.ig
:!cat %|tbl|pic|eqn|troff |dpost >%.ps;ghostview %.ps&
:!cat %|tbl|pic|eqn|troff |dpost >%.ps
:g/omega hat sub size -2 alpha/s//Wa/g
:g/w1/s//w1/g
..
.ig
.in +1i
.DS I
.EQ (z)
.EN
.DE
.in
..
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.EQ
delim $$
define Angstrom '~ up 17 "\(oa" back 60 A'
.EN
.EQ
define xbar  ` chi bar `
define xhat  ` chi hat `
define lhat  ` "\fI" L hat "\fP"`
define qlhat  ` "\fI" Q hat L hat "\fP"`
define xpop  ` "\fI" P "\fP"`
define xqop  ` "\fI" Q "\fP"`
define tmic  ` tau sub MIC`
define trxn  ` tau sub RXN`
define t*    ` t sup * `
define qdag  ` q sup "\(dd" `
define dag   ` "\(dd" `
.EN
.SP 7
OVERVIEW AND COMMENTS ON RATE PROCESSES
.SP 3
I. SIMULATIONS OF RATE PROCESSES
.P
Ghosh and McCammon (1987) and Karplus and coworkers in previous work
described quantitatively the barrier traversal for Tyr-35 isomerization
of BPTI.
.P
In the demonstration, we showed movies of the motions of Tyr-35 and
other atoms of BPTI at equilibrium (equivalent for Tyr-35 to motions
associated with the reactant well of the isomerization).  It is likely
that the dynamics of Tyr-35 at the barrier top are qualitatively
similar to those at the well bottom, in being diffusive and in being
correlated with motions of other parts of the structure.
.P
The simulations of Ghosh and McCammon together with the trajectories
shown in the demonstration give a picture of the complex dynamics of
barrier traversal.  
.P
This picture should apply generally, to protein reactions in which
there are Angstrom-level movements of the structure (ES complex
isomerizations, etc.).
.P
Diffusive dynamics implies that there are two time scales, $tau sub MIC$ and
$tau sub BROWNIAN$. For reaction dynamics, two additional characteristic times
need be considered, that for barrier-top traversal, $tau sub BARRIER$, and that of the chemical reaction, $tau sub RXN$.
.P
Motions on the time scales of $tau sub MIC$ and $tau sub BROWNIAN$
could be distinguished in the trajectories of BPTI and the $alpha-$helix.
Which motions?
.SK
II. THEORIES OF RATE PROCESSES
.SP 2
1. COLLISION THEORY (not discussed)
.SP
kinetic theory of gases.
.SP 2
2. TRANSITION STATE THEORY (TST)
.SP
Simple model - "done" fully in class; widely and successfully used;
the first modern reaction rate theory; one has a duty to understand TST.
.SP
TST has some unusual, even nonphysical, assumptions.
.SP 2
3. KRAMERS THEORY
.SP
The theory has a standard and proper physical foundation and development.
.SP
It treats solvent effects & reactions in a dense medium;
static (equilibrium) effects - TST ok; dynamic effects - beyond
	scope of TST.

Kramers theory needed to account for collisions between solvent and
activated complex that reduce rate of passage over barrier.

4. TIME CORRELATION FUNCTIONS (TCF)

essentially same model as Kramers theory.

more general theoretical framework (TCF).

treat time-dependent friction, particularly the case of high, sharp
barriers, for which Kramers theory fails.

2

SHOULD HAVE FEELING FOR .......

1. How the picture of a protein reaction, from the simulations, relates
to theories of rate processes and the models behind them (e.g., there
is an obvious tie to Kramers theory).


2. How the theoretical understanding of rate proce3sses has evolved:

(collision ->) TST -> Kramers -> TCF -> ???


3. The scope of the various theories, i.e., when they apply.

Why does TST do so well, considering its flawed underpining?


4. A model (or theory) is not a completely accurate description of
reality (experiment).  IT IS NOT INTENDED TO BE.  A model is successful
if it leads to new understanding and insights. A model necessarily
abstracts one or a few of the most significant features of a process:

	TST - barrier height, 1 control of rate Kramers - diffusion and
	solvent effects,
		in addition to barrier height Hynes - barrier shape, in
	addition to
		above; remove restriction of constant f from Kramers
		picture

3 4. The understanding of rate processes relevant to biochemistry is
incomplete. For example, not yet adequately considered are:

a) time scales: tBrownian -> treaction rate, with regard to:

	gating;

	coupling of dihedral transitions to dynamics along the reaction
	coordinate.


b) the complexity of the transverse coordinate dynamics, which are
integrated to obtain the friction f, deserve more careful treatment to
resolve specific motions crosscorrelated with barrier traversal.


c) a time range of .1 - 1 ps for barrier traversal is that for
maximally dissipative dynamics, which means, more plainly, that the
crosscorrelations of the transverse motions are maximally complex, and
that the barrier traversal is not along a minimum energy barrier
(adiabatic path).







4 WHAT IS IMPORTANT TO KNOW?

1. The picture from the MD simulations of barrier traversal in the
isomerization of Tyr-35 of BPTI.  This should be the reference point
you carry with you, for thoughts about the dynamics and mechanism of
action of enzymes and other biomolecules.

2. TST - the model and the assumptions; why it remains an important
theory; the meaning of
	k2 = kT/h ....  and how it relates to
	k = wR/2p ....

3. Kramers theory - model and assumptions; how these differ from TST
and are similar to TST; how result reduces to TST; what k represents;
dynamic solvent effects; Langevin equation; the friction.

4. Hynes - model and assumptions; differences and similarities to
Kramers model; why important.

5. What the several time scales are and how they are constrained by the
assumptions of the several theories (and constrain the scopes of the
theories).

6. Scopes of the various theories.

7. The use of a model to focus on one element of a complex problem, and
so derive insight.

5
