew

P.S. Don't be offended by this, but if it helps, here's a few
textbooks which describe Langevin dynamics in more detail:
Van Kampen "Stochastic Processes in Physics and Chemistry"
David Chandler "Introduction to Modern Statistical Mechanics"
Donald McQuarrie "Statistical Mechanics"
Among these books, the most concise explanation is either in Chandler
or Van Kampen. (Perhaps there are more modern books available by
now.)