JP7257663B2 - BIOPOLYMER 3D STRUCTURE DISPLAY DEVICE, PROGRAM AND DISPLAY METHOD - Google Patents

Description

The present invention relates to a method capable of displaying not only three-dimensional structural features of biopolymers such as proteins, but also fluctuations.

Biomolecules such as proteins and DNA are often in a macromolecular state in which many molecules are bound together. This biopolymer is constantly fluctuating. It is thought that the fluctuation is closely related to the reaction between biopolymers. Therefore, investigating the fluctuations of biopolymers is an important requirement for the analysis of biological functions and drug action mechanisms.

For example, the structure itself (atomic model) of a protein, which is a type of biopolymer, has been obtained by crystallizing the target substance and obtaining it by X-ray analysis and NMR (nuclear magnetic resonance), as technology for mass expression of proteins has been established. ing. The data are registered in PDB (Protein Data Bank) and can be used freely.

The data registered in the PDB are represented by Euclidean coordinates in the order of atoms constituting the biopolymer. Therefore, the positional relationship of each atom constituting the biopolymer can be obtained from this data.

A large amount of software for expressing biopolymers based on this data and displaying them has also been published. For example, the wire frame method, ball & stick method, space filling method, backbone method, ribbon method, molecular surface method, etc. are often used as display methods.

Software for simulating the fluctuation of each atom based on this atomic model has already been released.

On the other hand, a protein analysis support apparatus has been disclosed that enables extraction of amino acid residue portions of proteins that interact with low-molecular-weight compounds in a form that includes more information about the structure of the proteins (Patent Document 1).

Here, an amino acid residue containing each atom of the specified type in the specified compound and the atom of the specified type in the specified protein existing within a predetermined distance range is searched using information in the database (PDB). Then, each amino acid residue obtained as a search result is arranged in the order of the primary sequence of the amino acid residues constituting the specified protein according to a predetermined notation rule to generate a patterned sequence pattern, and this sequence pattern is generated. It can be obtained as information representing the primary sequence structure of the portion containing the amino acid residue portion of the protein that interacts with the designated compound.

JP-A-2000-222421

Biopolymers often have a repeating structure. In many cases, the strain on the repeating structure is the key to the drug efficacy and the function of the biopolymer itself. However, although the atomic model based on the above representation method can display the whole picture of the biopolymer, it is not easy to distinguish the distortion of the repeating structure from the atomic model.

Moreover, the fluctuation of each atom can be obtained by the atomic model of the biopolymer and the fluctuation simulation. However, there are not many methods that can evaluate the fluctuation while overlooking the entire biopolymer. This means that the evaluation of so-called allosterically-acting drugs, in which the other sites are affected by the control of one site, could not be correctly evaluated.

For example, Root-Mean Square Deviation (RMSD) representation, which expresses deviations in atomic coordinates, has been conventionally used as a method of expressing fluctuations. However, it often fails to evaluate the joint fluctuations of biopolymers properly because the part with large deviation is emphasized.

More specifically, the biopolymer three-dimensional structure display device according to the present invention includes:
From the coordinate data of the biopolymer, one atom constituting the biopolymer, or a plurality of atoms that are strongly bonded to each other and maintain their relative positional relationship even when the entire biopolymer fluctuates. an element vector assigning unit that assigns, as an element vector, a vector having a part as an element, starting from the coordinates of the specific element and ending at the coordinates of the other element ;
a unit element vector conversion unit that converts an element vector of any three elements from among the elements into a unit vector;
a characteristic partial circle calculation unit that calculates a characteristic partial circle formed on the unit sphere by the end points of the three unit vectors;
A feature normal vector calculation unit for obtaining a feature normal vector from the center of the unit sphere to the feature partial circle is provided, and the feature normal vector is displayed.

In the biopolymer three-dimensional structure display device according to the present invention, information such as the periodicity of the structure in the biopolymer model and the deviation from the periodicity can be obtained, so that the static structural characteristics of the biopolymer can be obtained. easier to comprehend.

In drug discovery for biopolymers, drug effects have been predicted by static structural analysis of target substances. Therefore, it was not possible to evaluate allosterically acting drugs. Since the biopolymer three-dimensional structure display device according to the present invention can also analyze dynamic changes in biopolymers, it is possible to evaluate the effects (including side effects) of allosterically acting drugs.

FIG. 4 is a wireframe representation of the Helix 1 portion of GPR40. FIG. 4 is a diagram showing a state in which unit element vectors are displayed on a unit sphere (a sphere with a radius of 1); FIG. 4 is a diagram showing a portion of one of the helical coils of the collagen triplex by the display method according to the present invention. FIG. 10 is a diagram showing the distance d from the center O of the unit sphere to the characteristic partial circle obtained and displayed for each element. In the collagen triplex, the result (a) when the vicinity of the portion shown in FIGS. 3 and 4 is displayed in a wire frame, and the Ramachandran plot (b ). It is a figure which shows what drew the unit sphere of FIG. 3 by the Mercator method. Ribbon representation of GFP. FIG. 8 is a diagram showing a part of the β-strand shown in FIG. 7 by the display method of the present invention; PDB-ID: 2ZK6 (referred to as PPARγ (Peroxisome Proliferator-Activated Receptor γ)) is shown by the ribbon method using Euclidean coordinates. FIG. 10 is a diagram showing the fluctuation of the β-strands formed from Nos. 350 to 356 in FIG. 9; It is the figure which made FIG. 10 the Mercator projection and its enlarged view by the display method of this invention. 1 is a conventional view of PPARg and a display according to the present invention; FIG. 4 is a diagram showing changes in q0, which is an angle between unit element vectors, in fluctuations of PPARg. Amino acids in the vicinity of a specific amino acid in FIG. 13 are taken out, and the time change of q0 is displayed. FIG. 10 is a diagram showing fluctuations of end points of unit element vectors from 281 to 290 of PPARg; It is a figure which shows the structure of the display apparatus which can implement the display method which concerns on this invention. 3 is a diagram showing the internal structure of a control unit 12; FIG. FIG. 10 is a diagram showing the flow of data when displaying a fluctuation simulation; 4 is a flow showing processing of the display device according to the present invention. It is a flow which shows the process of a parameter conversion part. This is the result of principal component analysis based on coordinate information from time-series motion simulation of nucleosomes. The nucleosome of FIG. 21 is displayed by the method for displaying a three-dimensional structure of a biopolymer according to the present invention. FIG. 22 is a graph showing changes in color over time of the angle q0 between adjacent unit element vectors for the nucleosomes of FIG. 21. FIG. It is a figure explaining the principle of the method of distinguishing the change and fluctuation of the binding state of amino acids. This is the result of Bayesian inference for a specific amino acid. The results of Bayesian analogy of state transitions for other amino acids are shown. The positions of histone H2A to which the amino acids shown in FIG. 26 correspond are indicated. 2 is a flow showing a process for identifying changes and fluctuations in binding state of amino acids.

A method for displaying a three-dimensional structure of a biopolymer according to the present invention (hereinafter simply referred to as "a display method according to the present invention"), an apparatus, and a program will be described below with reference to drawings and examples. In addition, the following description illustrates one embodiment and one example of the present invention, and the present invention is not limited to the following description. The following description can be modified without departing from the spirit of the invention.

In the display method according to the present invention, by converting the coordinate information of the target biopolymer into a unique parameter, the whole can be easily viewed. Known information may be used as the coordinate information of each atom of the biopolymer.

In the display method according to the present invention, first, an element vector is assigned to each element that constitutes the biopolymer. Here, the term “element” refers to an atom or a group of atoms constituting a biopolymer. Also, the elements need not all have the same number of atoms. In other words, a portion of a single atom and a group of multiple atoms may be mixed.

FIG. 1 is a wireframe representation of the helix 1 portion of GPR40. Here, Cα atoms constituting amino acids are defined as “elements”. In FIG. 1, an element vector is assigned to every three consecutive elements. Element vectors are aa _n , aa _n+1 and aa _n+2 . An element vector may be a vector from the previous element to the next element. Other methods of assigning vectors may also be used.

Next, each element vector is transformed into a unit vector. A unit vector has a magnitude (in this case, length) of 1 and a starting coordinate of zero. An element vector that is made a unit vector is called a "unit element vector".

FIG. 2 shows a state in which unit element vectors are displayed on a unit sphere (a sphere with a radius of 1). The frame and fine dots on the unit sphere are drawn to make the unit element vectors easier to see. Three unit element vectors from the center O of the unit sphere have endpoints on the surface of the unit sphere. Thus, the unit sphere forms a partial circle defined by the endpoints of the three element vectors. This is called a “characteristic partial circle”. In the display method according to the present invention, the unit element vector obtained from the three elements of the biopolymer is represented by this characteristic partial circle.

Next, a normal vector from the center O of the unit sphere to the characteristic partial circle is obtained. This normal vector is called a "feature normal vector v3". The feature normal vector v3 is a parameter representing the feature partial circle. Therefore, it can be said that it represents three element vectors.

The angle formed by aa _n and aa _n+1 is assumed to be θ(theta). Let q0 be the angle between the end points of the unit element vector aa _n and the unit element vector aa _n+1 on the characteristic partial circle. Furthermore, let d be the distance from the center O of the unit sphere to the characteristic partial circle.

The feature normal vector v3 can be represented by x, y, z coordinates. The quaternion of the projection angle q0 on the characteristic partial circle of adjacent unit element vectors is important in the display method according to the present invention. However, at least the feature normal vector v3 should be obtained.

FIG. 3 shows a portion of one of the helical coils of the collagen triplex by the display method according to the present invention. Here, as a method of selecting three elements, three consecutive elements are selected, and a characteristic partial circle and characteristic normal vector v3 are obtained. Then, for the next three elements, three elements shifted from the previous element by one are selected. That is, if the elements (Cα atoms) of this protein are a1, a2, a3, . . . , the first three sets are three elements (a1, a2, a3). And the next three pairs are (a2, a3, a4).

Referring to FIG. 3, the end points of the feature normal vector v3 are connected by a solid line. A dotted line represents a feature circle, and a point on the feature circle indicates each unit element vector. Proteins have many repeating structures, and planes formed by three consecutive element vectors appear periodically. Therefore, in FIG. 3, feature circles are clustered at similar positions. However, if there is distortion, a characteristic partial circle is generated at a position different from the others, such as A, and it can be seen at a glance that there is a distorted portion.

In FIG. 4, the distance d from the center O of the unit sphere to the characteristic circle is obtained and displayed for each element. Referring to FIG. 4, the horizontal axis indicates the element number, and the vertical axis indicates the distance d from the center of the unit sphere to the characteristic partial circle. In the repeated structure, the sizes of the feature circles do not change much. Therefore, all elements are at similar distances from the center O of the unit sphere. However, the characteristic partial circle deviating greatly from it represents the distortion of the original structure. Therefore, a point such as B in FIG. 4 indicates that the position is distorted.

Such information is very difficult to find from Euclidean coordinates. FIG. 5 shows the result of wire frame display of the vicinity of the portion shown in FIGS. A Ramachandran plot (FIG. 5(b)), represented by φ, is shown. In both cases, the arrowed portion is the amino acid portion (Cα atom) of the characteristic circle in FIG.

The wire frame is easy to see for grasping the overall shape, but it is not easy to judge whether or not there is slight distortion in the periodic portion (Fig. 5(a)). In addition, the Ramachandran plot (FIG. 5(b)) does not show this at all. As described above, the display method according to the present invention enables the strain of the biopolymer in a static state to be known. Small strains, especially in periodic structures, can be easily detected.

By the way, since FIG. 3 is still in a state of three-dimensional display using the unit sphere, it is difficult to see the state behind the unit sphere. Therefore, this unit sphere is expanded two-dimensionally. There are several mappings from a sphere to a two-dimensional plane, but they are not particularly limited. However, the Mercator method can display the characteristic subcircle on the unit sphere well. Of course, an orthographic projection, an azimuthal equidistant projection, or the like can be used.

FIG. 6 shows the unit sphere of FIG. 3 drawn by the Mercator method. The reason why the world map is described is that it is displayed by the Mercator method and because it is easy to grasp the latitude and longitude. From near 15 degrees longitude to near 75 degrees longitude, an orbit-like pattern of characteristic partial circles can be seen. A black triangle is the feature normal vector v3, which stably exists near 70 degrees latitude. "v3" is indicated in three black triangles. Of course, the other black triangles are also feature normal vectors v3.

On the other hand, it can be seen that there is a characteristic partial circle C distorted to the southern hemisphere below 0 degrees longitude. This is the characteristic partial circle of FIG. 3A, and it can be seen that the elements on this characteristic partial circle are distorted from the surroundings.

FIG. 7 is a representation of GFP (Green Fluorescent Protein) by the ribbon method. The structure exhibits a β-barrel-like structure with coiled β-strands. This β-strand expands outward from the center. However, there is a slightly recessed part (indicated by an arrow) in the middle from the outside to the inside.

This part is barely discernible with the ribbon method or other display methods. Moreover, it cannot even be expressed in the Ramachandran plot.

FIG. 8 shows part of the β-strand shown in FIG. 7 by the display method of the present invention. FIG. 8(a) shows the end points of the characteristic partial circle and the characteristic normal vector v3 on the unit sphere. FIG. 8(b) is a representation of FIG. 8(a) by the Mercator method.

In FIG. 8, there are three characteristic partial circles, two in the D part (D1, D2) and one in the E part. The feature normal vector v3 is two of D, the first on the opposite side of the feature circle (v3D1) and the second on the same side as the feature circle (v3D2).

Also, the feature normal vector v3 (v3E) is on the opposite side to the feature partial circle of E. Since the β-sheet has a zigzag arrangement of the main chain on a plane, the three element (Ca-Ccarbonyl in the case of β-sheet) vectors are not evenly arranged in the feature circle (as in the case of helices). . As the three main chain vectors align clockwise and counterclockwise from the zigzag arrangement, the feature normal vector v3 is located on opposite sides or on the same side.

Furthermore, the position of the next characteristic partial circle is determined from the degree of warping of the β sheet. If the β-sheet is completely straight, the feature partial circles overlap at the same place, and the feature normal vector v3 goes back and forth. As in GFP, when the degree of warpage changes within the β-sheet, the shift of the characteristic portion circle is greatly deviated. In other words, FIG. 8 shows exactly three amino acids whose β-sheets are not curved.

<Simulation>
Next, the effectiveness of the display method according to the present invention with respect to fluctuations of biopolymers will be shown. If the structure of a biopolymer is known, its fluctuation can be simulated under certain conditions. The result is the coordinates of each atom at each time.

In the display method according to the present invention, it is possible not only to easily specify the positions of atoms that change with time, but also to easily find atoms that change together with a certain atom in the entire biopolymer.

The simulation conditions were as follows. As the structure, PDB-ID: 2ZK6 (referred to as PPARγ (Peroxisome Proliferator-Activated Receptor γ)), whose three-dimensional structure has been solved experimentally, was used. FIG. 9 shows the ribbon method representation in Euclidean coordinates.

A hydrogen atom was added to this structure under standard pH conditions. This structure with added hydrogen atoms is placed in the center of a solvent box created with the TIP3P water model and fully equilibrated at a temperature of 300K and 1 atm, and protein molecule atoms and water molecules within 3A (Angstroms) are excluded. bottom. The size of the box was adjusted so that the shortest distance between the edge of the box and the protein atom was 12 A (angstroms) or more.

Furthermore, an appropriate number of Na ions and Cl ions were replaced with water molecules to make the ionic strength of the solvent 150 mM. At this time, the charge of the system was adjusted to zero. The system is treated under periodic boundary conditions. An Amber-based force field was used for the protein force field.

1000 steps of energy minimization were performed in order to eliminate contacts between atoms that were too close to each other, extra spaces, and the like from the constructed system. Water molecules were treated as rigid bodies in the SELLTE algorithm. Also, protein chemical bonds were treated as rigid bodies in the LINCS algorithm. Electrostatic interactions were calculated using the Particle Mesh Ewald method (PME). The cut-off in real space was 8A (angstream), and the grid spacing in reciprocal space was 1.2A (angstream).

The vdW interaction was handled with the 8A (angstream) cut-off method. After energy minimization, it is sufficient to perform 5000 steps of molecular dynamics simulation with constant number of particles and constant temperature and volume, followed by 50000 steps of molecular dynamics simulation with constant number of particles, constant temperature and pressure (NPT). equilibrated to

The time step width of the molecular dynamics simulation is 2 femtoseconds, and the leap-frog method is used as the time integration algorithm. The Nose-Hoover method was used to control the temperature, and the Andersen method was used to control the pressure. After the NPT molecular dynamics simulation, a production simulation for collecting data was performed for 500 ns. A 310K simulation was performed as a reference. The data are collected every 2 picoseconds for all position coordinates of the system. Gromacs 4.5.5 was used as a molecular dynamics simulation program, and the analysis program attached to gromacs was utilized for data analysis. The DSSP program was used to identify the secondary structure.

FIG. 10 shows the fluctuation of the β-strands formed from 350 to 356 in FIG. This is an orthographic projection of the unit sphere onto two dimensions. In this way, two-dimensional information can be obtained by methods other than the Mercarte projection method. An orthographic projection is a near-real view of the unit sphere. On the other hand, FIG. 10(b) is a two-dimensional image obtained by the azimuthal equidistant projection. FIG. 10(c) shows only the end point of the 349th amino acid unit element vector, and FIG. 10(d) shows only the end point of the 352nd amino acid unit element vector.

Referring to FIG. 10(a), the end point of the unit element vector corresponding to each amino acid fluctuates significantly over time. However, the feature normal vector v3 itself has not changed significantly. In other words, each amino acid merely revolves around the feature normal vector v3 with little change in the relative relationship with each other.

FIG. 11 shows the Mercator projection and its enlarged view. Referring to FIG. 11(a), the feature normal vector v3 from 350 to 356 in FIG. 9 is not very dispersed. FIG. 11(b) is an enlarged view of FIG. 11(a). The position of the point indicates the position of the feature normal vector v3. Also, the size of the point represents the standard deviation of the time variation of the distance d from the center of the unit sphere to the characteristic partial circle. In other words, it indicates that the variations in time change are large. This indicates that the distortion of the helix is large because the characteristic partial circle varies greatly in approaching and separating from the center O of the unit sphere. In FIG. 11(b), it is the 352nd amino acid.

On the other hand, the adjacent 353rd amino acid also has a large standard deviation of d, but the others do not. In other words, among the β-strands from 350 to 356, only 352 and 353 move significantly.

FIG. 12(a) reproduces the ribbon representation of the Euclidean coordinates of PPARg. FIG. 10 is the same view as FIG. 9; FIG. 12(b) shows coordinate movement conventionally performed by the ribbon method. On the other hand, FIG. 12(c) shows the result of the fluctuation by the display method according to the present invention, and expresses the standard deviation of the temporal fluctuation of d for each amino acid as the size of the sphere of each amino acid. Large spheres represent large thermal fluctuations.

Referring to FIG. 12(b), the fluctuations are spread over the entire coordinates, and there are portions in which there are large fluctuations. However, referring to FIG. 12(c), according to the display method of the present invention, some amino acids move relatively well, and other portions move well. It can be seen that it is being dragged and swayed passively.

In this manner, the display method according to the present invention enables the relative movement in the biopolymer to be seen, and the portion that is mainly fluctuating and the portion that is passively fluctuating along with it to be separated. .

FIG. 13 shows changes in q0, which is the angle between the unit element vectors. This simulates how PPARg fluctuates after the ligand of PPARg is separated. The horizontal axis is the simulation time (nsec). The vertical axis is all amino acids (amino acid numbers) of PPARg. A dark-colored portion has a small q0 (the angle between adjacent element vectors among the three selected element vectors is small), and a light-colored portion has a large q0. Since this change is relative, it is necessary to fix the reference amino acid. In FIG. 13, q0 of the 220th amino acid is fixed.

Since FIG. 13 shows the angles between adjacent element vectors in fluctuations of all amino acids, it is difficult to obtain detailed information. However, the circled area clearly changes from light to dark, and the color above it changes from dark to light. This just corresponds to the amino acids in the portion corresponding to 283rd to 288th amino acids.

FIG. 14 shows the temporal change of q0 by extracting neighboring amino acids. It may be considered that the encircled portion in FIG. 13 is enlarged. Referring to FIG. 14, the horizontal axis represents time, and the vertical axis represents the angle (radian) of q0. The q0 of No. 285 is increased and the q0 of No. 286 is decreased. This shows that 285th and 286th approached each other, and it can be seen that the helix broke at this portion when PPARg changed.

In other words, this kind of movement does not indicate that the bond between amino acids fluctuates, but indicates that the bond state has clearly changed. It is thought that it displays an allosteric movement, which is a movement that occurs due to the presence of

FIG. 15(a), 281 to 290, shows the fluctuation state of the end point of the unit element vector. FIG. 15B is an enlarged view of the feature normal vector v3. As in FIG. 11, the position of the point represents the position of the end point of the feature normal vector v3, and the size of the point represents the standard deviation (SD) of the fluctuation magnitude of the feature normal vector v3. In Nos. 285 and 284, the feature normal vector v3 itself also fluctuates greatly.

As described above, by using the display method according to the present invention, the fluctuation state of biopolymers can be viewed macroscopically, and the movement of detailed portions can also be visually grasped.

The display method according to the present invention can be implemented as an apparatus, and can also be implemented as a program for operating the apparatus. FIG. 16 shows the configuration of a display device 10 capable of implementing the display method according to the invention. A display device according to the present invention comprises a control section 12, a memory 12m, an input/output section 16, a display 18, and an input device 20. FIG.

The controller 12 can preferably use an MPU (Micro Processor Unit). The memory 12m stores programs and data for the control unit 12 to operate. The input/output unit 16 receives input signals from the input device 20 for operating the display device 10 and transmits the results calculated by the control unit 12 to the display 18 . Also, the input/output unit 16 can acquire data on the Internet by connecting to an external communication line, and can transmit data on the Internet.

FIG. 17 shows the internal structure of the control unit 12. As shown in FIG. A parameter conversion section 30 and a display processing section 50 are formed in the control section 12 by executing software. The parameter conversion unit 30 includes an element vector assignment unit 31 , a unit element vector conversion unit 32 , a characteristic partial circle calculation unit 33 , a characteristic normal vector calculation unit 34 , and an angular distance calculation unit 35 . The display processing unit 50 also includes a unit sphere display unit 51 , a plane display unit 52 and a statistical processing display unit 53 .

Next, operation of the display device 10 will be described. 19 and 20 show the processing flow. The description will be made with reference to these. The display device 10 first reads the coordinate data Pd of the biopolymer to be displayed (step S102). As the coordinate data Pd, data in which the three-dimensional coordinates of constituent atoms of the biopolymer are shown in the order of bonding can be preferably used. For example, proteins can be obtained from PBD or the like. This may be referred to as a biopolymer data acquisition step.

Next, the parameter conversion unit 30 converts the coordinate data Pd of the biopolymer into parameters suitable for the display method of the present invention (step S104). First, the element vector assigning unit 31 divides the biopolymer into elements and assigns an element vector to each element (step S204). As already explained, the element may be one atom constituting the biopolymer, or a plurality of atoms may be collectively used as the element. For example, a plurality of atoms that are strongly bound together and always retain their relative positional relationship as a single mass even when the entire biopolymer fluctuates can be used as an element.

An element vector is given by calculating a direction vector directed to an adjacent element from the coordinate data Pd, but the element vector may be given according to another rule. The coordinate data Pd becomes vector coordinate data VPd to which an element vector is added by the processing of the element vector assigning unit 31 . This can be called an element vector assignment step.

The unit element vector conversion unit 32 receives the vector coordinate data VPd and converts each element vector into a unit element vector (step S206). A unit element vector is a vector whose starting point is the coordinate center (0, 0, 0) and whose magnitude is 1 in absolute value. The vector coordinate data VPd is converted into unit vector coordinate data UPd by the processing of the unit element vector conversion section 32 . Note that this process may be performed at the same time when the element vector is given in the element vector giving step. This can be called a unit element vector conversion step.

Next, the characteristic partial circle calculator 33 receives the unit vector coordinate data UPd, selects arbitrary three elements, and obtains a characteristic partial circle on the unit sphere from those unit element vectors (step S208). More specifically, the plane formed by the coordinates of the end points of the three unit element vectors cuts the unit sphere and becomes the characteristic partial circle. It should be noted that the plane formed by the coordinates of the end points of the three unit element vectors may be obtained.

How to select the three elements is not limited. As described above, three consecutive elements in the order may be selected while being shifted one by one. Alternatively, one may be skipped or selected for each plurality. Through the processing of the characteristic portion calculator 33, the unit vector coordinate data UPd becomes characteristic circle data CUPd. This can be called a characteristic partial circle calculation step.

The feature normal vector calculator 34 receives the feature circle data CUPd, and obtains the feature normal vector v3 of each feature partial circle from the center of the unit sphere (step S210). The characteristic circle data CUPd is converted into the characteristic normal data PCUPd by the processing of the characteristic normal vector calculation unit 34 . This can be called a feature normal vector calculation step.

The angular distance calculation unit 35 receives the characteristic normal line data PCUPd, and calculates the distance between the plane vectors on the characteristic partial circle projected onto the characteristic partial circle by at least two unit element vectors out of the three unit element vectors forming each characteristic partial circle. angle q0 is obtained (step S212). At this time, the distance d from the unit sphere to the characteristic partial circle is also calculated at the same time. Through the processing of the angular distance calculator 35, the feature normal data PCUPd is converted into quaternion data qPCUPd. This can be called an angular distance calculation step.

The quaternion data qPCUPd includes at least six types of data: coordinate data Pd, unit element vector, feature partial circle, feature normal vector v3, angle q0, and distance d. These data may not exist as one data file, and may exist as separate data files.

As described above, the parameter conversion unit 30 converts the coordinate data Pd into data (parameters) of the characteristic partial circle, the characteristic normal vector v3, the angle q0, and the distance d. If at least the feature normal vector v3 is obtained, it can be considered that the processing of the parameter conversion unit 30 has been performed.

Next, operation of the display processing unit 50 will be described. This corresponds to the display processing in step S106. The display processing section 50 includes a unit sphere display section 51 , a plane display section 52 and a statistical processing section 53 . The unit sphere display unit 51 plots at least one of the characteristic partial circle, the unit element vector, and the characteristic normal vector calculated by the parameter conversion unit 30 on the unit sphere, and converts it into projection two-dimensional data with a fixed viewpoint. . The unit display data MU thus converted is transmitted to the display 18 and displayed. 3 and 8(a) show the unit display data MU by the unit sphere display section 51. FIG. This can be called a unit sphere display step.

The plane display section 52 replaces the state plotted on the unit sphere by the unit sphere display section 51 with the plane data MF. Here, the plane data MF means data developed in a display method such as a Mercator projection, an orthographic projection, or an azimuthal equidistant projection. The plane data MF is also transmitted to the display 18 and displayed. 6, 8(b), 9, 11, and 15 show plane data MF. This can be called a planar display step.

It should be noted that the display processing in step S106 determines whether or not to re-process after display (step S108). Therefore, unit sphere display and plane display can be performed continuously. After step S108, termination determination is made (step S110). If not finished (N branch of step S110), read the coordinate data again (step S102). Otherwise, the process ends (step S112).

The display device 10 according to the present invention can also display fluctuation simulation results. See FIG. In the fluctuation simulation, coordinate data Pdt(n) for each time is output. Here, n is a natural number or an integer. Also, one of the coordinate data Pdt(n) is called a set. That is, the coordinate data Pdt(n) includes multiple sets of coordinate data Pd.

The display device 10 receives these data, and the parameter conversion unit 30 converts each coordinate data Pdt(n) into quaternion data qPCUPd(n). That is, next, the display processing unit 50 displays parameters for each time from the quaternion data qPCUPd(n). When the unit element vector and the feature normal vector v3 are displayed as plane data MF, the display of FIG. 10 is obtained.

Also, if the standard deviation SD of the change in the distance d is used as the point size and displayed as plane data MF, the display of FIG. 11 is obtained. If the horizontal axis represents the time and the angle q0 is displayed for each element, the display shown in FIG. 13 can be created.

Next, another example of analysis using the biopolymer three-dimensional structure display method according to the present invention will be described. The biopolymer three-dimensional structure display method according to the present invention can clearly represent the movement of biopolymers with large molecular weights, and can also show allosteric sites, which are unique linkages for each protein.

FIG. 21 shows the results of principal component analysis based on coordinate information from time-series motion simulation of nucleosomes. Usually, when the coordinate data of proteins are obtained, simulation is almost always performed. The horizontal axis represents the first principal component, and the vertical axis represents the second principal component. 2, 100, .

Note that one frame corresponds to 0.5 ns. Conventional display methods cannot read the movement of the nucleosome core because histone tails move around. Here, the time-series motion simulation of nucleosomes is referred to as observation data.

FIG. 22 shows the movement of the nucleosomes in FIG. 21 by the biopolymer three-dimensional structure display method according to the present invention. FIG. 22(a) shows the distance d from the center of the unit sphere to the characteristic partial circle (see FIG. 2), and FIG. 22(b) shows the angle between the end points of adjacent unit element vectors ( ). The mean value of helix q0 (line) is denoted mq0.

The vertical axis on the right side indicates the average value, which is indicated by a circle in the graph. The vertical axis on the left side represents variance, which corresponds to a bar graph in the graph. Here, the average value is the average from the 1st frame to the 1000th frame. Therefore, it can be said that it is a temporal average value. In both graphs, the horizontal axis is the element number.

A portion with a lower element number corresponds to a histone tail portion, and a region with a higher element number indicates a histone core (helix) portion.

In the histone tail portion, both the distance d to the characteristic portion circle (FIG. 22(a)) and the angle q0 between adjacent unit element vectors (FIG. 22(b)) have large variances, and there are many moving portions. However, it can be seen that even in the Hilton core, which is said to not move much, there is a portion (symbol Mv) in which the variance between adjacent unit element vectors is large and moves well.

In addition, even in the portion of histone tail that is said to move well, the variance is large and even in the portion where the bar graph is extended, the variance of the distance d to the characteristic partial circle and the variance of the angle between adjacent unit element vectors are both There was a portion (marked Ms) that was not large and did not move much. Such a display is impossible with conventional display methods.

In FIG. 23, the vertical axis is the amino acid number of the nucleosome in FIG. 21, and the horizontal axis is the frame (time). The time change of the angle q0 between adjacent unit element vectors is indicated by color change (same as in FIG. 13). As in the case of FIG. 13, it is possible to search from FIG. 23 for locations where adjacent unit vectors show allosteric movement in which the previous connection state changes greatly. For example, the 283rd amino acid and the 265th amino acid do not move relatively from frame 700 (350 ns from the start of the simulation), and as a result, it can be seen that they move together.

However, when the number of amino acids increases as shown in FIG. 21, it is not easy to determine the location where the linkage state changes significantly even if such a display method is performed. This is because the angle q0 between adjacent unit element vectors fluctuates over time, and it may be difficult to visually determine whether the binding state between amino acids has changed or is simply fluctuation.

Therefore, we introduced a method to distinguish between changes and fluctuations in the binding state of amino acids. FIG. 24 shows the principle. The q0 (angle between adjacent unit element vectors) of an amino acid that undergoes an allosteric change due to a change in binding state with adjacent amino acids changes from a true angle A to an angle B at a certain time (a certain frame). On the other hand, what can actually be observed is that the true angle A is fluctuated, and the time average is observed to have a distribution. Here, when the binding state of amino acids changes, the true angle B fluctuates and changes in state, and not only the average value of q0 but also its variance are observed to change.

By applying Bayesian analogy to this state, the time at which the state changed is extracted. The analogous amino acid q0 may be the mean of the observed results. A fluctuation component is generated at the angle q0 by the Markov chain Monte Carlo method (hereinafter referred to as the "MCMC method") to create a distribution. This is called the MCMC model.

Then, the identity of the observation data of the current state and the state one frame before and the MCMC model are obtained by Bayesian analogy, and it is determined that the true angle q0 has changed (the binding state of amino acids has changed: an allosteric change has occurred). I asked for the probability.

FIG. 25 shows the results of Bayesian inference for specific amino acids. The horizontal axis is the frame (corresponding to time), and the right vertical axis is the observation data of the angle q0 between adjacent unit element vectors. The angle q0 is represented by a black circle. The left vertical axis is the probability of state transition by Bayesian analogy, represented by line Lb below the graph.

At frame 350, the observed data change, and there appears to be a change in the mean value that is clearly greater than the variance. At this frame, the probability of state transition by Bayesian analogy is also high, and it can be seen that the binding state of amino acids changed greatly at this frame and allosteric changes occurred.

FIG. 26 shows the results of Bayesian analogy of state transitions for other amino acids. FIG. 26(a) shows that amino acid number 38 has a high probability of state transition at frame 950, indicating that the state transition occurred here. On the other hand, in the observation data at this time, the variance of the angle q0 between adjacent unit element vectors is large, and this change cannot be read visually.

Also, in FIG. 26(b), amino acid number 90 has a high probability of state transition at the same frame 950. FIG. In this case, the variance of q0 is larger than in the case of FIG. 26(a), and this change cannot be read visually. It can be seen that these 38th and 90th amino acids undergo state transitions in the same frame and move in conjunction with each other.

Figure 27 shows the positions of histone H2A to which these relevant amino acids correspond. Amino acid number 38 and amino acid number 90 are separated in coordinate positions. However, it was found that these amino acids are interlocked and undergo state transitions. In this way, the method for displaying the three-dimensional structure of a biopolymer according to the present invention can represent the location of allosteric state transition, which cannot be done by the conventional display method.

FIG. 28 shows a flow of performing the above processing in the biopolymer stereostructure display device and the biopolymer stereostructure display method according to the present invention. This flow can be incorporated into the display processing (step S106) in the main processing of FIG. Also, it can be arranged in the statistical processing unit 53 of FIG. This flow is called state transition search (processing). This flow can be called and executed in the display processing (step S106) of FIG.

Referring to FIG. 28, when state transition search is executed (step S300), an amino acid number is entered (step S302). This may be manually input from an input/output device or the like, or a file containing amino acid numbers to be searched for state transition may be read. Amino acid numbers may cover all amino acids (here, all amino acids in observed data).

Next, the frame t is reset as initial setting (step S304). Here, it is assumed that the first frame starts at frame zero (0). Note that the frame may be read as time. This is because observation data is simulated every 0.5 ns per frame.

Next, P _t (A) is calculated (step S306). The suffix t indicates a frame. In Bayesian estimation, the true parameter A (here the true value of the angle q0 between adjacent unit element vectors), the observed data X, the probabilities of their occurrence P _t (A), P _t (X) and the true parameter A From the probability P _t (X|A) _of the observed data X occurring when .

P _t (A) obtains the mean mu_l and variance σ_l of q0 from frame t ₀ to frame t in the observed data and the mean mu_r and variance σ_r of q0 from frame t+1 to frame t _end , and MCMC generate a distribution of possible values of q0 by modulus. Then, P _t (A) is obtained from the cumulative sum of the probability distribution from frame 0 to frame t and the probability distribution from frame t+1 to frame t _end . This P _t (A) is called the prior probability.

Next, P _t (X) is obtained (step S308). P _t (X) is obtained as the cumulative sum of the left and right probability distributions when q0 of observation data is divided by frame t.

Next, P _t (X|A) is obtained (step S310). This is obtained as the sum of the probability of obtaining the average mu_l of q0 from frame _t0 to frame t in the observed data and the average mu_r of q0 from frame t+1 to frame t- _end .

From P _t (A), P _t (X), and P _t (X|A) calculated as described above, P _t (A|X) at frame t is calculated based on equation (1) ( step S312). This P _t (A|X) is the probability that q0 data can be obtained with the expected mean variance of the true state.

Next, it is determined whether or not the frame is the last frame (t _end ) (step S314). If not (N branch of step S314), the frame number is incremented (step S316) and the process returns to step S306. If it is the final frame (N branch of step S314), the probability from P ₀ (A|X) to P _end (A|X) is displayed.

The lines below the graphs of FIGS. 25, 26(a) and 26(b) represent this probability. This indicates that the probability of change is high. In other words, the change in q0 in other frames is due to fluctuations rather than changes in true q0, meaning that the probability of true q0 is low.

As described above, by using the biopolymer three-dimensional structure display device and the biopolymer three-dimensional structure display method according to the present invention, it is possible to express allosteric movements in the three-dimensional structure of biopolymers, which could not be displayed conventionally. can.

The present invention can be suitably used not only for displaying biopolymer proteins, but also for displaying DNA, RNA, fat, and the like.

10 display device 12 control unit 16 input/output unit 18 display 20 input device

Claims (9)

From the coordinate data of the biopolymer, one atom constituting the biopolymer, or a plurality of atoms that are strongly bonded to each other and maintain their relative positional relationship even when the entire biopolymer fluctuates. an element vector assigning unit that assigns, as an element vector, a vector having a part as an element, starting from the coordinates of the specific element and ending at the coordinates of the other element ;
a unit element vector conversion unit that converts an element vector of any three elements from among the elements into a unit vector;
a characteristic partial circle calculation unit that calculates a characteristic partial circle formed on the unit sphere by the end points of the three unit vectors;
A biopolymer three-dimensional structure display device, comprising: a feature normal vector calculator for obtaining a feature normal vector from the center of the unit sphere to the feature partial circle, and displaying the feature normal vector. reading a plurality of sets of coordinate data for each time of the biopolymer;
2. The biopolymer three-dimensional structure display device according to claim 1, wherein the characteristic normal vector is displayed for each set of the coordinate data. 3. The biopolymer stereostructure display device according to claim 1 or 2, wherein an angle q0 formed between said adjacent unit vectors is obtained, and a probability that the temporal change of said q0 is an allosteric change is obtained by Bayesian analogy. to the computer,
a biopolymer data acquisition step of reading the coordinate data of the biopolymer;
Based on the coordinate data of the biopolymer, one atom constituting the biopolymer, or a plurality of atoms that are strongly bonded and always maintain relative positional relationships as one mass even when the entire biopolymer fluctuates. an element vector assigning step of assigning, as an element vector, a vector having a common portion as an element, starting from coordinates of a specific element, and ending at coordinates of another element ;
a unit element vector converting unit step of converting an element vector of any three elements from among the elements into a unit vector;
a characteristic partial circle calculation step of calculating a characteristic partial circle formed on the unit sphere by the end points of the three unit vectors;
a feature normal vector calculating step of obtaining a feature normal vector from the center of the unit sphere to the feature partial circle;
A program for executing a unit sphere display step of displaying the characteristic normal vector. The biopolymer data acquisition step acquires a plurality of sets of coordinate data of the biopolymer at each time ,
5. The program according to claim 4, wherein said unit sphere display step displays said characteristic normal vector for each of said coordinate data. determining the angle q0 between the adjacent unit vectors;
6. The program according to claim 4 or 5, causing execution of a step of obtaining a probability that the temporal change of q0 is an allosteric change by Bayesian analogy. a step of obtaining coordinate data of the biopolymer;
From the coordinate data, the element is a single atom that constitutes the biopolymer, or a common portion of a plurality of atoms that are strongly bonded and always maintain a relative positional relationship as a single mass even when the entire biopolymer fluctuates. , giving as an element vector a vector having the coordinates of the specific element as the starting point and the coordinates of the other element as the ending point;
making an element vector of any three elements a unit vector;
obtaining a characteristic partial circle formed by the end points of the three unit vectors on the unit sphere;
determining a feature normal vector from the center of the unit sphere to the feature partial circle;
A biopolymer three-dimensional structure display method, comprising the step of drawing the characteristic normal vector. In the step of acquiring the coordinate data, a plurality of sets of coordinate data for each time of the biopolymer are acquired;
8. The method for displaying a three-dimensional structure of a biopolymer according to claim 7, wherein, in the step of drawing said characteristic normal vector, said characteristic normal vector is drawn for each of said coordinate data. determining the angle q0 between the adjacent unit vectors;
9. The biopolymer stereostructure display method according to claim 7 or 8, further comprising the step of determining the probability that the temporal change in q0 is an allosteric change by Bayesian analogy.

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