You have to run multiple simulations at multiple pulling speeds. The loading rate in simulations is then simply obtained by multiplying the spring constant with the pulling speed. Or alternatively you could take the slope of the Force-Time curve around the maximum force to obtain the Loading rate.

e.g The loading rate for your plot now is , k*v = 16.6 *10^12 pN/s,

and just by looking at the curve, from the slope around the maxima it comes around ~(850-400)*1.66/50 ~ 15*10^12 pN/s.

Thank you Mohd Ibrahim You took some time out to answer my question, you have elaborated well the problem I was facing, please if you can let me know about the conversion you are using with the velocity part in K * V formula

as I have FC = 1000 KJ/mol nm , and v = 0.01 nm/ps

so for K * V = 1000 (1.66) * 0.01 * 10^12 equals 16.6 * 10^12 pN/s?

as 1 ps = 1*10^-12 but I am confused how nm is being converted

Secondly in the method where I can calculate LR from the slope please let me know:

850-400 is y2-y1 part of the slope calculation

1.66 is the conversion factor for KJ/mol nm to PN

and the conversion factor is divided by 50 is that x2-x1 part for the calculation of slope if not what is 50 in the formula?

Thirdly with these slopes coming out from the Force * time plot, I will plot the LR vs Max peak force but how will I implement Bells and Evans fitting

F*(r) = FBeta Ln(r/KoffFBeta)

where F*(r) is the most probable unbinding force, r is the loading rate, FBeta= KbetaT/XBeta, kB is the

Boltzmann's constant and T is the absolute temperature

This sort of fitting on our LR vs Force plot will give me Koff values.

Have a good day

Thank you

1: K = 1000kJ/mo-nm^2 = 1.66 *1000 pN/nm

v = 0.01nm/ps

kv = xxx( pN/nm) (nm/ps) = xxx pN/ps = xxxx 10^12pN/s

2. Yes 50 ps is approximately the x2-x1 part

3. As I mentioned before you have to repeat the same pulling at different velocities to make a Force Vs Loading rate plot. Even then, since the simulation loading rate is orders of magnitude higher than in experiments (due to high pulling speed), the Force Vs Loading Rate plot will most probably not follow a Bell-Evans model. So you won't be able to estimate K_off from the Bell-Evans model from simulations. E.g At very high loading rates as in the simulations, the Force varies as the square root of the loading rate, as shown in,

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and

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Mohd Ibrahim Thanks for sharing your knowledge and sharing the articles with me, I got your point that I need multiple simulations at different velocities for my systems. I am simulating 4 GPCR systems already with three simulations for each one of them at same 0.01 nm/ps velocity. I am planning to perform simulations at 0.05, 0.1 and 1 nm/ps now.

I was following the paper to perform the analysis, the link to the paper is as follows

Article Improving estimation of kinetic parameters in dynamic force ...

if you see the figure 2 in the paper you will see the protocol to perform the analysis as :

1. they are calculating the probability density function for all of their systems relevant to peak force

2. Calculate freely jointed model

3. Add noise

4. Calculate force vs loading rate

5. Record unbending event

6. record several unbending events for their systems

The protocol which I am following in the light of your previous answers is as follows:

1. View the force vs time plots and take the plot/profile up to first peak even the first peak is smaller than the maximum force peak

2. Then calculate the slope of the line and perform unit conversions to get the loading rate

3. Take the value of the peak force from the plot force vs time plot

4. Plot that peak force vs loading rate (which is difficult to fit according to Bell and Evans fitting ).

Now the question is that the protocol which I am following would still be difficult to fit according to Bell and Evans even if I perform multiple simulations at different velocities.

The other thing which I am doing is that according to my protocol point 4 I am just taking the slope again to say this is the Koff value is that right, if it is right what is the unit of the Koff in my case. I have attached the figures for my analysis. Pictiure 1.png is the plots up to the first peak and their slopes which was multiplies with 1.66 to get the loading rate

Picture.png is the peak force vs loading rate plot for three simulations of the same system at same velocity 0.01 nm/ps and then with simple line fitting the slope which in my view is Koff value of this system. The pictures attached are for the same system figures attached initially in the question. But here in this reply the figures are with two more simulations of the same system as attached previously.

Please let me know if I am going in the right direction, your quick reply will solve my problem and determine my direction to solve this issue.

Mohd Ibrahim The value of 110.27 I am taking as Koff which is the slope of the Peak force vs LR graph is in Ps or minutes or what would be its unit. Because for force the unit is KJ/mol nm and for LR it is pN/sec....