Murali april 28, may 3, 2016 coping with np completeness. Protein folding is known to be a hard problem and formal models of the problems were shown to be np complete e. The physicalstructure, which specifies the level of detail at which. This result augments existing proofs that the direct protein folding problem is np complete by providing the corresponding proof for the inverse protein folding problem. An optical fiber network oracle for npcomplete problems. If x is an npcomplete problem, and y is a problem in np with the property that x. Robust proofs of nphardness for protein folding citeseerx. Hp hydrophobicpolar energy function favors hhcontacts structures are discrete, simple, and originally 2d model only backbone c positions structures are drawn originally on a square lattice z 2. I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, malamenthogarth spacetimes, quantum gravity, closed timelike curves, and anthropic computing. In the final section 4 we speculate about possible ramifications of this and other np complete models of fragments of nature. Protein folding in the hydrophobichydrophilic hp model is npcomplete bonnie berger tom leightont abstract one of the simplest and most popular biophysical mod els of protein folding is the hydrophobichydrophilic hp model. Protein folding has been studied extensively in vitro, but much less is known about how folding proceeds in vivo. The model in three dimensions is also np complete, as determined by berger and.
Introduction recently, i heard a researcher present a colloquium on computational aspects of proteinfolding. Is protein folding problem really a npcomplete one. Algorithm design and analysis penn state college of. Protein structure analysis iosif vaisman 2015 binf 731 protein structure hierarchy primary the sequence of amino acid residues secondary ordered regions of primary sequence helices, betasheets, turns tertiary the threedimensional fold of a protein subunit quaternary the. It provides a theoretical basis for understanding algorithms currently in use and indicates that computational strategies from other np complete problems may be useful for predictive algorithms. Several lattice models of protein folding have been proven to be. Class of problems which are at least as hard as the hardest problems in np. Np hardness wikipedia an np problem is one that once given an answer, you can verify it in polynomial time. Molecular mechanisms of protein folding and misfolding molecules and cells terry oas department of biochemistry rm. It is considered to be the paradigmatic lattice protein model. Protein folding is a remarkably complex physicochemical process via which a polymer of amino acids that samples many, many conformations in its unfolded state adopts a well. The computational complexity of protein structure prediction in. That is, any np problem can be transformed into any of the npcomplete problems.
This is a simple to understand model, but i cant extract a correspondingly simple explanation of why it would be npcomplete using the turing machine model. It pro vides a theoretical basis for understanding algorithms curren tly in use, and indicates that computational strategies from other npcomplete problems ma y b e useful for. Feb 28, 2019 which shows a complicated proof for a simple model of protein folding using a self avoiding walk on a 3d lattice being np complete. Protein folding in the hydrophobichydrophilic hp model is np. Pdf is protein folding problem really a npcomplete one. I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, malamenthogarth spacetimes, quantum gravity.
More precisely, to determine the backbone structure. Molecular mechanisms of protein folding and misfolding. The hp model abstracts the hydrophobic in teraction in protein folding by labeling the amino acids. We also indicate how the proof can be extended to a three dimensional model. Detailed descriptions of class 20, and lectures 20 and 21. Can np complete problems be solved efficiently in the physical universe.
Can npcomplete problems be solved efficiently in the physical universe. Protein folding in the hydrophobichydrophilic hp is np. Finding lowenergy conformations of lattice protein models by quantum annealing. In this paper, the protein folding problem under the hp model on the cubic lattice is shown to be npcomplete. It provides a theoretical basis for understanding algorithms currently in use and indicates that computational strategies from other npcomplete problems may be useful for predictive algorithms. P np if and only if hamiltoniancycle is in p there are thousands of npcomplete problems. Abstractas protein folding is a npcomplete problem, arti. Most folding and unfolding problems are attractive from a pure mathematical standpoint, from the beauty of the problems themselves. In fact, it is widely believed that no such polynomialtime algorithm exists.
Abstract we show that the protein folding problem in the twodimensional hp model is np complete. Murali april 28, may 3, 2016 coping with npcompleteness. I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation. Informally, an npcomplete problem is an np problem that is at. Solving npcomplete problemssmall vertex coverstreesload balancingset cover. Since the protein folding problem is generally regarded as np complete, i have discarded from consideration any conventional problemsolving techniques such as exhaustive search of the solution space. Nonetheless, most of the problems have close connections to important industrial applications. Finding the lowest free energy conformation of a protein is an np.
The hydrophobicpolar protein model is the original lattice protein model. Abstract we show that the protein folding problem in the twodimensional hp model is npcomplete. Ric arti cial in telligence lab oratory usetts institute of t. It provides a theoretical basis for understanding algorithms currently in use and indicates that computational strategies from other npcomplete problems may be useful. A lattice model is suggested to capture the essence of protein. If an algorithm solves a problem that is npcomplete in polynomial time, then all problems in npare solvable within polynomial time. The p versus np problem is a major unsolved problem in computer science. This result augments existing proofs that the direct protein folding problem is npcomplete by providing the corresponding proof for the inverse protein folding problem. There is another very important driving force for protein folding, however. Complexity of protein folding department of mathematics.
Npcomplete problems and physical reality scott aaronson. Importance of proteins as the machines of the cell 1. The second hardness result concerns the intractability of protein folding for a class of energy formulas that contains a broad range of mean force potentials whose form is similar to commonly used pair potentials e. Solving npcomplete problemssmall vertex coverstreesapprox. If x is an npcomplete problem, and y is a problem in np with the property that x p. As a response to this failure of conventional computers, a number of physics approaches have been considered for np problems. Since the protein folding problem is generally regarded as npcomplete, i have discarded from consideration any conventional problemsolving techniques such as exhaustive search of the solution space. The protein threading problem with sequence amino acid. Recipe to establish np completeness of problem y step 1. Protein folding is np complete problem but it appears to be taking place very efficiently in biological systems. Protein folding is npcomplete problem but it appears to be taking place very efficiently in biological systems. The sequencestructure threading problem is np complete. Linkage folding has applications in robotics, hydraulic tube bending, and has connections to protein folding.
Because the protein folding problem is considered to be an npcomplete problem, most investigators have given up on trying to find polynomial time solutions, and turned to massively parallel computers to derive solutions by brute force. In this paper, the protein folding problem under the hp model on the cubic lattice is shown to be np complete. This means that the protein folding problem belongs to a large set of problems that are believed to be computationally intractable. The main result is that hp stringfold is np complete when g is z3. Because the protein folding problem is considered to be an np complete problem, most investigators have given up on trying to find polynomial time solutions, and turned to massively parallel computers to derive solutions by brute force. These results show that the psp problem is np hard in many simple lattice models, and thus widely believed to be intractable.
Finding lowenergy conformations of lattice protein models. There was a hope that by inverting the folding problem and formulating it as a threading problem, its formal complexity will be lower. Algorithm design and analysis lectures 3031 npcompleteness definition npcompleteness proof for circuitsat. For a while it was believed that the structure prediction problem in the hp model would be solvable in polynomial time, but recently it was shown npcomplete 2. It is attractive in the way that problems and even results can be easily understood, with little knowledge of mathematics or computer science, yet the solutions are difficult and involve many sophisticated techniques. The main result is that hp stringfold is npcomplete when g is z3. It provides a theoretical basis for understanding algorithms currently. More precisely, to determine the backbone structure of the protein using the. Protein folding in the hydrophobichydrophilic hp model. Jun 06, 20 to find the 3d conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a np complete one. Nphardness wikipedia an np problem is one that once given an answer, you can verify it in polynomial time.
Once we establish first natural npcomplete problem, others fall like dominoes. In the final section 4 we speculate about possible ramifications of this and other npcomplete models of fragments of nature. Solving np complete problemssmall vertex coverstreesload balancingset cover coping with np completeness t. The protein threading problem with sequence amino acid interaction preferences is npcomplete. Protein folding problem is a way to predict the best and optimal 3d molecular structure tertiary structure of a protein which is then considered to be a sign for the proteins proper functionality. The problem wether p nphas a lot of practical implications, since a lot of problems today, like protein folding and rsa encryption are. To attack the p np question, the concept of npcompleteness is very useful. Hart and sorin istrail abstract this paper addresses the robustness of intractability arguments for simplified models of proteinfolding that use lattices to discretize the space of conformations that a protein can assume. Lattice protein folding models a lattice protein foldingmodel represents conformations of proteinsas vertexindependentembeddings ofthe proteinstructure in a lattice i. We argue that protein folding is fundamentally an isoperimetric problem, and will then consider several combinatorial problems related to protein folding in the hp model. The proof follows by showing that the following folding problem is nphard.
The proof follows by showing that the following folding problem is np hard. Proteins are of different types, whereas each protein plays an important role in th. He states the assumption informally as npcomplete problems are intractable in the physical world. An analytical study of nphard protein folding problems ieee. Protein folding problem is a non deterministic polynomial hard problem. Protein folding problem is a way to predict the best and optimal 3d molecular structure tertiary structure of a protein which is then considered to be a sign for the protein s proper functionality. This driving force is called the hydrophobic effect, which can. Lattice models can be classified based on the followingproperties. Npcomplete problems are a set of problems to each of which any other npproblem can be reduced in polynomial time and whose solution may still be verified in polynomial time. The protein folding problem and the notion of npcompleteness and np hardness are discussed. To find the 3d conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a np complete one.
The sequencestructure threading problem is npcomplete. It provides a theoretical basis for understanding algorithms currently in use and indicates that computational strategies from other np complete problems may be useful for. Scott aaronson proposed using the np hardness assumption as a principle of physics. Nphard involves a transformation from the strongly.
It provides a theoretical basis for understanding algorithms currently in. This is a simple to understand model, but i cant extract a correspondingly simple explanation of why it would be np complete using the turing machine model. Therefore, no polynomial time algorithm is possible unless p np. Introduction recently, i heard a researcher present a colloquium on computational aspects of protein folding. I npcomplete means that a problem is hard to solve in the worst case. This means that the protein fold ing problem belongs to a large set of problems that are believed to be computationally intractable. It provides a theoretical basis for understanding algorithms currently in use and indicates that computational strategies from other npcomplete problems may be. Lathrop artificial intelligence laboratory, massachusetts institute of technology, cambridge, ma 029, usa in recent protein structure prediction research there has. He states the assumption informally as np complete problems are intractable in the physical world. The role of long and short range interactions in complex biomolecular reactions, including protein and dna folding. Npcomplete means that a problem is hard to solve in the worst case. Intractability of npcomplete problems as a principle of. Protein folding in the hydrophobichydrophilic hp model is.