JP6765040B2 - Method of reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity - Google Patents

Description

In the present invention, 3 of biomolecule data for reconstructing the 3D structure of biomolecule data from binary information as to whether or not subregions of biomolecules such as nucleic acids and proteins are close to each other in 3D space. It relates to a method of reconstructing a three-dimensional structure.

DNA and RNA are macromolecules in which nucleotides are linked in a double-stranded or single-stranded chain. A protein is a macromolecule in which amino acids are linked in a chain.

In general, DNA, RNA, and protein form a three-dimensional structure in a cell by nucleic acid-to-protein, protein-to-nucleic acid, or nucleic acid-protein interaction. The three-dimensional structures of DNA, RNA, and proteins are considered to be closely related to their functions, and are considered to be important information for understanding biological functions and diseases.

An experimental method called chromosome conformation certificate (3C assay) is used to analyze the three-dimensional structure of chromosomes by detecting spatially adjacent sequences. Furthermore, for 3C, methods such as 4C, 5C, and Hi-C have been developed for comprehensively analyzing information on nucleic acid fragments that are spatially close to each other using a microarray or a next-generation sequencer. From the data that measures the spatial distance between chromosomes in these cells, information on whether or not the distance between subsequences in the three-dimensional space is short is often used in order to reconstruct the three-dimensional structure. Be done. However, at present, it is common to use a probabilistic analysis method or auxiliary information on the distance between subsequences to reconstruct the three-dimensional structure (Non-Patent Documents 1 and 2 below). reference).

For three-dimensional structural analysis of proteins and nucleic acids, in addition to analysis using X-ray crystal structure analysis and cryo-electron microscopy, nuclear magnetic resonance (NMR) method is used to interact between nuclei, bond atoms, and electronic states. Is used as a spectrum.

WO2009 / 084524 WO2010 / 01675

Marc A. Marti-Renomm and Leonid A. Mirny, Brigging the resolution gap in strategy modeling of 3D genome organization, PLos12 Annik Lesne, Julien Riposo, Paul Roger, Axel Cournac, and Julien Mosiziconacci, 3D genome resonance from chromosome 14th.m.14 J.-P. Eckmann, S.O. Kamforst, and D. Ruelle, Recurrence plots of dynamic systems, Europhysics Letters 4, 973-977 (1987). N. Marwan, MC Romano, M. Thiel, andJ. Kurths, Recurrence plots for the analysis of complex systems, Physics Reports 438, 2 Yoshito Hirata, Shunsuke Horai, and Kazuyuki Aihara, Reproduction of distance matrices and original time series from recurrence plots and their applications, European PhysicalJournal Special Topics 164, 13-22 (2008) Yoshito Hirata, Kazuyuki Aihara, Random Number Generation Mechanism Following Normal Distribution, Japanese Patent Application No. 2009-548835, CPT / JP2008 / 073389, Patent No. 4947476. (US Patent, Patent No .: US8,438,202B2, Date of Patent: May7, 2013) Yoshito Hirata, Kazuyuki Aihara, Simultaneous reconstruction method of multiple external forces received by one system and its device, CPT / JP2009 / 003355. Yoshito Hirata, Motomasa Komuro, Shunsuke Horai, and Kazuyuki Aihara, Faithfulness of recurrence certificate plots: Mathematics no. 155168 (2015) E. W. Dijkstra, A note on two problems in context with graphs, Numericche Mathematics 1, 269-271 (1959). J. C. Goer, Some distance properties of latent method and vector methods used in multivariate analysis, Biometrika, 53, 325-338 (1966). Masaaki Tiano, Yoshito Hirata, and Hideyuki Suzuki, Reconstruction of driving forces stroke, physics9,Physics9, Physics Letters, Physics Letters Zhijun Duan, Mirela Andronescu, Kevin Schutz, Sean Mcllwain, Yoo Jung Kim, Choli Lee, Hay Shendure, Stanley Fields, C. Anthony Blau, and WilliamS. Noble, A three-dimensional model of the yeast genome, Nature 465, 363- 367 (2010).

Therefore, in the present invention, biomolecular data such as nucleic acids and proteins are 3 using binary information as to whether or not the distance between partial sequences and partial regions is close in a three-dimensional space by a mathematical analysis method. We propose a method for reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity to reconstruct the three-dimensional structure (see Non-Patent Documents 3 and 4 above).

In view of the above situation, the present invention reconstructs a three-dimensional structure of a biomolecule from binary information on whether or not partial sequences of DNA or RNA are close to each other, and the present invention uses the concept of spatial proximity. It is an object of the present invention to provide a method for reconstructing a three-dimensional structure of molecular data.

In order to achieve the above object, the present invention
[1] A method for reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity, from the Hi-C data of the biomolecule by regarding the primary sequence of the biomolecule as the time axis. A step to generate a recurrence plot, a step to generate a distance matrix that gives the distance between any two vertices of the recurrence plot, and time series data for the distance matrix using multidimensional scaling. It is characterized by including a step of reconstructing and a step of reconstructing the three-dimensional structure of the biomolecule from the reconstructed time-series data .

[2] The method for reconstructing the three-dimensional structure of biomolecule data using the concept of spatial proximity described in [1] above is characterized in that the biomolecule is a nucleic acid.

[3] In the method for reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity described in [2] above, the nucleic acid is DNA or RNA.

[4] The method for reconstructing the three-dimensional structure of biomolecule data using the concept of spatial proximity described in [1] above is characterized in that the biomolecule is a protein.

According to the present invention, the following effects can be obtained.

While the conventional method estimates a plurality of plausible models, the method of the present invention is not a probabilistic method but a method based on the reconstruction of the distance between sequences. Therefore, the method of the present invention is used for reconstruction. The three-dimensional structure created has uniqueness and reproducibility. In that respect, the method of the present invention has a great advantage over the existing method.

It is a conceptual diagram of this invention. It is a figure which shows the reconstruction of the three-dimensional structure of yeast. It is an enlarged view of FIG. FIG. 4 (a) shows the Lorenz attractor, FIG. 4 (b) shows the recurrence plot of the Lorenz attractor, and FIG. 4 (c) shows the recurrence plot of the Lorenz attractor at random 1%. As a result of reconstructing the prototype after adding an error, FIG. 4D is a diagram showing the result of reconstructing the prototype by removing 90% of the data from the recurrence plot of the Lorenz attractor. FIG. 5 (a) shows the wrestler attractor, FIG. 5 (b) shows the recurrence plot of the wrestler attractor, and FIG. 5 (c) shows the recurrence plot of the wrestler attractor at random 1%. As a result of reconstructing the prototype after adding an error, FIG. 5D is a diagram showing the result of reconstructing the prototype by removing 90% of the data from the recurrence plot of the wrestler attractor. It is a figure which shows the example (chromosome 2) of the rearrangement of a mouse genome.

The method for reconstructing the three-dimensional structure of biomolecule data using the concept of spatial proximity of the present invention is whether or not any two molecular regions in the biomolecule or sequences are spatially close to each other. The three-dimensional structure of a biomolecule is reconstructed by calculating the distance between two sequences in a three-dimensional space using the binary information of.

Hereinafter, embodiments of the present invention will be described in detail.

The recurrence plot was originally a tool for visualizing time series data. In a two-dimensional plan view, both the vertical axis and the horizontal axis have the same time axis. It can be obtained by comparing the states corresponding to the two time points, and if the distance between the states is short, a point is placed at the corresponding place, and if not, no point is placed.

Since the recurrence plot has converted continuous time series data into binary matrix information indicating whether the distance is short, it may seem that the information about the time series data has dropped considerably. Absent. It is true that the absolute value information of the time series value is lost, but it is known that the outline of the time series data can be restored from the recurrence plot. In particular, when the points are uniformly distributed, a metric space equivalent to the original metric space is reconstructed (see Non-Patent Documents 5 to 8 above).

Restoring the outline of the original time series data from the Recurrence plot is easy. First, think of the Recurrence plot as a graph. In this graph, if the time point of the recurrence plot is the apex and the point is struck at the place corresponding to the two time points, the corresponding vertices are connected by a branch. At this time, the following distances are assigned to the branches.

1- ｜ G _i ∩ G _j ｜ / ｜ G _i ∪ G _j ｜.
Here, G _i is a set of time points corresponding to the points struck by the recurrence plot on the i-th row, and | A | represents the number of elements in the set A. Next, the shortest path between any two vertices on this graph is found. This can be easily done by using, for example, the Dijkstra method (see Non-Patent Document 9 above). Then we get a distance matrix given the distance between any two vertices. By using the multidimensional scaling method for this distance matrix, time series data that reproduces the outline of the original time series data can be reconstructed.

Here, by regarding the primary sequence of the biopolymer as the time axis, the method related to the recurrence plot can be directly applied to the nucleic acid sequence and the amino acid sequence. That is, the three-dimensional structures of DNA, RNA, and protein can be obtained by looking at the top three components when reconstructed using the multidimensional scaling method (see Non-Patent Document 10 above).

Therefore, by using the method of Non-Patent Document 11 and thickening the diagonal line at the center of the corresponding recurrence plot as if it were a line with a width of 3 or more, the information that the continuous sequences are spatially close to each other is always 3 It is possible to construct a method in which the dimensional structure can be reconstructed.

FIG. 2 is a diagram showing a reconstruction of the three-dimensional structure of yeast showing an embodiment of the present invention, in which the horizontal axis is the first constituent molecule and the horizontal axis is the second constituent molecule. FIG. 3 is an enlarged view of FIG. 1, where the horizontal axis is the first coordinate and the horizontal axis is the second coordinate. In addition, the position of the centromere is indicated by a cross.

Here, the method of the present invention was confirmed using the yeast data used in Non-Patent Document 12. Here, the Hi-C data obtained by using four separate cleavage enzymes were integrated to reconstruct the three-dimensional data. FIG. 1 shows the position of the present invention in Hi-C data analysis and an overview of previous studies.

The results are shown in FIGS. 2 and 3. In FIG. 2, among chromosomes 1 to 16, chromosome 12 is shown in black, and the others are shown in gray. A large loop was conspicuous in the rDNA region encoding rDNA located on chromosome 12 shown in black. Further, in FIG. 3, the centromeres are illustrated by black dots, and it can be seen that the centromeres are particularly close to each other. In fact, the cost required to construct the minimum tree tends to be lower when the minimum tree between centromeres is found than when one point is randomly searched on each chromosome to find the minimum tree. It turned out. Previous studies have also suggested that centromeres tend to aggregate and rDNA forms large loops in the budding yeast used to obtain this data, suggesting the validity of the method of the present invention.

In addition, it is generally known that DNA and related factors are densely packed in the nucleus during transcription and replication. In fact, when the space of the chromosomes reconstructed by this method was divided into 64,000 cubes, 26 places where the majority of the chromosomes were densely localized in a single cube were found. Therefore, the method of the present invention can also be used to estimate functional domains such as transcription factories and replication factories.

Another advantage of the present invention is that it is not easily affected by noise. For example, even if the information about whether or not the distance is spatially close by about 1% is incorrect, in the example of the numerical experiment, the correlation between the original distance and the reconstructed distance is maintained at 0.70 or more. The present invention is effective because it is expected that the experimental data for observing the neighborhood points of the molecule in the living body contains false positive noise or cannot cover all the neighborhood points.

(A) to (c) of FIGS. 4 and 5 show an example in which the outlines of the Lorenz attractor and the wrestler attractor are reconstructed from the recurrence plot as toy models, and 1% noise flip on each recurrence plot. The result of the reconstruction after adding is shown.

Furthermore, the present invention is extremely resistant to data loss. In fact, when 50% and 90% of the data were randomly deleted in the toy model and the reconstruction was tried, there was a correlation of 0.96, 0.87 or more, respectively, compared with the data without the deletion. [FIG. 4 (d), FIG. 5 (d)].

It has been pointed out that the data obtained are not comprehensive and coarse due to the technical limitation of detection sensitivity in the observation at the single cell level that is generally performed at present. The present invention is also considered to be superior to such biological data.

It is said that the method of Non-Patent Document 2 can handle up to 1000 points. On the other hand, the examples shown in FIGS. 2 and 3 deal with 111986 points. That is, the present invention can reconstruct the three-dimensional structure of large data with finer resolution. According to the present invention, it is possible to handle size data including human and mouse mammalian genomes without reducing the resolution. FIG. 6 shows an example of mouse genome rearrangement.

To reconstruct the data in FIGS. 1 and 2, the calculation is completed in about 2 days using a program written in MATLAB on a computer equipped with a 2X2.66GHz6-Core Intel Xeon CPU and 64GB of memory. it can.

While the conventional method estimates a plurality of plausible models, the method of the present invention is not a probabilistic method but a method based on the reconstruction of the distance between sequences. Therefore, the method of the present invention is used for reconstruction. The three-dimensional structure created has uniqueness and reproducibility. In that respect, the method of the present invention has a great advantage over the conventional method.

The present invention is not limited to the above examples, and various modifications can be made based on the gist of the present invention, and these are not excluded from the scope of the present invention.

The method for reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity of the present invention is not a probabilistic method but a method based on the reconstruction of the distance between sequences, and is unique and reproducible. It can be used as a method for reconstructing the three-dimensional structure of biomolecular data using the concept of spatial proximity.

Claims (4)

A step of generating a recurrence plot from Hi-C data of the biomolecule by regarding the primary sequence of the biomolecule as the time axis.
A step of generating a distance matrix that gives the distance between any two vertices of the recurrence plot,
Steps to reconstruct time series data using multidimensional scaling for the distance matrix,
A method for reconstructing a three-dimensional structure of biomolecule data using the concept of spatial proximity , which comprises a step of reconstructing the three-dimensional structure of the biomolecule from the reconstructed time-series data. .. Reconstruction method of a three-dimensional structure of a biomolecule data using the concept of spatial proximity of claim 1 prior Symbol biomolecule is a nucleic acid. Reconstruction method of a three-dimensional structure of a biomolecule data using the concept of spatial proximity of claim 2 before Symbol nucleic acid is DNA or RNA. Reconstruction method of a three-dimensional structure of a biomolecule data using the concept of spatial proximity of claim 1 prior Symbol biomolecule is a protein.

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