If you have already the potential (of Mean Force) then to compute the force (the mean force) you need to take the derivative of that potential (with minus). Why can't you fit your PMF with a polynomial or a set of few Gaussians and differentiate those analytically? 

Should give you a nice smooth curve.

if your PMF is not a K*x than your force won't be constant, and will be below the force which is needed to pull/push the system over the barrier.

Also free energy change corresponds to infinitely slow change when system is well described using equilibrium TD.  The actual non-equilibrium work will be higher.

Hope this helps. 

If you have already the potential (of Mean Force) then to compute the force (the mean force) you need to take the derivative of that potential (with minus). Why can't you fit your PMF with a polynomial or a set of few Gaussians and differentiate those analytically? 

Should give you a nice smooth curve.

if your PMF is not a K*x than your force won't be constant, and will be below the force which is needed to pull/push the system over the barrier.

Also free energy change corresponds to infinitely slow change when system is well described using equilibrium TD.  The actual non-equilibrium work will be higher.

Hope this helps. 

Hi Agnivo,

In my experience (with GROMAC), a pulling simulations gives more than just one output files. In fact, I do get a pull force file (plot force vs time) and a reaction coordinate file (plot reaction coordinate vs time). This may have something to do with your initial parameter setting for the MD run.

I am not sure what you are looking for exactly, but people do use maximum force (a.k.a. rupture force) and work (integration of force over distance, which is reaction coordinate in this case) to evaluate the difficulty of pulling.

Yun

First of all, the derivative of the PMS should give you the force as it has been calculated by integrating the mean force at first place. As Nikolay suggested you need to fit your PMF analytically and then calculate the derivative to get smooth data. The other way would be to use an regularization method (denoising) for smooth first order derivative (see this: Data smoothing and numerical differentiation by a regularization method by J.Stickle).

Beside the computational aspects, What is your reasining to look for mean force? Where do you want to cut the reaction coordinate to calculate the mean (the longer you go the smaller is the mean)? As Yun suggested, the work required to pull or maximum force required to pull are usually meaningful parameters in this case!

Hope this helps.

Abolfazl

Hi everyone, thanks to Nikolay , Yun and Abolfazi. I calculated the PMF by doing umbrella sampling simulations upon a steered molecular dynamics (SMD) simulation result. In the SMD , I position restrained a molecule and pulled apart the other molecule by applying a pull constant along the reaction coordinate. I use GROMACS.

I want to calculate the free energy of binding between the two molecules and the umbrella sampling generated the PMF curve.

Now I was thinking if I can calculate the "binding force" between the two molecules and if that can be achieved by differentiating the PMF.

If anyone can suggest a book/literature on this topic , then I would like to read and understand the physical significance / theory behind my proposition. I realize that it is mathematically possible but is it actually giving the "binding force" ?

Hi, Dr. Plotnikov suggested simulating the PMF with a polynomial or a set

of Gaussian functions. Can anyone direct me to literature where this or a similar

method (i.e., using functions other than Gaussians) has been used successfully?

Thank you, Eva.

Use gmx wham  for PMF calculation use

g_wham –it tpr.dat –if pullf.dat –o profile.xvg –hist histogram.xvg –bsprof bsProf.xvg –bsres bsResult.xvg

-bsprof for bootstrapping profiles

-bsres for Average profile and standard deviations

in umbrella sampling you have restrained one molecule (bio molecule with flexible active site) and pull the other molecule and you are looking for binding force between the molecules . So you have to modify the simulation accordingly. 

see

http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node15.html