Ron Unger

Finding the lowest free energy conformation of a protein is an NP-hard problem: Proof and implications

The protein folding problem and the notion of NP-completeness and NP-hardness are discussed. A lattice model is suggested to capture the essence of protein folding. For this model we present a proof that finding the lowest free energy conformation belongs to the class of NP-hard problems. The implications of the proof are discussed and we suggest that the natural folding process cannot be considered as a search for the global free energy minimum. However, we suggest an explanation as to why, for many proteins, the native functional conformation may coincide with the lowest free energy conformation.

Towards computing with proteins

Can proteins be used as computational devices to address difficult computational problems? In recent years there has been much interest in biological computing, that is, building a general purpose computer from biological molecules. Most of the current efforts are based on DNA because of its ability to self‐hybridize. The exquisite selectivity and specificity of complex protein‐based networks motivated us to suggest that similar principles can be used to devise biological systems that will be able to directly implement any logical circuit as a parallel asynchronous computation. Such devices, powered by ATP molecules, would be able to perform, for medical applications, digital computation with natural interface to biological input conditions. We discuss how to design protein molecules that would serve as the basic computational element by functioning as a NAND logical gate, utilizing DNA tags for recognition, and phosphorylation and exonuclease reactions for information processing. A solution of these elements could carry out effective computation. Finally, the model and its robustness to errors were tested in a computer simulation. Proteins 2006.

IgTree © : Creating Immunoglobulin variable region gene lineage trees

Lineage trees describe the microevolution of cells within an organism. They have been useful in the study of B cell affinity maturation, which is based on somatic hypermutation of immunoglobulin genes in germinal centers and selection of the resulting mutants. Our aim was to create and implement an algorithm that can generate lineage trees from immunoglobulin variable region gene sequences. The IgTree program implements the algorithm we developed, and generates lineage trees. Original sequences found in experiments are assigned to either leaves or internal nodes of the tree. Each tree node represents a single mutation separating the sequences. The mutations that separate the sequences from each other can be point mutations, deletions or insertions. The program can deal with gaps and find potential reversion mutations. The program also enumerates mutation frequencies and sequence motifs around each mutation, on a per-tree basis. The algorithm has proven useful in several studies of immunoglobulin variable region gene mutations.

CHAOS IN PROTEIN DYNAMICS

MD simulations, currently the most detailed description of the dynamic evolution of proteins, are based on the repeated solution of a set of differential equations implementing Newtons second law. Many such systems are known to exhibit chaotic behavior, i.e., very small changes in initial conditions are amplified exponentially and lead to vastly different, inherently unpredictable behavior. We have investigated the response of a protein fragment in an explicit solvent environment to very small perturbations of the atomic positions (10−3–10−9 Å). Independent of the starting conformation (native‐like, compact, extended), perturbed dynamics trajectories deviated rapidly, leading to conformations that differ by approximately 1 Å RMSD within 1–2 ps. Furthermore, introducing the perturbation more than 1–2 ps before a significant conformational transition leads to a loss of the transition in the perturbed trajectories. We present evidence that the observed chaotic behavior reflects physical properties of the system rather than numerical instabilities of the calculation and discuss the implications for models of protein folding and the use of MD as a tool to analyze protein folding pathways. Proteins 29:417–425, 1997.

A tale of two tails: why are terminal residues of proteins exposed?

MOTIVATION It is widely known that terminal residues of proteins (i.e. the N- and C-termini) are predominantly located on the surface of proteins and exposed to the solvent. However, there is no good explanation as to the forces driving this phenomenon. The common explanation that terminal residues are charged, and charged residues prefer to be on the surface, cannot explain the magnitude of the phenomenon. Here, we survey a large number of proteins from the PDB in order to explore, quantitatively, this phenomenon, and then we use a lattice model to study the mechanisms involved. RESULTS The location of the termini was examined for 425 small monomeric proteins (50-200 amino acids) and it was found that the average solvent accessibility of termini residues is 87.1% compared with 49.2% of charged residues and 35.9% of all residues. Using a cutoff of 50% of the maximal possible exposure, 80.3% of the N-terminal and 86.1% of the C-terminal residues are exposed compared to 32% for all residues. In addition, terminal residues are much more distant from the center of mass of their proteins than other residues. Using a 2D lattice, a large population of model proteins was studied on three levels: structural selection of compact structures, thermodynamic selection of conformations with a pronounced energy gap and kinetic selection of fast folding proteins using Monte-Carlo simulations. Progressively, each selection raises the proportion of proteins with termini on the surface, resulting in similar proportions to those observed for real proteins.

A simple algorithm for detecting circular permutations in proteins

MOTIVATION Circular permutation of a protein is a genetic operation in which part of the C-terminal of the protein is moved to its N-terminal. Recently, it has been shown that proteins that undergo engineered circular permutations generally maintain their three dimensional structure and biological function. This observation raises the possibility that circular permutation has occurred in Nature during evolution. In this scenario a protein underwent circular permutation into another protein, thereafter both proteins further diverged by standard genetic operations. To study this possibility one needs an efficient algorithm that for a given pair of proteins can detect the underlying event of circular permutations. A possible formal description of the question is: given two sequences, find a circular permutation of one of them under which the edit distance between the proteins is minimal. A naive algorithm might take time proportional to N3 or even N4, which is prohibitively slow for a large-scale survey. A sophisticated algorithm that runs in asymptotic time of N2 was recently suggested, but it is not practical for a large-scale survey. RESULTS A simple and efficient algorithm that runs in time N2 is presented. The algorithm is based on duplicating one of the two sequences, and then performing a modified version of the standard dynamic programming algorithm. While the algorithm is not guaranteed to find the optimal results, we present data that indicate that in practice the algorithm performs very well. AVAILABILITY A Fortran program that calculates the optimal edit distance under circular permutation is available upon request from the authors. CONTACT ron@biocom1.ls.biu.ac.il.

The importance of short structural motifs in protein structure analysis

SummaryProteins tend to use recurrent structural motifs on all levels of organization. In this paper we first survey the topics of recurrent motifs on the local secondary structure level and on the global fold level. Then, we focus on the intermediate level which we call the short structural motifs. We were able to identify a set of structural building blocks that are very common in protein structure. We suggest that these building blocks can be used as an important link between the primary sequence and the tertiary structure. In this framework, we present our latest results on the structural variability of the extended strand motifs. We show that extended strands can be divided into three distinct structural classes, each with its own sequence specificity. Other approaches to the study of short structural motifs are reviewed.

Shuffling biological sequences

Abstract This paper considers the following sequence shuffling problem: Given a biological sequence (either DNA or protein) s, generate a random instance among all the permutations of s that exhibit the same frequencies of k-lets (e.g. dinucleotides, doublets of amino acids, triplets, etc.). Since certain biases in the usage of k-lets are fundamental to biological sequences, effective generation of such sequences is essential for the evaluation of the results of many sequence analysis tools. This paper introduces two sequence shuffling algorithms: A simple swapping-based algorithm is shown to generate a near-random instance and appears to work well, although its efficiency is unproven; a generation algorithm based on Euler tours is proven to produce a precisely uniform instance, and hence solve the sequence shuffling problem, in time not much more than linear in the sequence length.

Global regulation of alternative splicing by adenosine deaminase acting on RNA (ADAR)

Alternative mRNA splicing is a major mechanism for gene regulation and transcriptome diversity. Despite the extent of the phenomenon, the regulation and specificity of the splicing machinery are only partially understood. Adenosine-to-inosine (A-to-I) RNA editing of pre-mRNA by ADAR enzymes has been linked to splicing regulation in several cases. Here we used bioinformatics approaches, RNA-seq and exon-specific microarray of ADAR knockdown cells to globally examine how ADAR and its A-to-I RNA editing activity influence alternative mRNA splicing. Although A-to-I RNA editing only rarely targets canonical splicing acceptor, donor, and branch sites, it was found to affect splicing regulatory elements (SREs) within exons. Cassette exons were found to be significantly enriched with A-to-I RNA editing sites compared with constitutive exons. RNA-seq and exon-specific microarray revealed that ADAR knockdown in hepatocarcinoma and myelogenous leukemia cell lines leads to global changes in gene expression, with hundreds of genes changing their splicing patterns in both cell lines. This global change in splicing pattern cannot be explained by putative editing sites alone. Genes showing significant changes in their splicing pattern are frequently involved in RNA processing and splicing activity. Analysis of recently published RNA-seq data from glioblastoma cell lines showed similar results. Our global analysis reveals that ADAR plays a major role in splicing regulation. Although direct editing of the splicing motifs does occur, we suggest it is not likely to be the primary mechanism for ADAR-mediated regulation of alternative splicing. Rather, this regulation is achieved by modulating trans-acting factors involved in the splicing machinery.

On the applicability of genetic algorithms to protein folding

Discusses the protein folding problem and suggests the use of genetic algorithms for protein folding simulations. The issues of protein energy functions, search algorithms, and folding pathways are discussed. The authors review the current approaches to the protein folding problem, point out the limitations of the approaches, and present the genetic algorithm method, which is based on viewing evolution as an optimization process. The schemata theorem is proved in the context of protein structure, showing that during a genetic algorithm search more and more attention will be given to favorable local structures while unfavorable local structures will be rapidly abandoned. It is shown that genetic algorithms are a suitable tool in protein structure predictions. A version of the genetic algorithm is presented that is suitable for protein structure prediction. The behavior of the algorithm is explored in a single model of folding, and it is shown that the algorithm behaves as expected and is able to find the correct conformation.<<ETX>>