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From: Ilyas Yildirim <yildirim.pas.rochester.edu>

Date: Tue, 18 Oct 2005 13:48:40 -0700

Hi Dave,

Sorry for the late reply. I was busy with moving to a new apartment, so

could not check out my emails regularly. The purpose of this modification

was to use the dummy atoms in the initial state, too. According to AMBER

8, we can have dummy atoms at the final state. We (me and Dr. Harry Stern

from U of R, Dept. of Chemistry) tried to mimic the smooth transition of

the original mixing function, (1-lambda)^klambda, around lambda=0, too. In

order to do that, we have put some extra constraints on the mix. function

when lambda=0 and lambda=1. Normally, the function needs to satisfy the

following conditions (I will use the notation 'x' rather 'lambda'):

f(x=0)=1

f(x=1)=0

where f(x) is the mix. function. We put the following constraints:

f^(n)(x=1)=f^(n)(x=0)=0

where f^(n)(x) is the 'n'th derivative of the new mix. function. As

n->infinity, the new mix. function becomes a step function. Using a large

'n' value is, therefore, not a good choice. We used n=6 and n=7 cases,

for the test cases. So, when someone solves this new mix. function with

the added new constraints, the mix. function becomes as

f(x,k) = (1-x)^k * sum_(i=0 to k-1) { combination(k-1+i,i) * x^i }

Here, combination(x,y) is the combination function. Namely,

combination(x,y) = x!/[(x-y)!*y!]

where

x! = x*(x-1)*(x-2)*...*2*1

As I wrote above, the reason why we did this modification is to make use

of dummy atoms at the initial state too. Hopefully I will prepare an

example case, such as for c->ic and ic->c transformations. I have done

these transformations, and the delta(G) for each transformation was as

follows:

delta(G) of c->ic ~= +49.49 kcal/mol

delta(G) of ic->c ~= -48.64 kcal/mol

These simulations were 700 ps simulations in explicit water, and only the

last 200 ps is used in the calculations. If you have any other questions,

just send me an email.

Best,

PS: icfe=1 will use the old mix. function while icfe=2 will use the new

mix. function.

On Tue, 11 Oct 2005, David A. Case wrote:

*> On Mon, Oct 10, 2005, Ilyas Yildirim wrote:
*

*> >
*

*> > I have modified some files in $AMBERHOME/src/sander to include a new
*

*> > mixing function for the TI approach. The old mixing function is
*

*> >
*

*> > f(x,k) = (1-x)^k
*

*> >
*

*> > while the new mix. function is
*

*> >
*

*> > f(x,k) = (1-x)^k * sum_(i=0 to k-1) { combination(k-1+i,i) * x^i }
*

*> >
*

*> > The old mixing function is still available. In order to use the old
*

one,

*> > set icfe=1. If u want to use the new mix. function, use icfe=2 option.
*

I

*> > put a test case in $AMBERHOME/test/ti_eth2meth_gas directory. A
*

0README

*> > file is available in this test case directory.
*

*>
*

*> Thanks, Ilyas. Can you expand on the above description some? What is
*

the

*> definition of "combination"? And can you add a few setences about what
*

the

*> purpose of this is, and what values of "k" you find to be good ones,
*

etc?

*> Readers will need some guidance about how/when/why to use icfe=2 rather
*

than

*> icfe=1.
*

*>
*

*> ...thanks...dave
*

*>
*

*>
*

Date: Tue, 18 Oct 2005 13:48:40 -0700

Hi Dave,

Sorry for the late reply. I was busy with moving to a new apartment, so

could not check out my emails regularly. The purpose of this modification

was to use the dummy atoms in the initial state, too. According to AMBER

8, we can have dummy atoms at the final state. We (me and Dr. Harry Stern

from U of R, Dept. of Chemistry) tried to mimic the smooth transition of

the original mixing function, (1-lambda)^klambda, around lambda=0, too. In

order to do that, we have put some extra constraints on the mix. function

when lambda=0 and lambda=1. Normally, the function needs to satisfy the

following conditions (I will use the notation 'x' rather 'lambda'):

f(x=0)=1

f(x=1)=0

where f(x) is the mix. function. We put the following constraints:

f^(n)(x=1)=f^(n)(x=0)=0

where f^(n)(x) is the 'n'th derivative of the new mix. function. As

n->infinity, the new mix. function becomes a step function. Using a large

'n' value is, therefore, not a good choice. We used n=6 and n=7 cases,

for the test cases. So, when someone solves this new mix. function with

the added new constraints, the mix. function becomes as

f(x,k) = (1-x)^k * sum_(i=0 to k-1) { combination(k-1+i,i) * x^i }

Here, combination(x,y) is the combination function. Namely,

combination(x,y) = x!/[(x-y)!*y!]

where

x! = x*(x-1)*(x-2)*...*2*1

As I wrote above, the reason why we did this modification is to make use

of dummy atoms at the initial state too. Hopefully I will prepare an

example case, such as for c->ic and ic->c transformations. I have done

these transformations, and the delta(G) for each transformation was as

follows:

delta(G) of c->ic ~= +49.49 kcal/mol

delta(G) of ic->c ~= -48.64 kcal/mol

These simulations were 700 ps simulations in explicit water, and only the

last 200 ps is used in the calculations. If you have any other questions,

just send me an email.

Best,

PS: icfe=1 will use the old mix. function while icfe=2 will use the new

mix. function.

On Tue, 11 Oct 2005, David A. Case wrote:

one,

I

0README

the

the

etc?

than

-- Ilyas Yildirim --------------------------------------------------------------- - Department of Chemisty - - - University of Rochester - - - Hutchison Hall, # B10 - - - Rochester, NY 14627-0216 - Ph.:(585) 275 67 66 (Office) - - http://www.pas.rochester.edu/~yildirim/ - ---------------------------------------------------------------Received on Wed Apr 05 2006 - 23:49:52 PDT

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