# Re: Colvars Harmonic Bias Force Direction

From: Mortimer Hemmit (mortimer.hemmit_at_gmail.com)
Date: Wed Sep 02 2020 - 20:02:03 CDT

Hi Jerome,

Thank you very much, it makes a lot more sense now. The visualization
with the dashboard was very helpful.

Mortimer

On Wed, Sep 2, 2020 at 9:03 AM Jérôme Hénin <jerome.henin_at_ibpc.fr> wrote:
>
> Hi Mortimer,
>
> If x are the Cartesian coordinates of atoms, let's define a collective variable f(x).
> A harmonic potential on the colvar, centered on f0 and with force constant k will be:
> V(x) = 1/2*k*(f(x)-f0)^2
>
> This is a function of x indirectly, through the function f(x). The corresponding force on atoms is the negative gradient of the potential with respect to atomic positions x:
> F(x) = - dV(x) / dx = - k * (f(x)-f0) * df(x)/dx
>
> Here df(x)/dx means the gradient of the colvar with respect to Cartesian coordinates x. That's a vector pointing in the direction in Cartesian coordinates along which f(x) increases the fastest.
> The magnitude and direction of the force also depend on the magnitude and sign of (f(x)-f0), that is where the colvar is with respect to the set restraint center.
>
> So to summarize, the biasing force will be applied in the direction that causes the maximum change in the value of the colvar.
>
> If you use the latest VMD under Linux, you can easily visualize the gradients of any scalar colvar using the Colvars Dashboard plugin.
>
> Best,
> Jerome
>
>
> ----- On 2 Sep 20, at 14:28, Mortimer Hemmit mortimer.hemmit_at_gmail.com wrote:
>
> > Hello,
> >
> > I am performing some steered molecular dynamics simulations. I was
> > wondering how the harmonic biases worked.
> >
> > I understand how a simple colvar with a harmonic bias on the distance
> > between atoms could work. I can picture it as a spring attached
> > between the atoms which exerts a force that pulls each atom towards
> > the other.
> >
> > However, for more complicated colvars such as radius of gyration,
> > coordination number, dihedral angle, RMSD, to name a few, how exactly
> > does the added potential manifest itself to restrain these quantities
> > to their desired values? In which direction do the forces/springs
> > point (or are there even forces at all) if I put a harmonic bias on
> > these colvars?
> >
> > I have looked at the user guide and the Colvars paper, but I am still
> > confused about the forces.
> >
> > If anyone could help me clear this up or point me in the right
> > direction with some references, that would be greatly appreciated.
> >
> > Thank you very much,
> > Mortimer

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