Spectral approaches for identifying kinetic features in molecular dynamics simulations of globular proteins

Proteins live in an environment of random thermal vibrations yet they convert this constant disorder into selective biological function. As data acquisition methods for resolving protein motions improve more of the randomness is also captured; there is thus a parallel need for analysis methods that filter out the disorder and clarify functionally-relevant protein behavior. Few behaviors are more relevant than folding in the first place, and this thesis opens by addressing which conformational states are kinetically relevant for promoting or inhibiting attainment of the folded native state. Our modeling approach discretizes simulation data into a network of nodes and edges representing, respectively, different protein conformations and observed conformational transitions. A perturbative strategy is then invoked to quantify the importance of each node, i.e. conformational substate, with regard to theoretical folding rates. On a test of 10 proteins this framework identifies unique ‘kinetic traps’ and ‘facilitator substates’ that sometimes evade detection with traditional RMSD-based analysis. We then apply spectral approaches and auto-regressive models to (1) address efficiency concerns for more general networks and (2) mimic protein flexibility with compact linear models

Discovering Conformational Sub-States Relevant to Protein Function

Background: Internal motions enable proteins to explore a range of conformations, even in the vicinity of native state. The role of conformational fluctuations in the designated function of a protein is widely debated. Emerging evidence suggests that sub-groups within the range of conformations (or sub-states) contain properties that may be functionally relevant. However, low populations in these sub-states and the transient nature of conformational transitions between these substates present significant challenges for their identification and characterization. Methods and Findings: To overcome these challenges we have developed a new computational technique, quasianharmonic analysis (QAA). QAA utilizes higher-order statistics of protein motions to identify sub-states in the conformational landscape. Further, the focus on anharmonicity allows identification of conformational fluctuations that enable transitions between sub-states. QAA applied to equilibrium simulations of human ubiquitin and T4 lysozyme reveals functionally relevant sub-states and protein motions involved in molecular recognition. In combination with a reaction pathway sampling method, QAA characterizes conformational sub-states associated with cis/trans peptidyl-prolyl isomerization catalyzed by the enzyme cyclophilin A. In these three proteins, QAA allows identification of conformational sub-states, with critical structural and dynamical features relevant to protein function. Conclusions: Overall, QAA provides a novel framework to intuitively understand the biophysical basis of conformational diversity and its relevance to protein function. © 2011 Ramanathan et al

Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides

Genome-wide identification of autosomal genes with allelic imbalance of chromatin state

In mammals, monoallelic gene expression can result from X-chromosome inactivation, genomic imprinting, and random monoallelic expression (RMAE). Epigenetic regulation of RMAE is not fully understood. Here we analyze allelic imbalance in chromatin state of autosomal genes using ChIP-seq in a clonal cell line. We identify approximately 3.7% of autosomal genes that show significant differences between chromatin states of two alleles. Allelic regulation is represented among several functional gene categories including histones, chromatin modifiers, and multiple early developmental regulators. Most cases of allelic skew are produced by quantitative differences between two allelic chromatic states that belong to the same gross type (active, silent, or bivalent). Combinations of allelic states of different types are possible but less frequent. When different chromatin marks are skewed on the same gene, their skew is coordinated as a result of quantitative relationships between these marks on each individual allele. Finally, combination of allele-specific densities of chromatin marks is a quantitative predictor of allelic skew in gene expression

Relationships between the magnitudes of allelic skew of different marks on the same gene.

<p>For all genes with sufficient number of allelically assigned reads, allelic skews (log2 of <i>mus</i>:<i>cas</i> ratio) are plotted for one mark vs. another: <b>A,</b> K27me3 vs. K4me3; <b>B,</b> K36me3 vs. K4me3; <b>C,</b> POL2S2 vs. K4me3. Horizontal and vertical dashed lines mark the 2-fold allelic difference. The majority of genes do not show significant skew in any mark (gray points around origin). Most of the genes with skewed chromatin state (colored points) have a skew in only one mark and no significant skew in the other (purple triangles and magenta squares). However, when both marks are skewed (cyan circles), these skews are anticorrelated for active vs. repressive mark (A) and correlated for two active marks (B, C).</p

Relationships between chromatin marks on individual alleles are similar to the relationships on the composite level.

<p><b>A, B</b>, Scatter plots of composite densities of K4me3 in TSS-proximal regions vs. (A) K27me3 in TSS-proximal regions and (B) K36me3 on gene bodies. Color represents composite levels of gene expression measured by FPKM values based on RNA-Seq. Active genes (upper part of the plots) show higher levels of active marks K4me3 and K36me3, general anticorrelation between K4me3 and K27me3, and positive correlation between K4me3 and K36me3. Permanently silenced genes (lower part of the plots) show depletion of K4me3 and K36me3, and the corresponding depletion of K27me3. Bivalent region is the area of highest K27me3 densities and intermediate K4me3 densities that connects active and permanently silenced branches in (A). <b>C, D,</b> Scatter plots of inferred mark densities on individual allele (maternal “M” allele as an example) for K4me3 in TSS-proximal regions vs. (C) K27me3 in TSS-proximal regions and (D) K36me3 on gene bodies. Color represents allelic levels of expression measured by FPKM values based on RNA-Seq.</p

Pairwise combinations of allelic chromatin states that result in observed allelic skew of a chromatin mark.

<p>Allelic promoters are shown as points in the space of K4me3 and K27me3 densities. <b>A,</b> Schematic of major types of allelic chromatin states and their possible combinations on two alleles. Regions 1, 2, and 3 correspond to silent, bivalent, and active alleles, respectively. Combinations observed in larger numbers of genes (“observed”) are shown as cyan lines. Combination observed in fewer genes (“unobserved”) is shown as orange line. <b>B,</b> Scatter plot of K4me3 vs. K27me3 promoter densities on maternal (M) <i>mus</i> allele of all autosomal genes shown as gray points; genes with allelic skew in K4me3 are highlighted in blue. Regions 1, 2, and 3 are marked by dashed lines. <b>C-E,</b> Scatter plots of K4me3 vs. K27me3 promoter densities on paternal (P) <i>cas</i> allele, shown as gray points. Red points in these three plots highlight three subgroups of genes shown in <b>B</b>: genes whose maternal allele belongs to silent, bivalent, or active type (regions 1, 2, and 3 in <b>B</b>, marked for the reference by a blue rectangle in each corresponding plot <b>C-E</b>). Hue indicates the local density of paternal alleles with similar K4me3/K27me3 densities. <b>C,</b> Among genes with K4me3 skew whose maternal allele is in a silent state (region 1 in <b>B,</b> <i>n</i> = 24), paternal allele (P) generally has medium to high K4me3 density and low K27me3 density. <b>D,</b> Among genes with K4me3 skew whose maternal allele is in a bivalent state (region 2 in <b>B,</b> <i>n</i> = 66), paternal allele (P) generally also resides in a bivalent state. <b>E,</b> Among genes with K4me3 skew whose maternal allele is in an active state (region 3 in <b>B,</b> <i>n</i> = 281), paternal allele (P) most often resides in an active or bivalent state; there are much fewer cases of a fully silent paternal allele.</p