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JIANPENG MA |
Novel Mathematical Methods for Computing Reaction Paths of the Large Scale Conformational Changes in Protein |
Keywords: Computer simulation, conformational change, reaction path,
ras p21 |
Specific Aims: Large scale conformational change (LSCC) in protein
structures plays an important role in a variety of cellular processes. 1
Many diseases arise from alteration in the LSCC that result from malignant
mutations. A complete understanding of it is essential to molecular biology
and biomedical research. With detailed knowledge of the LSCC, it may be
possible to design ligands (drug candidates) molecules that can alter the
behavior so as to prevent the diseases from taking place. |
Computer simulation, 2 aided with the high
resolution structures of proteins, provides a powerful tool to study the
details of the energetics of LSCC. Methods including normal mode analysis,
reaction path calculation and free energy simulation are particularly useful. 2
However, due to the computationally-intensive nature, these methods are
restricted to applications to fairly small systems and short time scales
from a molecular biology perspective. Reliable methods for simulation of
large scale problems still need to be developed. |
In this proposal, we describe two new computational
methods that are well-suited for determining the reaction path for LSCC.
We propose application of the new methods to ras p21, the protein
product of the ras oncogene and a key protein in the signal transduction
pathway. 3 Understanding rasp21 is very important to
human health care because the mutant forms of ras p21 are involved
in at least 30% of all human cancers. |
Background/Significance: Despite intense efforts, the determination
of transition states and reaction paths in biomolecular simulations remains
a daunting problem. Historically, there have been two classes of methods,
each with certain advantages and disadvantages. |
An early method for searching for a reaction path
or transition state is the local propagation method. 4,5One starts
from the structure of the reactant state (R) and marches uphill
on the potential surface towards the transition state (the saddle point
on the potential surface). The direction of the search follows the direction
of the eigenvector of the lowest frequency normal mode. 2 Therefore,
the search direction is also in the ìsoftestî direction on the potential
surface. The advantage of such a method is that it does not require information
about the product state (P). Propagation of the path is automatic,
and relies solely on the features of the potential surface, i.e., gradient
and curvature. For certain simple systems, this is a very useful method.
However, for large biological macromolecules, this method is not computationally
feasible due to the very large number of degrees of freedom. |
A second class of methods were developed more recently.
A common feature of these methods is the use of the product state, in addition
to reactant state, to guide the search. These include the statistical method,
6
the constraint minimization method, 7 steepest descent method, 8
self-avoiding walk method, 9 and most recently the Conjugate Peak
Refinement (CPR) method; 10 the latter appears to be the most powerful
method to date. Many of these methods begin with an initial guess for the
path and subsequently refine it until it converges to a reasonable low
energy path. A commonly used initial guess is a linear interpolation between
the two end structures. The advantage is that one always gets a path which
runs from the reactant to a desired product. However, in many molecular
systems, the linear interpolation between two end structures may result
in an unrealistic molecular conformation in the middle of the initial path.
Such a ìbadî initial guess is often difficult to refine. This situation
may become very severe when the conformational change involve secondary
structure transition such as the winding or unwinding of *-helices, as
occurs in protein ras p21. 11 In addition, there are essentially
no methods that allow inclusion of explicit solvent. This is a particular
disadvantage when one deals with the secondary structure transition where
hydrogen bonds to solvent molecules play an important role. Thus, the development
of a new reaction path method for large biomolecular system would represent
a significant advance in the elucidation of key conformational transitions. |
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