arXiv subjects

Jie Liang

Publications and source records attributed to Jie Liang.

125 records · Page 7Linked to original sources

arXiv2011

On the Performance of Selection Cooperation with Outdated CSI and Channel Estimation Errors

In this paper, we investigate the performance of selection cooperation in the presence of imperfect channel estimation. In particular, we consider a cooperative scenario with multiple relays and amplify-and-forward protocol over frequency flat fading channels. In the selection scheme, only the "best" relay which maximizes the effective signal-to-noise ratio (SNR) at the receiver end is selected. We present lower and upper bounds on the effective SNR and derive closed-form expressions for the average symbol error rate (ASER), outage probability and average capacity per bandwidth of the received signal in the presence of channel estimation errors. A simulation study is presented to corroborate the analytical results and to demonstrate the performance of relay selection with imperfect channel estimation.

cs.IT↗

arXiv2011

On the Performance of Selection Cooperation with Imperfect Channel Estimation

In this paper, we investigate the performance of selection cooperation in the presence of imperfect channel estimation. In particular, we consider a cooperative scenario with multiple relays and amplify-and- forward protocol over frequency flat fading channels. In the selection scheme, only the "best" relay which maximizes the effective signal-to-noise ratio (SNR) at the receiver end is selected. We present lower and upper bounds on the effective SNR and derive closed-form expressions for the average symbol error rate (ASER), outage probability and average capacity per bandwidth of the received signal in the presence of channel estimation errors. A simulation study is presented to corroborate the analytical results and to demonstrate the performance of relay selection with imperfect channel estimation.

cs.IT↗

arXiv2006

Empirical Potential Function for Simplified Protein Models: Combining Contact and Local Sequence-Structure Descriptors

An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only $C_α$ or backbone atoms are attractive because they enable efficient search of the conformational space. We show residue specific reduced discrete state models can represent the backbone conformations of proteins with small RMSD values. However, no potential functions exist that are designed for such simplified protein models. In this study, we develop optimal potential functions by combining contact interaction descriptors and local sequence-structure descriptors. The form of the potential function is a weighted linear sum of all descriptors, and the optimal weight coefficients are obtained through optimization using both native and decoy structures. The performance of the potential function in test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. Our potential function requiring only backbone atoms or $C_α$ atoms have comparable or better performance than several residue-based potential functions that require additional coordinates of side chain centers or coordinates of all side chain atoms. By reducing the residue alphabets down to size 5 for local structure-sequence relationship, the performance of the potential function can be further improved. Our results also suggest that local sequence-structure correlation may play important role in reducing the entropic cost of protein folding.

q-bio.BM↗

arXiv2006

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.

q-bio.BM↗

arXiv2006

Interstrand pairing patterns in $β$-barrel membrane proteins: the positive-outside rule, aromatic rescue, and strand registration prediction

$β$-barrel membrane proteins are found in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts. We have developed probabilistic models to quantify propensities of residues for different spatial locations and for interstrand pairwise contact interactions involving strong H-bonds, side-chain interactions, and weak H-bonds. The propensity values and p-values measuring statistical significance are calculated exactly by analytical formulae we have developed. Contrary to the ``positive-inside'' rule for helical membrane proteins, $β$-barrel membrane proteins follow a significant albeit weaker ``positive-outside'' rule, in that the basic residues Arg and Lys are disproportionately favored in the extracellular cap region and disfavored in the periplasmic cap region. Different residue pairs prefer strong backbone H-bonded interstrand pairings (e.g. Gly-Aromatic) or non-H-bonded pairings (e.g. Aromatic-Aromatic). In addition, Tyr and Phe participate in aromatic rescue by shielding Gly from polar environments. These propensities can be used to predict the registration of strand pairs, an important task for the structure prediction of $β$-barrel membrane proteins. Our accuracy of 44% is considerably better than random (7%) and other studies. Our results imply several experiments that can help to elucidate the mechanisms of in vitro and in vivo folding of $β$-barrel membrane proteins. See supplementary material after the bibliography for detailed techniques.

q-bio.BM↗

arXiv2006

Computation of protein geometry and its applications: Packing and function prediction

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The algorithms of Delaunay triangulation, computation of voids and pockets, as well volume/area computation are also described. In addition, applications in packing analysis of protein structures and protein function prediction are also discussed.

q-bio.BM↗

arXiv2006

Estimation of Amino Acid Residue Substitution Rates at Local Spatial Regions and Application in Protein Function Inference: A Bayesian Monte Carlo Approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.

q-bio.BM↗

arXiv2006

Protein folding dynamics via quantification of kinematic energy landscape

We study folding dynamics of protein-like sequences on square lattice using physical move set that exhausts all possible conformational changes. By analytically solving the master equation, we follow the time-dependent probabilities of occupancy of all 802,075 conformations of 16-mers over 7-orders of time span. We find that (i) folding rates of these protein-like sequences of same length can differ by 4-orders of magnitude, (ii) folding rates of sequences of the same conformation can differ by a factor of 190, and (iii) parameters of the native structures, designability, and thermodynamic properties are weak predictors of the folding rates, rather, basin analysis of the kinematic energy landscape defined by the moves can provide excellent account of the observed folding rates.

q-bio.BM↗

arXiv2004

Developing optimal nonlinear scoring function for protein design

Motivation. Protein design aims to identify sequences compatible with a given protein fold but incompatible to any alternative folds. To select the correct sequences and to guide the search process, a design scoring function is critically important. Such a scoring function should be able to characterize the global fitness landscape of many proteins simultaneously. Results. To find optimal design scoring functions, we introduce two geometric views and propose a formulation using mixture of nonlinear Gaussian kernel functions. We aim to solve a simplified protein sequence design problem. Our goal is to distinguish each native sequence for a major portion of representative protein structures from a large number of alternative decoy sequences, each a fragment from proteins of different fold. Our scoring function discriminate perfectly a set of 440 native proteins from 14 million sequence decoys. We show that no linear scoring function can succeed in this task. In a blind test of unrelated proteins, our scoring function misclassfies only 13 native proteins out of 194. This compares favorably with about 3-4 times more misclassifications when optimal linear functions reported in literature are used. We also discuss how to develop protein folding scoring function.

q-bio.BM↗

arXiv2004

Order independent structural alignment of circularly permuted proteins

Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because current detection methods can miss many occurances, mistaking random repeats as circular permutation. Here we develop a method for detecting circularly permuted proteins from structural comparison. Sequence order independent alignment of protein structures can be regarded as a special case of the maximum-weight independent set problem, which is known to be computationally hard. We develop an efficient approximation algorithm by repeatedly solving relaxations of an appropriate intermediate integer programming formulation, we show that the approximation ratio is much better then the theoretical worst case ratio of $r = 1/4$. Circularly permuted proteins reported in literature can be identified rapidly with our method, while they escape the detection by publicly available servers for structural alignment.

q-bio.BM↗

arXiv2004

Potential function of simplified protein models for discriminating native proteins from decoys: Combining contact interaction and local sequence-dependent geometry

An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only $C_α$ atoms need to be specified, an accurate potential function is important. Such a simplified model is essential for efficient search of conformational space. In this work, we present a formulation of potential function for simplified representations of protein structures. It is based on the combination of descriptors derived from residue-residue contact and sequence-dependent local geometry. The optimal weight coefficients for contact and local geometry is obtained through optimization by maximizing margins among native and decoy structures. The latter are generated by chain growth and by gapless threading. The performance of the potential function in blind test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. This potential function have comparable or better performance than several residue-based potential functions that require in addition coordinates of side chain centers or coordinates of all side chain atoms.

q-bio.BM↗

arXiv2004

Importance of chirality and reduced flexibility of protein side chains: A study with square and tetrahedral lattice models

In simple models side chains are often represented implicitly (e.g., by spin-states) or simplified as one atom. We study side chain effects using square lattice and tetrahedral lattice models, with explicitly side chains of two atoms. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L-residues, and their side chains adopt different rotameric states. Short chains are enumerated exhaustively. For long chains, we sample effectively rare events (eg, compact conformations) and obtain complete pictures of ensemble properties of these models at all compactness region. We find that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side-chain entropy for a given back bone structure. We show that simple rotamer counting often underestimates side chain entropy significantly, and side chain entropy does not always correlate well with main chain packing. Among compact backbones with maximum side chain entropy, helical structures emerges as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.

q-bio.BM↗

arXiv2003

Are residues in a protein folding nucleus evolutionarily conserved?

It is important to understand how protein folding and evolution influences each other. Several studies based on entropy calculation correlating experimental measurement of residue participation in folding nucleus and sequence conservation have reached different conclusions. Here we report analysis of conservation of folding nucleus using an evolutionary model alternative to entropy based approaches. We employ a continuous time Markov model of codon substitution to distinguish mutation fixed by evolution and mutation fixed by chance. This model takes into account bias in codon frequency, bias favoring transition over transversion, as well as explicit phylogenetic information. We measure selection pressure using the ratio $ω$ of synonymous vs. non-synonymous substitution at individual residue site. The $ω$-values are estimated using the {\sc Paml} method, a maximum-likelihood estimator. Our results show that there is little correlation between the extent of kinetic participation in protein folding nucleus as measured by experimental $ϕ$-value and selection pressure as measured by $ω$-value. In addition, two randomization tests failed to show that folding nucleus residues are significantly more conserved than the whole protein. These results suggest that at the level of codon substitution, there is no indication that folding nucleus residues are significantly more conserved than other residues. We further reconstruct candidate ancestral residues of the folding nucleus and suggest possible test tube mutation studies of ancient folding nucleus.

q-bio.BM↗

arXiv2003

Simplicial edge representation of protein structures and alpha contact potential with confidence measure

Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of protein structure. This representation can eliminate implausible neighbors not in physical contact, and can avoid spurious contact between two residues when a third residue is between them. We develop statistical alpha contact potential. A studentized bootstrap method is then introduced for assessing the 95% confidence intervals for each of the 210 parameters. We found with confidence that there is significant long range propensity (>30 residues apart) for hydrophobic interactions. We test alpha contact potential for native structure discrimination using several decoy sets, and found it often has comparable performance with atom-based potentials requiring more parameters. We also show that alpha contact potential has better performance than potential defined by cut-off distance between geometric centers of side chains. Clustering of alpha contact potentials reveals natural grouping of residues. To explore the relationship between shape representation and physicochemical representation, we test the minimum alphabet size for structure discrimination. We found that there is no significant difference in discrimination when alphabet size varies from 7 to 20, if geometry is represented accurately by alpha simplicial edges. This result suggests that the geometry of packing plays an important role, but the specific residue types are often interchangeable.

physics.bio-ph↗

arXiv2003

On Design of Optimal Nonlinear Kernel Potential Function for Protein Folding and Protein Design

Potential functions are critical for computational studies of protein structure prediction, folding, and sequence design. A class of widely used potentials for coarse grained models of proteins are contact potentials in the form of weighted linear sum of pairwise contacts. However, these potentials have been shown to be unsuitable choices because they cannot stabilize native proteins against a large number of decoys generated by gapless threading. We develop an alternative framework for designing protein potential. We describe how finding optimal protein potential can be understood from two geometric viewpoints, and we derive nonlinear potentials using mixture of Gaussian kernel functions for folding and design. The optimization criterion for obtaining parameters of the potential is to minimize bounds on the generalization error of discriminating protein structures and decoys not used in training. In our experiment we use a training set of 440 protein structures repre senting a major portion of all known protein structures, and about 14 million structure decoys and sequence decoys obtained by gapless threading. We succeeded in obtaining nonlinear potential with perfect discrimination of the 440 native structures and native sequences. For the more challenging task of sequence design when decoys are obtained by gapless threading, we show that there is no linear potential with perfect discrimination of all 440 native sequences. Results on an independent test set of 194 proteins also showed that nonlinear kernel potential performs well.

cond-mat.soft↗

arXiv2003

Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers

Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further demonstrate that protein-like scaling relationship between packing density and chain length is observed in off-lattice self-avoiding walks. A key problem in studying compact chain polymer is the attrition problem: It is difficult to generate independent samples of compact long self-avoiding walks. We develop an algorithm based on the framework of sequential Monte Carlo and succeed in generating populations of compact long chain off-lattice polymers up to length $N=2,000$. Results based on analysis of these chain polymers suggest that maintaining high packing density is only characteristic of short chain proteins. We found that the scaling behavior of packing density with chain length of proteins is a generic feature of random polymers satisfying loose constraint in compactness. We conclude that proteins are not optimized by evolution to eliminate packing voids.

cond-mat.soft↗

arXiv2002

Statistical Geometry of Packing Defects of Lattice Chain Polymer from Enumeration and Sequential Monte Carlo Method

Voids exist in proteins as packing defects and are often associated with protein functions. We study the statistical geometry of voids in two-dimensional lattice chain polymers. We define voids as topological features and develop a simple algorithm for their detection. For short chains, void geometry is examined by enumerating all conformations. For long chains, the space of void geometry is explored using sequential Monte Carlo importance sampling and resampling techniques. We characterize the relationship of geometric properties of voids with chain length, including probability of void formation, expected number of voids, void size, and wall size of voids. We formalize the concept of packing density for lattice polymers, and further study the relationship between packing density and compactness, two parameters frequently used to describe protein packing. We find that both fully extended and maximally compact polymers have the highest packing density, but polymers with intermediate compactness have low packing density. To study the conformational entropic effects of void formation, we characterize the conformation reduction factor of void formation and found that there are strong end-effect. Voids are more likely to form at the chain end. The critical exponent of end-effect is twice as large as that of self-contacting loop formation when existence of voids is not required. We also briefly discuss the sequential Monte Carlo sampling and resampling techniques used in this study.

physics.bio-ph↗