A dimensionality reduction approach to modeling protein flexibility

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A dimensionality reduction approach to modeling
protein flexibility

• By Miguel L. Teodoro, George N. Phillips J
• and Lydia E. Kavraki
• Rice University and University of
  Wisconsin-Madison
• Presented 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
• Transform the original high dimensional
  representation of protein motion into a lower
  dimensional representation that captures the
  dominant modes of motions of the protein.
• 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).
Models for the binding of RII to the glycophorin
A receptor on red blood cells (erythrocytes).
Backbone of the RII dimer showing glycan binding
sites.
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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, lets 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