NUS CS5247 A dimensionality reduction approach to modeling protein flexibility By, By Miguel L. Teodoro, George N. Phillips J* and Lydia E. Kavraki Rice University and University of Wisconsin-Madison* Presented by Zhang Jingbo

NUS CS52472 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

NUS CS52473 Motivation  Introduce a method to obtain a reduced basis representation of protein flexibility.

NUS CS52474 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.

NUS CS52475 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.

NUS CS52476 The focus of this paper  How to obtain a reduced representation of protein flexibility from raw protein structural data

NUS CS52477 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.

NUS CS52478

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10 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.

NUS CS 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).

NUS CS 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.

NUS CS The benefit of our method in this paper (1)  Using the approximation  Make including protein flexibility in the drug process a computationally efficient way.

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

NUS CS An alternative to experimental methods  Computational methods based on classical or quantum mechanics to approximate protein flexibility.  Limits:

NUS CS 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.

NUS CS 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.

NUS CS 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:

NUS CS 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.

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

NUS CS 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.

NUS CS 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.

NUS CS 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.

NUS CS Application to Specific Systems  Now, let’s see about

NUS CS HIV-1 Protease

NUS CS 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.

NUS CS In the first experiment situation

NUS CS The second situation  The advantage of PCA

NUS CS The last situation  As a validation of our method.

NUS CS Another application: Aldose Reduction

NUS CS Summary

NUS CS Thank you