Michael E. Wall

Singular Value Decomposition and Principal Component Analysis

This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the precise relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aim is to provide definitions, interpretations, examples, and references that will serve as resources for understanding and extending the application of SVD and PCA to gene expression analysis.

Design of gene circuits: lessons from bacteria

Researchers are now building synthetic circuits for controlling gene expression and considering practical applications for engineered gene circuits. What can we learn from nature about design principles for gene circuits? A large body of experimental data is now available to test some important theoretical predictions about how gene circuits could be organized, but the data also raise some intriguing new questions.

Allostery in a Coarse-Grained Model of Protein Dynamics

We propose a criterion for optimal parameter selection in coarse-grained models of proteins and develop a refined elastic network model (ENM) of bovine trypsinogen. The unimodal density-of-states distribution of the trypsinogen ENM disagrees with the bimodal distribution obtained from an all-atom model; however, the bimodal distribution is recovered by strengthening interactions between atoms that are backbone neighbors. We use the backbone-enhanced model to analyze allosteric mechanisms of trypsinogen and find relatively strong communication between the regulatory and active sites.

SVDMAN—singular value decomposition analysis of microarray data

SUMMARY We have developed two novel methods for Singular Value Decomposition analysis (SVD) of microarray data. The first is a threshold-based method for obtaining gene groups, and the second is a method for obtaining a measure of confidence in SVD analysis. Gene groups are obtained by identifying elements of the left singular vectors, or gene coefficient vectors, that are greater in magnitude than the threshold W N(-1/2), where N is the number of genes, and W is a weight factor whose default value is 3. The groups are non-exclusive and may contain genes of opposite (i.e. inversely correlated) regulatory response. The confidence measure is obtained by systematically deleting assays from the data set, interpolating the SVD of the reduced data set to reconstruct the missing assay, and calculating the Pearson correlation between the reconstructed assay and the original data. This confidence measure is applicable when each experimental assay corresponds to a value of parameter that can be interpolated, such as time, dose or concentration. Algorithms for the grouping method and the confidence measure are available in a software application called SVD Microarray ANalysis (SVDMAN). In addition to calculating the SVD for generic analysis, SVDMAN provides a new means for using microarray data to develop hypotheses for gene associations and provides a measure of confidence in the hypotheses, thus extending current SVD research in the area of global gene expression analysis.

Quantifying allosteric effects in proteins.

In allosteric regulation, protein activity is altered when ligand binding causes changes in the protein conformational distribution. Little is known about which aspects of protein design lead to effective allosteric regulation, however. To increase understanding of the relation between protein structure and allosteric effects, we have developed theoretical tools to quantify the influence of protein–ligand interactions on probability distributions of reaction rates and protein conformations. We define the rate divergence,

Mechanisms associated with cGMP binding and activation of cGMP-dependent protein kinase

\bar{D}

Design principles for regulator gene expression in a repressible gene circuit

k, and the allosteric potential,

Activation of the Escherichia coli marA/soxS/rob regulon in response to transcriptional activator concentration.

\bar{D}

Fast dynamics perturbation analysis for prediction of protein functional sites.

x, as the Kullback–Leibler divergence between either the reaction‐rate distributions or protein conformational distributions with and without the ligand bound. We then define Dx as the change in the conformational distribution of the combined protein/ligand system, derive Dx in the harmonic approximation, and identify contributions from 3 separate terms: the first term, D  xω , results from changes in the eigenvalue spectrum; the second term, D  xΔx , results from changes in the mean conformation; and the third term, D  xv , corresponds to changes in the eigenvectors. Using normal modes analysis, we have calculated these terms for a natural interaction between lysozyme and the ligand tri‐N‐acetyl‐D‐glucosamine, and compared them with calculations for a large number of simulated random interactions. The comparison shows that interactions in the known binding‐site are associated with large values of D  xv . The results motivate using allosteric potential calculations to predict functional binding sites on proteins, and suggest the possibility that, in Nature, effective ligand interactions occur at intrinsic control points at which binding induces a relatively large change in the protein conformational distribution. Proteins 2005. Published 2005 Wiley‐Liss, Inc.

Conformational dynamics of a crystalline protein from microsecond-scale molecular dynamics simulations and diffuse X-ray scattering

Using small-angle x-ray scattering, we have observed the cGMP-induced elongation of an active, cGMP-dependent, monomeric deletion mutant of cGMP-dependent protein kinase (Δ1–52PKG-Iβ). On saturation with cGMP, the radius of gyration of Δ1–52PKG-Iβ increases from 29.4 ± 0.1 Å to 40.1 ± 0.7 Å, and the maximum linear dimension increases from 90 Å ± 10% to 130 Å ± 10%. The elongation is due to a change in the interaction between structured regulatory (R) and catalytic (C) domains. A model of cGMP binding to Δ1–52PKG-Iβ indicates that elongation of Δ1–52PKG-Iβ requires binding of cGMP to the low-affinity binding site of the R domain. A comparison with cAMP-dependent protein kinase suggests that both elongation and activation require cGMP binding to both sites; cGMP binding to the low-affinity site therefore seems to be a necessary, but not sufficient, condition for both elongation and activation of Δ1–52PKG-Iβ. We also predict that there is little or no cooperativity in cGMP binding to the two sites of Δ1–52PKG-Iβ under the conditions used here. Results obtained by using the Δ1–52PKG-Iβ monomer indicate that a previously observed elongation of PKG-Iα is consistent with a pure change in the interaction between the R domain and the C domain, without alteration of the dimerization interaction. This study has revealed important features of molecular mechanisms in the biochemical network describing PKG-Iβ activation by cGMP, yielding new insight into ligand activation of cyclic nucleotide-dependent protein kinases, a class of regulatory proteins that is key to many cellular processes.