George,
In this discussion I was missing so far that the force is calculated
dynamically in each MD time step, from the gradient of the according
potential.
This means we're dealing with a self-correcting system. Via pulling
velocity v and the two distance endpoints we define a *desired* linear
distance-time curve d(t). In each time step, the *actual* distance-time
state of the system slightly deviates from this curve and a
'correctional' force with a certain magnitude and direction is applied
to the system in order to enforce the desired d(t) relation. Hence, the
direction of the correctional force may vary from time step to time step.
Then it is obvious that the trajectory of the two restrained atoms still
is random and that in the final state each atom must be on a spherical
surface with center=other_atom and radius=target_distance.
Regards,
Jan-Philip
On 13.12.2012 16:17, George Tzotzos wrote:
> Thank you all. Now it's clear.
>
> Regards
>
> George
>
> On Dec 13, 2012, at 3:45 PM, Adrian Roitberg wrote:
>
>> Dear all
>>
>> I am not sure if I understand Gerrge's diagram correctly, but what seems
>> to be missing from it is the biomolecule.
>>
>> Imagine that you push 'radially', meaning away from the center you
>> defined. If you now hit a hard wall because a protein residue stands in
>> the way, you can then move at an angle with ZERO cost for the restraint
>> (because you are still at the same distance) and find yourself a better
>> escape route.
>>
>> All this fails if you move the restraint too fast or if you use a force
>> constant that is to high. In that case, you will try to push outwards
>> regardless of the biomolecule and you can imagine how that would be very
>> bad...
>>
>> adrian
>>
>> On 12/13/12 9:41 AM, Jason Swails wrote:
>>> On Thu, Dec 13, 2012 at 8:54 AM, George Tzotzos <gtzotzos.me.com> wrote:
>>>
>>>> Jason,
>>>>
>>>> Thank you.
>>>>
>>>> You say "Their reference to a sphere is simply that the locus of points
>>>> that are, say, 10 angstroms away from a certain point make up a sphere of
>>>> radius 10 with that point at the center"
>>>>
>>>> This is UNDERSTOOD.
>>>>
>>>> Next: "a ligand that is moved 10 Angstroms away from the active site could
>>>> lie anywhere on the resulting sphere, not necessarily where you 'want it
>>>> to' or 'think it should' land."
>>>>
>>>> This is also UNDERSTOOD as it stands. The next sentence though is not.
>>>> Apologies for my lack of "vision".
>>>>
>>>> "while the applied force has a well-defined direction (as any vector in
>>>> this case must have), the 'escape path' of the ligand does not".
>>>>
>>>> Do you mean that although the force is applied in one direction the ligand
>>>> may escape according to the diagram below?
>>>>
>>> The force always has a direction. It must, otherwise, how would you know
>>> in what direction to move the particle that time step? However, the
>>> direction of the steering force could be any direction away from the
>>> binding site. Consider a 2-particle system with that biasing force. The
>>> direction of the force would simply push the particles apart along the
>>> initial displacement vector. As a result, the direction of travel (apart
>>> from being "away" from the binding pocket) depends strongly on the initial
>>> conditions and environment.
>>>
>>> HTH,
>>> Jason
>>>
>>
>> --
>> Dr. Adrian E. Roitberg
>> Professor
>> Quantum Theory Project, Department of Chemistry
>> University of Florida
>> roitberg.ufl.edu
>>
>>
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Received on Fri Dec 14 2012 - 09:30:03 PST
