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A dimensionality A dimensionality reduction approach to reduction approach to

modeling protein modeling protein flexibilityflexibility

By By Miguel L. Teodoro, , George N. Phillips J* and Lydia E. Kavraki

Rice University and University of Wisconsin-Madison*

Presented by Zhang JingboPresented by Zhang Jingbo

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Outline Motivation, Background and Our goal Protein flexibility The problems in current methods and the benefit

of our methods in this paper Dimensionality reduction techniques Obtaining conformational Data Application to Specific Systems Summary

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Motivation Introduce a method to obtain a reduced basis

representation of protein flexibility.

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Background Proteins are involved either directly or indirectly in all

biological processes in living organisms. Conformational changes of proteins can critically affect

their ability to bind other molecules. Any progress in modeling protein motion and flexibility

will contribute to the understanding of key biological functions.

Today there is a large body of knowledge available on protein structure and function and this amount of information is expected to grow even faster in the future.

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Our method and goal Method:

A dimensionality reduction technique — Principal Component Analysis

Goal: 1. Transform the original high dimensional representation

of protein motion into a lower dimensional representation that captures the dominant modes of motions of the protein.

2. Obtain conformations that have been observed in laboratory experiments.

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The focus of this paper How to obtain a reduced representation of

protein flexibility from raw protein structural data

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What is Protein flexibility ? Definition: A crucial aspect of the relation

between protein structure and function. Proteins change their three-dimensional shapes

when binding or unbinding to other molecules.

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Why we want to modeling protein flexibility?

Several applications for our work: 1. Pharmaceutical drug development

2. To model conformational changes that occur during protein-protein and protein-DNA/RNA interactions.

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RII molecular "handshake" (donut with two holes).

Backbone of the RII dimer showing glycan binding sites.

Models for the binding of RII to the glycophorin A receptor on red blood cells (erythrocytes).

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The problems in current methods The computational complexity of explicitly

modeling all the degrees of freedom of a protein is too high.

Modeling proteins as rigid structures limits the effectiveness of currently used molecular docking mithods.

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The benefit of our method in this paper (1)

Using the approximation Make including protein flexibility in the drug

process a computationally efficient way.

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Two most common structural biology experimental methods in use today Protein X-ray crystallography Nuclear magnetic resonance (NMR)

Limits:

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An alternative to experimental methods Computational methods based on classical or

quantum mechanics to approximate protein flexibility.

Limits:

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The benefit of our method in this paper (2)

Transform the basis of representation of molecular motion.

The new degrees of freedom will be linear combinations of the original variables.

Some degrees of freedom are significantly more representative of protein flexibility than others.

Consider only the most significant dof and the transformed dof are collective motions affecting the entire configuration of the protein.

Some tradeoff between the loss of information and effectively modeling protein flexibility in a largely reduced dimensionality subspace.

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What we acutually do in this paper? Start from initial coordinate information from different

data sources Apply the principal component analysis method of

dimensionality reduction. Obtain a new structural representation using collective

degrees of freedom.

Here, we will focus on a. the interpretation of the principal components as

biologically relevant motions b. how combinations of a reduced number of these

motions can approximate alternative conformations of the protein.

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Dimensionality reduction techniques Aim: find a mapping between the data in a space

and its subspace. Two methods:

a. Multidimensional scaling (MDS)

b. Principal component analysis (PCA)

Merits:

Limits:

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PCA of conformational data Merits: 1). the most established method 2). the most efficient algorithms 3). guaranteed convergence for computation 4). a upper bound on how much we can reduce the representation of conformational flexibility in proteins. 5). the principal components have a direct physical interpretation. 6). can readily project the high dimensional data to a low dimensional space and do it in the inverse direction recovering a representation of the original data with minimal reconstruction error.

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PCA of conformational data (continued) Linear and non-linear

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PCA of conformational data (continued)

Conformational Data 1. The input data for PCA: Several atomic

displacement vectors (3N dimension) corresponding to different structural conformations, which as the form

corresponds to Cartesian coordinate information for the ith atom.

2. All atomic displacement vectors constitute the conformational vector set.

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Singular value decomposition (SVD)

We use the singular value decomposition (SVD) as an efficient computational method to calculate the principal components.

The SVD of a matrix, A, is defined as:

where U and V are orthonormal matrices and

is a nonnegative diagonal matrix whose diagonal elements are the singular values of A.

the columns of matrices U and V are called the left and right singular vectors, respectively.

the square of each singular value corresponds to the variance of the data in A.

The SVD of matrix A was computed using the ARPACK library.

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Obtaining conformational Data The most common data sources:

1. experimental laboratory methods:

a. X-ray crystallography

b. NMR,

2. computational sampling methods based forcefield such as molecular dynamics.

laboratory methods VS computational methods:

- laboratory methods generate less data

- computational methods have a lower accuracy.

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Application to Specific Systems

Now, let’s see about

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HIV-1 Protease

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The advantages of using the PCA methodology to analyze protein flexibility Can be used at different levels of detail： 1. the overall motion of the backbone.

2. the simplified flexibility of the protein as a whole.

3. include only the atoms that constitute the binding site.

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In the first experiment situation

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The second situation The advantage of PCA

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The last situation As a validation of our method.

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Another application: Aldose Reduction

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Summary

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Thank you