JP2008090777A - Protein folding order prediction method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for identifying an order of folding a portion of a protein to be predicted, in three-dimensional protein structure prediction, by characteristics of an amino acid residue sequence of the protein. <P>SOLUTION: The method divides an amino acid residue sequence of a protein to be predicted into fragments of a length n (n=5-9), computes a standard deviation of an energy value based on multidimensional mean force field potential in different three-dimensional structures of the sequence fragment of each fragment, and predicts that three-dimensional structure folding proceeds in descending order of the standard deviation value. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for estimating the order of protein folding, which is part of a three-dimensional structure prediction method for predicting the three-dimensional structure of a protein with an unknown three-dimensional structure from an amino acid sequence.

  A protein is a chain polymer formed by peptide bonds of about several hundreds of biological amino acids, which are in a specific three-dimensional shape by folding. The specific three-dimensional shape of each protein is called the conformation, which is closely related to the function of the protein. In particular, a molecular recognition function common to many proteins is realized by a specific region in this three-dimensional structure specifically binding to a specific molecule.

  The three-dimensional structure of each protein can be determined by X-ray crystallography or nuclear magnetic resonance (NMR). In X-ray crystal analysis, it is necessary to make a single crystal of one type of protein. If this single crystallization is not successful, X-ray crystal analysis cannot be performed. In NMR, there is no need for crystallization, and a three-dimensional structure in an aqueous solution can be obtained. However, a large amount of information on a three-dimensional structure cannot be obtained with a large protein, and a three-dimensional structure is not necessarily obtained accurately. The database PDB (Protein Data Bank), which collects the three-dimensional structures of proteins that have been identified so far, currently has tens of thousands of proteins registered. Compared with DNA sequence databases that are already known, the number registered is quite small.

  This is because it may take several months to one year or more to determine the three-dimensional structure of one protein by X-ray crystallography or NMR. On the other hand, even if the three-dimensional structure is unknown, the amino acid residue sequence can be obtained relatively easily from genetic information or even directly from the protein. Therefore, even if the three-dimensional structure is not known, the protein whose sequence is known is 10 times or more of the protein whose three-dimensional structure is known. Therefore, a technique for predicting the three-dimensional structure of a protein from an amino acid residue sequence is required.

  A protein is a chain molecule in which several hundred amino acids are bonded as described above. That is, it is a molecular structure in which a side chain unique to each amino acid grows from a main chain along the chain. In the main chain, there are hydrogen atoms and oxygen atoms that form hydrogen bonds, and in many cases, a hydrogen bond is formed between the main chains in the vicinity of the array or at a distant position to form a stable structure. The most typical is a helical structure, in particular, the hydrogen bonded to the nitrogen atom of the i-th amino acid residue main chain hydrogen bonds with the oxygen atom bonded to the carbon atom of the i + 4th main chain. The α helical structure is the local structure that appears most frequently. In addition, a β sheet structure that forms hydrogen bonds between amino acid residue main chains that are separated from each other in sequence is a structure that appears quite frequently. The β sheet is constituted by a long, extended β-strand structure, which is an element of the β-sheet, bonded to another β-strand distant from the array by an inter-chain hydrogen bond. Both the α helix and the β sheet have a semi-regular structure. In addition, special partial structures may be created with hydrogen bonds, and these may be called turn structures. There are various types of turn structures. These characteristic partial structures such as α helix, β sheet, and turn and other random structures are collectively referred to as a secondary structure. The three-dimensional structure of the protein is such that each part on the sequence forms a secondary structure, and this secondary structure is further folded.

  Attempts to predict the three-dimensional structure of a protein from amino acid residue sequences began immediately after the three-dimensional structure of myoglobin was revealed by X-ray crystallography in the 1960s. In the 1970s, research on secondary structure prediction that predicts which part takes which secondary structure in protein sequences was performed mainly based on statistical methods. The secondary structure in which each of the 20 types of amino acid residues is often found is statistically determined from proteins with known three-dimensional structures, and based on that, each residue is in which secondary structure. It is to predict whether there is. However, the tendency of each of the 20 types of amino acid residues to be each secondary structure was not so strong, and at that time there were very few proteins with known three-dimensional structures (about several dozen), so the prediction accuracy Was very bad.

  In the 1980s, mainly physicists tried to physically analyze the protein folding phenomenon itself, and what conditions were necessary to successfully fold an actual protein using a modeled lattice model or the like? Much research has been conducted on whether or not it is necessary (Go N., Abe H., (1983) Randomness of the process of protein folding. In J. Pept Protein Res 22 622-632).

  However, in these studies at that time, knowledge about protein folding was not sufficient either experimentally or by simulation, so this study did not lead to actual protein structure prediction technology.

  In the 1990s, when the number of proteins with known three-dimensional structures became more than a thousand, rather than predicting the structure of the protein, the given sequence was assigned to which of the known proteins. Research has begun on whether it may be similar to the structure. This is called “Fold Recognition”. The amino acid residue sequence of the protein whose structure is to be predicted is determined based on the secondary structure of each amino acid, whether it is on the surface of the protein, or whether it is buried inside. By applying to the three-dimensional structure of a protein with a known structure, the fitness between the sequence and the structure is calculated. If the fitness is high, the sequence is considered to be similar to the structure with high fitness. This is sometimes called a sequence profile method (Non-patent Document 3).

  Under these circumstances, Sippl (Non-patent Document 1) proposes a method for obtaining an average force field potential from the distribution of amino acid residues in the three-dimensional structure of a protein with a known structure, and using this to evaluate the fitness between the sequence and the structure. (FIG. 5).

  Statistical processing of the distance at which amino acid residues A and B of 20 kinds of amino acid residues are distributed in a known protein three-dimensional structure, and using the logarithm of the frequency distribution for that distance as potential It is.

  With the introduction of the sequence profile method and average force field potential, and the number of proteins with known structures reaching 10,000 or more in the 1990s, the fold recognition method has a certain degree of accuracy that can withstand practical use as a three-dimensional structure prediction technique. It became so. Alongside this, based on the knowledge that proteins with similar sequences have similar structures, comparative modeling methods that predict structures from sequence comparisons have also been developed. By using these methods, proteins with unknown structures can be identified. About half of the structures can now be predicted with considerable accuracy.

  At the end of the 1990s, a fragment binding method was proposed as a method capable of dealing with a protein having a completely new three-dimensional pattern, which cannot be predicted by folding recognition or comparative modeling methods. This is because a fragment of a length (for example, a length of about 10 amino acids) in which the sequence of the protein whose structure is to be predicted is fixed is cut out, and the three-dimensional structure that can be taken from this fragment is obtained from the three-dimensional structure data of the known protein. The whole structure is formed by cutting out and connecting them (FIG. 7 and FIG. 8). Even if the whole structure is completely new, if it is a fragment of about 10 residues, typical secondary structures etc. are included in the structure of proteins with known structures, so the whole structure can be constructed by joining these together. It is a method based on the expectation that it may be.

  Various refinements have been made to the method of extracting structural fragment candidates that can be taken as sequence fragments, and as a result, the fragment bonding method sometimes can predict the three-dimensional structure fairly accurately.

  The protein structure prediction method has reached a practical level to some extent by folding recognition and fragment binding methods, but this does not reveal the protein folding mechanism. In the fragment binding method, about 100 candidate structures are given to each sequence fragment, and candidates are assigned to each sequence portion in a randomly created three-dimensional structure, and the fitness of the whole structure is calculated, and the fitness is high. Thus, a convergence method is used. This is the use of a so-called combinatorial optimization method. Compared to a completely random Monte Carlo method, the convergence time is short, and the final structure obtained is sometimes quite close to the correct three-dimensional structure. However, this does not reveal the mechanism of protein structure construction or folding.

From the latter half of the 1990s, an attempt to find the protein folding process by numerical simulation also started, and for small proteins (the number of amino acids is about tens of amino acids), a calculation result that a stable structure close to a certain correct structure was obtained by simulation. Was also announced. However, proteins are folded in an aqueous solution, and there are various problems such as difficulty in introducing the solvent effect of the aqueous solution into the simulation, and the calculation time is not practical. However, it is worthwhile that these simulations allow the protein folding process to be followed by methods other than experiments.
Sippl MJ, (1990) "Calculation of Conformational Ensembles form Potentials of Mean Force: An Approach to the Knowledge-based Prediction of Local Structure in Globular Proteins." J. Mol. Biol., 213,850-883 Onizuka K., Noguchi T., Akiyama Y., Matsuda H., (2002) "Using Data Compression for Multidimensional Distribution Analysis" IEEE Intelligent Systems 17 (3), 48-54 Bowie JU, Luthy RL, Eisenberg D., (1991) "A Method to Identify Protein Sequence That Fold into a Known Three-Dimensional Structure." Science, 256,164-170

  The biggest problem in protein tertiary structure prediction in the prior art is due to the unknown folding mechanism. For this reason, in structure optimization, which is the final step in predicting the three-dimensional structure of proteins, as in the fragment binding method, the structure is randomly changed to approach the optimal structure. . For this reason, a useless search is performed in the optimization, the prediction accuracy is unstable, and the calculation time for prediction becomes very long.

  In order to solve this problem, we need to know what process or state the main chain from before the protein begins to fold, and then to the final stable structure. Is to get. This knowledge can be obtained by developing a method for predicting the order of folding.

  The problem to be solved by the present invention is therefore how to estimate the order of protein folding. That is, it is the development of a method for identifying from the characteristics of the amino acid residue sequence of a protein which protein begins to fold first, then which part is folded, and which part is finally folded.

  Assuming that the principle of statistical mechanics is working in protein folding, the stagnation time in that state when each possible partial sequence fragment in the entire amino acid residue sequence of the protein is taken is Suppose that it is determined statistically by the energy value of the substructure fragment and the ambient temperature.

Under this assumption, a partial sequence fragment s (n, i) for n consecutive residues from the i-th amino acid residue of the amino acid residue sequence S of a given protein is selected from the protein three-dimensional structure database. Fit to all possible substructure fragments c (k, n, j) of length n residues of K template protein structures, where k is one of K and n is the fragment length , J represents that this structural fragment starts from the jth amino acid residue) The energy value when the sequence fragment s (n, i) takes the structure of the structural fragment c (k, n, j) The step of calculating E (n, i, k, j) and the standard deviation of the energy values obtained by calculating this energy value E (n, i, k, j) for all possible k, j calculating σE (n, i) and calculating this standard deviation σE (n, i) for all i possible in the array S, and this standard deviation σE (n, i) is the most Big i = I Folding starts from the place where the sequence fragment is located, and the order of protein folding is estimated by assuming that folding proceeds from the corresponding partial sequence region in descending order of σE (n, i) (claim) Item 1).

The partial sequence fragment s consisting of n amino acid residues is assumed to have E (s, c) when taking a partial structural fragment c, and the energy when taking another partial structural fragment c ′ is E (s, c ′), if the temperature of this system is T and the Boltzmann constant is K, the stagnation time in which the substructure fragment takes c and the stagnation in which the substructure fragment c ′ is taken according to the principle of statistical mechanics The statistical ratio of time is exp [(E (s, c) -E (s, c ')) / KT]. When the average energy <E (s, c)> when the partial sequence fragments have various structures is adopted as an estimate of the energy in the random structure when the folding is not in progress, the specific structure c ' The difference between the energy value of the measured value and the estimated energy value of the random structure E (s, c ')-<E (s, c)> is how long the structure c' It becomes a standard of. If this difference is a very large negative value, the sequence fragment should change from a random structure to a c ′ structure in a very short time. Therefore, the standard deviation sqrt [<E (s, c) ² >-<E (s, c)> ² ] of energy values when a variety of structures are taken for a sequence fragment is It is a measure of how much the energy value fluctuates when various structures are taken. If this value is large, the partial sequence fragment should transition to take a structure with low energy relatively quickly. . On the other hand, when this value is small, it is considered that various structures will be tried for a while while the structure is random. Therefore, when a sequence fragment having a possible length of n residues is taken out from the full length of the protein sequence and the standard deviation of the energy value when applied to various structural fragments is calculated for each sequence fragment, each sequence fragment is It can be estimated how fast it will change towards a specific energy optimal structure. In the entire sequence, the place where the fragment sequence energy standard deviation is the largest is considered to be that the structure first transitions from random to a specific good structure fragment, so the place corresponding to this sequence fragment is folded first. Is considered to be the starting point.

  Here, each s (n, i) is applied to c (k, n, j) to calculate the energy value, and in the step of performing this for all k, j, the energy value becomes the smallest , K, j, and, for a fragment with i = I where the standard deviation σE (n, i) is largest, the structural fragment c ( k, n, j) can be predicted to be very close to the structure that the partial sequence s (n, i = I) of the part takes in the final three-dimensional structure (claim 2).

  The three-dimensional structure of a protein is obtained by folding a secondary structure such as a relatively regular α helix or β sheet as described above. Therefore, when protein folding starts, the partial structures that are spatially distant from each other in the random structure stage approach to form a β sheet or an α helical bundle structure. In the folding of these secondary structures, first, in order to finally come close to form a β sheet or an α spiral bundle structure, first, a plurality of partial structures that are close to each other are suitable for their approach or connection in advance. It is necessary to have a shape. For example, the two parts constituting the β sheet must both constitute β strands. In this case, if this part is an α helix, the sheet cannot be formed unless it is rewound and stretched.

  In addition, when two partial structures are close to each other, the main chain structure of the portion connecting the two partial structures needs to allow or encourage the proximity of the two partial structures. No matter how the two structures become stable by making a sheet or bundle, if the part connecting the two parts is a main chain structure that does not allow it, the two structures will not approach, so There is no stabilization. The portion not taking the α-helical or β-sheet (or β-strand constituting this) which is a stable secondary structure is a turn structure or a loop structure with a random coil. These portions have relatively unstable structures because stabilization due to hydrogen bonding or the like is not so remarkable. Therefore, such a portion shows a relatively small standard deviation when the standard deviation of the fragment sequence energy is calculated. In addition, since the β-strand alone is energetically unstable, the sequence fragment of that portion also shows a relatively small standard deviation.

  From this, by calculating the value of the standard deviation of the energy of the sequence fragment, it is predicted that when this value is large, it becomes an α-helical structure, and when it is small, it becomes a β-strand or a loop region. is expected.

  The above is the outline of the energy standard deviation calculation of the sequence fragment for predicting the protein folding start position and the folding order, and the effect.

  What is important for realizing this technique is how to calculate the energy value when the sequence fragment has a specific structure. If this energy value does not sufficiently reflect reality, the prediction of the folding start position and the prediction of the folding order will be extremely inaccurate.

  Therefore, in the step of calculating energy by applying the sequence fragment s (n, i) to the structural fragment c (k, n, j), the sum of the average force field potentials extracted and defined from the protein structure database is defined as The folding order can be predicted by calculating energy (claim 3).

In addition, the average force field potential is the amino acid residue species constituting the pair, the relative arrangement on the sequence (the relative arrangement of the i-th amino acid residue and the j-th amino acid residue is given by ij, and In particular, the relative position of amino acid residues in space is not only the distance between amino acid residues, but also the position and posture of the other viewed from one amino acid residue. By calculating the energy of the structural fragment using the multi-dimensionally expanded average force field potential that also takes into account, it is possible to improve the accuracy of folding order prediction.

  Folding simulation based on the fragment binding method is performed for several proteins, and the order of folding when the correct three-dimensional structure is finally obtained and the analysis based on the standard deviation of the energy values of the sequence fragments are estimated. It was confirmed that the folding order was almost the same.

  Here, an outline of the invention will be described.

  The amino acid residue sequence S of the protein whose structure is to be predicted is given. Assume that the length of S is N. A fragment sequence s (n, i) having a length of n residues is extracted from the i-th amino acid residue of S. From the protein three-dimensional structure database PDB, select as many K structures as possible and use them as template templates. K needs to be 1000 or more in consideration of the stability of statistical processing. The k-th selected structure is C (k). Let c (k, n, j) be a partial structural fragment having a length from the jth amino acid residue to n residues in C (k).

  By applying the array s (n, i) to c (k, n, j), the energy value E (n, i, k, j) by the average force field potential at that time is calculated. This is performed for all k, j, and the standard deviation σE (n, i) of E (n, i, k, j) is calculated. This standard deviation σE (n, i) is calculated for all possible i.

The fragment length n is preferably 5 to 17 in consideration of the size and stability of the secondary structure and the diversity of partial structures in the database. In the standard deviation σE (n, i) obtained as a result, assuming that i = I when taking the largest value, i = I-th of the amino acid residue sequence of the protein whose structure is to be predicted The partial sequence consisting of amino acid residues up to the i = I + n-1th consecutive from the amino acid residues is folded at the earliest stage, and the resulting folded structure is E in the final conformation. It is predicted that the structure is very close to the structural fragment c (k, n, j) when (n, i = I, k, j) takes the smallest value. When the standard deviation σ takes the second largest value when i = I ₂ , on the original sequence S, the sequence fragment s (n, i = I) becomes the sequence fragment s (n, i = as long as it does not overlap with the I _{2), i.e., I 2> I + n-} 1 or both when it is I> I ₂ + n-1 are independent and some parts are the i = I _2, two Folding starts and the fragment sequence is very close to c (k, n, j) where E (n, i = I, k, j) takes the smallest value in the final conformation. It is thought that it is taking.

  In this way, it can be predicted from which part on the array S the folding starts. What is important here is that the same three-dimensional structure template C (k) is always used when calculating the standard deviation of the energy values of the sequence fragments by this method. This is because if a different three-dimensional structure template is used for each fragment, there is no standard for comparing the standard deviation.

  By finding out how protein folding occurs, it is expected to increase the accuracy and speed of protein structure prediction and the design method for proteins that take a given three-dimensional structure. That is, in many conventional structure prediction methods, in the process of optimizing the energy of the three-dimensional structure, the randomly generated three-dimensional structure is randomly changed little by little and the energy value is calculated each time. Although the simulated annealing (SA) method has been used, the random deviation structure is not created by using the present invention, and the initial structure suggests the standard deviation σE (n, i) of each fragment. Therefore, it is possible to fold the part according to the folding order, so that it is possible to obtain the optimum structure faster than random optimization, and to greatly improve the accuracy of the prediction result. It is. However, the present invention does not include the structure optimization algorithm itself such as a priority method when the folding order obtained in the present invention competes in the structure optimization.

  The present invention comprises the following parts.

1) Protein amino acid residue sequence input part for structure prediction (1 in FIG. 1)
Here, the amino acid residue sequence S of the protein whose structure is to be predicted is stored in a sequence in the memory of the calculation system.

2) Protein structure reading part as template (2 in FIG. 1)
Read three-dimensional structure C (k) selected from protein three-dimensional structure database PDB one by one.

3) Standard deviation calculator (3 in Fig. 1)
Every time C (k) is read, all sequence fragments s (n, i) are applied to the partial structural fragment c (k, n, j) of C (k), and the mean force field potential described below is applied. In the energy calculator, E (n, i, k, j) is being calculated. Here, E (n, i, k, j) is set to a value smaller than any previously calculated E (n, i, k, j) in preparation for 3D structure prediction by subsequent structural optimization calculation. In that case, k, j is stored in that case.

4) Energy calculation unit based on average force field potential (4 in Fig. 1)
From the sequence fragment s (n, i) and the partial structure fragment c (k, n, j) sent from the standard deviation calculation unit, the sequence s (n, i) is converted into the partial structure fragment c (k, n, j). The energy value of the mean force field potential when applied to is calculated. The average force field potential is calculated for all pairs of n amino acid residues contained therein, and this partial structural fragment c (k, n, j) is the sequence fragment s (n, i) with the sum The energy value is returned to the standard deviation calculator as a result. FIG. 6 (SEQ ID NO: 1) and FIG. 7 are conceptual diagrams of the average force field potential, and the average force field potential expanded multidimensionally in FIG. 7 is described.

  The flow of calculation is as follows. For the given entire array S, in FIG. 1 2, first, the k loop is rotated, and the selected three-dimensional structure C (k) is read one by one. Rotate the loop for j, and the innermost loop for i. By doing so, it is not necessary to store all the read C (k, n, j), and the calculation of the average force field potential can be speeded up.

  The average force field potential used in the energy calculator (3 in FIG. 1) is a multidimensional extension of the Sippl literature 1 (non-patent literature 1) (FIG. 6). Not only the distance in the three-dimensional structure between amino acid residues, but also the orientation and orientation were divided, and the frequency distribution was obtained in the form of a histogram. Regarding the orientation of amino acid residue B with respect to A, considering the local coordinates where the Cα atom of amino acid residue A is the origin, the N atom is on the XZ plane, and the Cβ atom is on the Z axis, the amino acid residue in this local coordinate is The position coordinates of the Cα atom of the base B are divided by the zenith angle θ and longitude φ when displayed in polar coordinates. Regarding the posture, Eu of the Euler angles (θ, φ, ψ) when rotating so that the amino acid residue B is in the same posture as A was used. This corresponds to the angle formed by the vector from the Cα atom to the Cβ atom of amino acid residue A and the same vector of amino acid residue B. Other Euler angles (φ, ψ) are ignored. However, here, data compression as described in Document 2 (Non-Patent Document 2) is not performed, and a simple histogram is used. The number of divisions is 3 for the zenith angle (however, the zenith on the opposite side of the zenith is not angle-divided, and that portion has a zenith angle of π / 6), 6 for longitude, and 3 for Euler angle θ. It is. As for the distance, the range from 0 to 12 cm is analyzed in divisions of 1 km.

  In selecting candidate structure fragments, the net potential (in the literature, the term net potentials is used) is used, as in the first method of Sippl.

(Example)
In carrying out the present invention, the first thing to do is to observe the process from a random structure to a final three-dimensional structure using a uniquely developed protein three-dimensional structure prediction system (FIG. 2). ).

As a protein three-dimensional structure prediction system, a fragment binding method was used (FIG. 8 (SEQ ID NO: 2), FIG. 9 (SEQ ID NO: 3) ).

  Multi-dimensional average force field potential was used to select candidate structure fragments in the fragment combination method. Also, in the structure optimization by the fragment coupling method, the same multidimensional average force field potential as that at the time of candidate selection was used (FIG. 5 and FIG. 6).

  Using a protein with a known structure (using 1QKK and 1STM registered in the PDB) as a target for structure prediction, various conditions are set so that each protein has a structure close to the X-ray structure registered in the PDB. In other words, we moved the structure prediction system and observed the process of structure optimization.

  Through this observation, it was found that the folding of both proteins progressed through a relatively constant stage in the process from the initial random structure to the X-ray structure (FIG. 3). Because of the fragment bonding method, the secondary structure is formed in a correct shape at a substantially correct position in a relatively early stage. That is, the positions of the α helix and β strand become substantially fixed at a considerably early stage in the optimization process by fragment bonding. Then, at the stage where these are folded to form the entire structure, a folded region having almost the same shape as the final structure is born in a specific region on the sequence, and then this is the core, so that the surrounding main chain is wound, It was observed that the final structure was reached.

  From this observation, it can be seen that there is a part that starts folding at a relatively early stage in the protein sequence, and that part leads to the whole structure.

  Therefore, we thought that it would lead to the elucidation of the folding mechanism to be able to predict which part of the protein sequence first started folding.

  Therefore, at the stage of selecting candidate structural fragments for the sequence fragments from the database, the average value and the standard deviation of the energy values by the average force field potential in the applied structure were obtained for each sequence fragment (Fig. 4 FIG. 5). As a result, it was found that the standard deviation takes various values depending on the sequence fragment, and the variation of the value is large. When a certain sequence fragment has various structures, the energy value is greatly different and the standard deviation is very large. On the other hand, the energy value of another sequence fragment does not change greatly with respect to various structures, and the standard deviation becomes small. Then, as a result of combining with the observation result of the folding process in the folding simulation described above, there is a possibility that the fragment portion where the standard deviation of the energy value is the first portion to start folding.

  The following explains each method in detail.

2) Method of selecting candidate structural fragments for sequence fragments (Fig. 8)
Taking the length of the fragment as W, all sequence fragments of length W are extracted from the N-terminal side from the sequence of the protein of the structure prediction target, and each sequence is extracted from each of 2700 protein tertiary structures selected from the PDB. The candidate structural fragments are extracted in descending order of fitness. The number of candidate structures for each sequence fragment was limited to about 16 to 32. The structure prediction target proteins 1QKK and 1STM are also included in these 2700 proteins, so if you use one with a high degree of precision, each fragment will always have a structure that corresponds to the structure of the target protein itself. Selected as

3) Mean force field potential (Fig. 6 Fig. 7)
The mean force field potential is a multidimensional extension of the above Sippl's (Fig. 6) (Fig. 7). Not only the distance in the three-dimensional structure between amino acid residues, but also the orientation and orientation were divided, and the frequency distribution was obtained in the form of a histogram. Regarding the orientation of amino acid residue B with respect to A, local coordinates (r, θ, φ) are set such that the Cα atom of amino acid residue A is the origin, the N atom is on the XZ plane, and the Cβ atom is on the Z axis. Consider and divide by zenith angle θ and longitude φ. As for the posture, Euler angle θ when rotated so that amino acid residue B is the same as A was used. This corresponds to the angle formed by the vector from the Cα atom to the Cβ atom of amino acid residue A and the same vector of amino acid residue B. The other Euler angles are ignored.

  In selecting the candidate structural fragment, the net potential was used in the same manner as Sippl's first method (Sippl literature), and in the folding optimization, a slight cohesive force was added. As the cohesive force, a very weak potential proportional to the square of the distance within a certain range was used.

4) Fragment combining algorithm (Figure 9)
As a general fragment joining method, the SA method is used. Here, a method obtained by adding elements of a genetic algorithm (hereinafter referred to as GA method) to this is used. Create 16 to 32 random structures, then select one of the candidate structure fragments for that location, and replace the fragment regions (small deformation of the structure, Mutation in the case of GA method), copy at least once every 10 times from one to the other region of less than half of the entire sequence length between two random structures (from GA method) The crossover of the structure is repeated, and it is determined whether to accept the deformation along the temperature parameter according to the SA method. The temperature was changed in the range of 300 ° K to 1200 ° K in absolute temperature with respect to the energy value.

  As a result of observing the process of folding in protein-folding simulation using the fragment binding method, in most simulations, folding progresses first in a specific sequence region, and then other parts begin to fold, which further affect each other. It turned out that the whole structure was folded. Furthermore, this folding process can always reach the final structure through almost the same process if the final structure is similar to the X-ray structure even if various parameters and conditions in the folding simulation are changed. all right. Therefore, in order to estimate where the folding starts from, the standard deviation of the energy value when the fragment sequence was applied to a number of structures was calculated. As a result, it was found that the place where the folding starts and the portion of the sequence fragment having a large standard deviation of energy substantially coincide.

  The following points were found from the examples.

  After all, protein folding is thought to follow the principles of statistical mechanics. Each sequence portion folds towards the lowest energy structure. This is because it follows the principle of statistical mechanics. When a sequence fragment A takes structure X, the energy is E (A, X), and when it takes structure Y, E (A, Y) If E (A, Y) has a smaller (stable) energy value than E (A, X), the time to stay in structure Y is exp [(E (A, X) -E (A, Y)) / KT] times longer. The large standard deviation of the energy value when a sequence fragment has various structures means that the energy of the sequence varies greatly with changes in the structure. Stabilization due to the small size greatly contributes to the stabilization of the entire structure. On the other hand, in a sequence fragment having a small standard deviation of energy value, stabilization of the portion does not contribute much to stabilization of the entire structure. In addition, a sequence fragment having a large standard deviation leads to a stable structure having a low energy in a short time due to the stagnation time when each structure is taken according to the principle of statistical mechanics. On the other hand, a sequence fragment with a small standard deviation takes a long time to reach a stable structure. Therefore, when considering the overall structure of a protein in which a large number of these sequences are connected, folding starts from a partial sequence having a large standard deviation, and each fragment tries to be stabilized by competition.

  It is necessary to bring in another point of view to stabilize the distant part of the array in the vicinity and create a sheet structure or a helix bundle structure (two α-helicals approach in parallel). First, in order for two distant parts on such an array to come close and stabilize, it is encouraged that the partial array sandwiched between the two arrays takes a specific structure to facilitate access. Must be. In that case, it is necessary for the portions to be bonded later to have a structure that facilitates bonding when both are bonded later. In order for the β sheet to consist of sequence fragments A and B, both A and B must be in the form of β strands. Even if that part stabilizes when it finally becomes a sheet, if both companies take an α-helical structure at an early stage of folding, even if these two structures approach each other, they will form a β-sheet It is almost impossible to do both stochastically and statistically. Therefore, the arrangement | sequence fragment which comprises (beta) sheet | seat must have the arrangement pattern which does not become low energy when it becomes (alpha) helix. This is also true for the part of the random structure that connects the α helix and β sheet. Such a portion needs to be arranged so that the energy does not decrease so much even if it becomes an α helix or β strand. As a result, the sequence fragment of the loop region has a small standard deviation of the energy value when it has various structures, and it does not take a specific structure until the end by folding, and remains a random structure. When the other part has reached a stable structure sufficiently, it is folded so as to take the final loop structure so as to be guided to the surroundings for the first time.

  In addition, it is necessary to consider a little more about the phenomenon in which the first fold in the initial stage of folding becomes the nucleus and attracts the surrounding parts, and the nucleus grows. In the structure that became the nucleus, each part is easy to make a nucleus, and the structure that became the nucleus is very stable. Therefore, it takes a long time to stay in that state. That is why the surrounding unstable structure is stabilized by combining with its core part.

  Protein folding is often referred to as origami. Rather, it will be close to origami with glue. If you fold it wrongly and stick it there with glue, it is difficult to remove it. In other words, folding has a folding order as conventionally known. If the order is incorrect, folding will not reach the final stable structure. The order of folding is determined by the rate of change aimed at a specific structure of each partial sequence fragment in the entire sequence. The first folded part is a part that takes very low energy when it becomes the structure, and the standard deviation of the energy of the sequence fragment is large. However, since the structure of the last folded part is not determined until the end, the folding speed to a specific structure is slow. Therefore, “an array with a slow folding speed” in which folding is performed later does not necessarily lead to the most stable structure having the lowest energy. If each part in the whole sequence is competing to be in the lowest energy state, the part that has the strongest tendency for a specific structure will begin to fold first, and others It is a very natural result that this part is influenced by it and determines the final structure.

  Of course, the folding mechanism described here does not work for all proteins. The inside of cells of organisms where protein folding proceeds is a very complex environment. Not only the temperature but also the PH value is different. In addition, electrolytes and lipids are floating in the surroundings, and there are many proteins of the same or different types. If it is “designed” to take the desired structure while avoiding them, it is a mistake to consider only a single fold. If the organism has evolved and the protein has evolved, the protein sequence is adjusted for the function of each protein so that each protein folds according to the folding environment. It has become. Depending on these conditions, some proteins may need to fold very quickly, while others may need to fold very slowly. In addition, there are proteins that need to proceed with folding only when the pH and temperature are specific. It is very difficult to build a theory that incorporates all of these. Therefore, it is currently impossible to construct a universal method for protein structure prediction.

  However, the folding mechanism described here is useful in considering an artificial protein that folds in an ideal environment. The folding mechanism obtained in this example applies the principle of statistical mechanics to the partial sequence fragments in the entire sequence as the basis, and reaches the final structure by competition between the sequence fragments. There is little room for doubt. When designing a protein with a specific target structure, first consider the order of folding to the target structure, and according to the order, the partial sequence fragments should be folded at the speed according to the order toward the final structure. You can do it. The optimal sequence design algorithm can thus be presented as deterministic.

  According to the present invention, a protein folding mechanism, a basic policy of an algorithm necessary for protein structure prediction, and a basic policy of an artificial protein sequence design are obtained as follows.

  To conclude, we summarize in three points.

1) Protein folding mechanism The mechanism of protein folding was revealed. The partial sequence fragments in the amino acid residue sequence of a protein can take various structures, but the stagnation time taking each structure is determined by the energy value of the structure according to the principle of statistical mechanics. In protein folding, partial sequences in the entire sequence compete with each other, and each protein is folded aiming at a structure having the lowest energy value.

2) Protein structure prediction Protein structure prediction is performed as follows. First, for each partial sequence fragment, calculate the standard deviation of the energy value when it takes various structures, and fold toward the optimal structure with the lowest allowed energy in order from the largest standard deviation. Like that. If there is a partial structure that approaches in the middle, the optimization is performed by adjusting each partial structure and the portion that connects the two partial structures so that the energy is lowered by the approach. However, some wild-type proteins may be folded in a special environment, and this method does not always predict the correct three-dimensional structure. However, many water-soluble proteins that are stable in a general environment can be predicted by this method.

3) Artificial protein sequence design In designing the sequence of a protein having the target structure, the folding order to reach the target structure is set, and the partial sequence is designed to have an appropriate folding speed according to the order. To do.

  By making it possible to predict the three-dimensional structure of a protein, it becomes possible to predict the structures of various unknown proteins. This makes it possible to create pharmaceuticals that act on proteins whose sequences are only known, and to estimate interactions based on the three-dimensional structure of proteins and proteins. It will be a big contribution. The present invention forms part of a protein tertiary structure prediction method.

Device configuration diagram Three-dimensional structure and schematic diagram of 1QKK used for folding simulation Conceptual diagram of simulation observation results Graph of energy standard deviation of sequence fragment (in the case of 1QKK) Graph of 3D structure of protein 1 STM and energy standard deviation of sequence fragments Conceptual diagram of mean force field potential (prior art) Conceptual diagram of multidimensional expansion of mean force field potential (prior art) Conceptual diagram explaining selection method of candidate structure fragment in fragment combination method (prior art) Conceptual diagram explaining structure optimization method by fragment combination combining SA method and GA method (prior art)

Claims (4)

In the method of estimating the folding process of a given protein, the order of folding during the process of folding (folding starts from which part of the sequence, folding proceeds in sequence, and finally the final structure is reached. The folding sequence until folding) in such a manner that the partial sequence fragment s (n, i) of n residues consecutive from the i-th amino acid residue of the amino acid residue sequence S of a given protein ) To all possible substructure fragments c (k, n, j) of length n residues of K template protein structures selected from the protein conformation database, where k 1 represents one, n represents the fragment length, j represents that this structural fragment starts at the j-th amino acid residue) sequence fragment s (n, i) represents the structural fragment c (k, n, j) Step to calculate the energy value E (n, i, k, j) when taking the structure And calculating a standard deviation σE (n, i) of energy values obtained by calculating this energy value E (n, i, k, j) for all possible k, j, and A standard deviation σE (n, i) is calculated for all i possible in the array S, and the standard deviation σE (n, i) is folded from a place where there is a sequence fragment where i = I is the largest. A protein folding order prediction method characterized in that it is estimated that folding proceeds from the region of the partial sequence corresponding to the order of σE (n, i) in descending order. When the energy value is the smallest in the step of calculating the energy value by applying each s (n, i) to c (k, n, j) in claim 1 and performing this for all k, j A step of storing k, j, and later, for a fragment with i = I where the standard deviation σE (n, i) is the largest, the structural fragment c with the smallest energy value A partial structure prediction method, wherein (k, n, j) predicts that the partial sequence s (n, i = I) of the part is very close to the structure taken in the final three-dimensional structure. In the step of calculating energy by applying the sequence fragment s (n, i) in claim 1 and claim 2 to the structure fragment c (k, n, j), an average defined by extracting from the protein structure database A protein folding order prediction method characterized by calculating energy as the sum of force field potentials. In claim 3, the mean force field potential is the amino acid residue species constituting the pair, the relative arrangement on the sequence (the relative arrangement of the i-th amino acid residue and the j-th amino acid residue is given by ij, And the relative arrangement of amino acid residues in the space, and in particular, as the relative arrangement of amino acid residues in the space, not only the distance between amino acid residues but also the other A protein folding order prediction method characterized by calculating the energy of structural fragments using multi-dimensional extended mean force field potential considering position and orientation.

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