i<\dZddlZddlZddlZddlZddlZddlm Z m Z ddl m Z m Z mZddlmZddlmZmZejeZdd Zd ZGd d e ZdS)aBond-Angle-Torsion coordinates analysis --- :mod:`MDAnalysis.analysis.bat` =========================================================================== :Author: Soohaeng Yoo Willow and David Minh :Year: 2020 :Copyright: Lesser GNU Public License, v2.1 or any higher version .. versionadded:: 2.0.0 This module contains classes for interconverting between Cartesian and an internal coordinate system, Bond-Angle-Torsion (BAT) coordinates :footcite:p:`Chang2003`, for a given set of atoms or residues. This coordinate system is designed to be complete, non-redundant, and minimize correlations between degrees of freedom. Complete and non-redundant means that for N atoms there will be 3N Cartesian coordinates and 3N BAT coordinates. Correlations are minimized by using improper torsions, as described in :footcite:p:`Hikiri2016`. More specifically, bond refers to the bond length, or distance between a pair of bonded atoms. Angle refers to the bond angle, the angle between a pair of bonds to a central atom. Torsion refers to the torsion angle. For a set of four atoms a, b, c, and d, a torsion requires bonds between a and b, b and c, and c and d. The torsion is the angle between a plane containing atoms a, b, and c and another plane containing b, c, and d. For a set of torsions that share atoms b and c, one torsion is defined as the primary torsion. The others are defined as improper torsions, differences between the raw torsion angle and the primary torsion. This definition reduces the correlation between the torsion angles. Each molecule also has six external coordinates that define its translation and rotation in space. The three Cartesian coordinates of the first atom are the molecule's translational degrees of freedom. Rotational degrees of freedom are specified by the axis-angle convention. The rotation axis is a normalized vector pointing from the first to second atom. It is described by the polar angle, :math:`\phi`, and azimuthal angle, :math:`\theta`. :math:`\omega` is a third angle that describes the rotation of the third atom about the axis. This module was adapted from AlGDock :footcite:p:`Minh2020`. See Also -------- :class:`~MDAnalysis.analysis.dihedrals.Dihedral` class to calculate dihedral angles for a given set of atoms or residues :func:`MDAnalysis.lib.distances.calc_dihedrals()` function to calculate dihedral angles from atom positions Example applications -------------------- The :class:`~MDAnalysis.analysis.bat.BAT` class defines bond-angle-torsion coordinates based on the topology of an atom group and interconverts between Cartesian and BAT coordinate systems. For example, we can determine internal coordinates for residues 5-10 of adenylate kinase (AdK). The trajectory is included within the test data files:: import MDAnalysis as mda from MDAnalysisTests.datafiles import PSF, DCD import numpy as np u = mda.Universe(PSF, DCD) # selection of atomgroups selected_residues = u.select_atoms("resid 5-10") from MDAnalysis.analysis.bat import BAT R = BAT(selected_residues) # Calculate BAT coordinates for a trajectory R.run() After :meth:`R.run()`, the coordinates can be accessed with :attr:`R.results.bat`. The following code snippets assume that the previous snippet has been executed. Reconstruct Cartesian coordinates for the first frame:: # Reconstruct Cartesian coordinates from BAT coordinates # of the first frame XYZ = R.Cartesian(R.results.bat[0,:]) # The original and reconstructed Cartesian coordinates should all be close print(np.allclose(XYZ, selected_residues.positions, atol=1e-6)) Change a single torsion angle by :math:`\pi`:: bat = R.results.bat[0,:] bat[bat.shape[0]-12] += np.pi XYZ = R.Cartesian(bat) # A good number of Cartesian coordinates should have been modified np.sum((XYZ - selected_residues.positions)>1E-5) Store data to the disk and load it again:: # BAT coordinates can be saved to disk in the numpy binary format R.save('test.npy') # The BAT coordinates in a new BAT instance can be loaded from disk # instead of using the run() method. Rnew = BAT(selected_residues, filename='test.npy') # The BAT coordinates before and after disk I/O should be close print(np.allclose(Rnew.results.bat, R.results.bat)) Analysis classes ---------------- .. autoclass:: BAT :members: :inherited-members: .. attribute:: results.bat Contains the time series of the Bond-Angle-Torsion coordinates as a (nframes, 3N) :class:`numpy.ndarray` array. Each row corresponds to a frame in the trajectory. In each column, the first six elements describe external degrees of freedom. The first three are the center of mass of the initial atom. The next three specify the external angles according to the axis-angle convention: :math:`\phi`, the polar angle, :math:`\theta`, the azimuthal angle, and :math:`\omega`, a third angle that describes the rotation of the third atom about the axis. The next three degrees of freedom are internal degrees of freedom for the root atoms: :math:`r_{01}`, the distance between atoms 0 and 1, :math:`r_{12}`, the distance between atoms 1 and 2, and :math:`a_{012}`, the angle between the three atoms. The rest of the array consists of all the other bond distances, all the other bond angles, and then all the other torsion angles. References ---------- .. footbibliography:: N) AnalysisBase ResultsGroup) calc_bonds calc_anglescalc_dihedrals) make_whole)dueDoiFc(t|d|S)aVSorts a list of atoms by mass and then by index The atom index is used as a tiebreaker so that the ordering is reproducible. Parameters ---------- ag_o : list of Atoms List to sort reverse : bool Atoms will be in descending order Returns ------- ag_n : list of Atoms Sorted list c|j|jfSN)massindex)as a/srv/www/vhosts/g4struct/public_html/venv/lib/python3.11/site-packages/MDAnalysis/analysis/bat.pyz%_sort_atoms_by_mass..s'8)keyreversesorted)atomsrs r_sort_atoms_by_massrs" %88' J J JJrc  g}t| t tkrAd} D] t fd jD}|D] t  fd jD}|D]k}t  fd|jD}|D]D}|t j ||g  d}|dur_tdtd Dtdtd |Dtd t tkA|S) a[Constructs a list of torsion angles Parameters ---------- root : AtomGroup First three atoms in the coordinate system atoms : AtomGroup Atoms that are allowed to be part of the torsion angle Returns ------- torsions : list of AtomGroup list of AtomGroup objects that define torsion angles Fc3,K|]}|v|v |VdSr).0rrselected_atomss r z!_find_torsions..sB**JJQn%<%<%<%<%<%<**rc3hK|],}|kr$t|jdkr |vr|v(|V-dS)rN)len bonded_atoms)rra0rr s rr!z!_find_torsions..sc..RAN++a//en,,  -,,, ..rc38K|]}|k|v |v|VdSrr)rra1rr s rr!z!_find_torsions..sJ22GG!u**1;N;N;N;N;N;N22rTzSelected atoms:c"g|] }|jdz Srrrrs r z"_find_torsions..s777117Q;777rzTorsions found:c<g|]}t|jdzSr))listindices)rts rr,z"_find_torsions..s&99914 A &&999rzAdditional torsions not found.) r.r#rr$appendmda AtomGroupprint ValueError) rootrtorsions torsionAddeda0_lista2_lista2a3_lista3r%r'r s ` @@@r_find_torsionsr>sH$ZZN n  E * *  " " B)********G   ......._..."B2222222!#222G &  r2r26F(G(GHHH'--b111'+ 7 8 5 # $ $ $ 77777 8 8 8 # $ $ $ 99999 : : :=>> >U n  E * *V OrceZdZdZdZedZeje ddddfd Z d Z d Z dd Z d ZdZedZdZxZS)BATaCalculate BAT coordinates for the specified AtomGroup. Bond-Angle-Torsions (BAT) internal coordinates will be computed for the group of atoms and all frame in the trajectory belonging to `ag`. .. versionchanged:: 2.8.0 Enabled **parallel execution** with the ``multiprocessing`` and ``dask`` backends; use the new method :meth:`get_supported_backends` to see all supported backends. TcdS)N)serialmultiprocessingdaskr)clss rget_supported_backendszBAT.get_supported_backendss   rz10.1002/jcc.26036z-Bond-Angle-Torsions Coordinate TransformationzMDAnalysis.analysis.bat.BAT) descriptionpathNc ttj|jjfi||_t jdstdtjj dkrtdtdjj Dd d nvrtd j d }jjd kr+tfd |j Ddd }n)tfd |j Ddd }tj||g_t%jj_fdjD_fdjD_djDfdt-tD_t1t3j_tjdjD_tjdjD_tjdjD_tjdjD_||dSdS)aParameters ---------- ag : AtomGroup or Universe Group of atoms for which the BAT coordinates are calculated. `ag` must have a bonds attribute. If unavailable, bonds may be guessed using :meth:`AtomGroup.guess_bonds `. `ag` must only include one molecule. If a trajectory is associated with the atoms, then the computation iterates over the trajectory. initial_atom : :class:`Atom ` The atom whose Cartesian coordinates define the translation of the molecule. If not specified, the heaviest terminal atom will be selected. filename : str Name of a numpy binary file containing a saved bat array. If filename is not ``None``, the data will be loaded from this file instead of being recalculated using the run() method. Raises ------ AttributeError If `ag` does not contain a bonds attribute ValueError If `ag` contains more than one molecule bondsz AtomGroup has no attribute bondsrz$AtomGroup has more than one moleculecBg|]}t|jdk|Sr))r#rJr+s rr,z BAT.__init__..Hs* < < <1#ag,,!*;*;Q*;*;*;rT)rNrz#Initial atom is not a terminal atomc:g|]}|jvr |kr|v|Sr_ag)rr initial_atomselfterminal_atomss rr,z BAT.__init__..YsFTX l**.00 100rc2g|]}|jv |k|SrrN)rrrPrQs rr,z BAT.__init__..ds8TX A,=,=,=,=,=rcvg|]5}jj|jkdd6SrrOr/rnonzerorrrQs rr,z BAT.__init__..rsH   >?TX  ( 1 1 3 3A 6q 9   rc,g|]}fd|DS)cvg|]5}jj|jkdd6SrUrVrXs rr,z+BAT.__init__...vs; F F Fqdh!') 2 2 4 4Q 7 : F F Frr)rr0rQs rr,z BAT.__init__..us>" " "  G F F FA F F F" " " rc:g|]\}}}}t||gSrr)rr%r'r;r=s rr,z BAT.__init__..|s-OOO,.}s8) ) ) 23K  k!n - -) ) ) rcg|] }|d SrUrrags rr,z BAT.__init__.."B"B"BR2a5"B"B"Brcg|] }|d Sr)rr`s rr,z BAT.__init__..rbrcg|] }|d S)r rr`s rr,z BAT.__init__..rbrcg|] }|d S)rLrr`s rr,z BAT.__init__..rbr) superr@__init__universe trajectoryrOhasattrAttributeErrorr# fragmentsr5rrr$n_atomsr2r3_rootr> _torsions_root_XYZ_inds_torsion_XYZ_indsrange_primary_torsion_indicesr.set_unique_primary_torsion_indices_ag1_ag2_ag3_ag4load) rQrarPfilenamekwargs second_atom third_atomr^rR __class__s ` ` @@rrgz BAT.__init__s_B "c4!"+"8CCFCCCtx)) E !CDD D tx! " "Q & &CDD D- < < < < "B"B"BCC M"B"B4>"B"B"BCC M"B"B4>"B"B"BCC M"B"B4>"B"B"BCC   IIh      rctj|jd|jjzftj|j_dS)NrL)dtype)npzerosn_framesrOrmfloat64resultsbatrQs r_preparez BAT._prepares;8 ]A 00 1    rc|jj|jj\}}}nt|jd\}}}||z }||z }t jt jd||}t jt jd||}t jtdtdt jd||t jt jd||t jd||zz }||z } t j | d| d} t j| d} t j | } t j | } t j | }t j | }t j | |z|| z| g| | dg| |z| |z|gg}|||z }t j |d|d}t j|| | ||||gf}t!|jj|jj|jj }t'|jj|jj|jj|jj }t+|jj|jj|jj|jj|jj }||j}d ||j<||z}|tjzdtjzztjz }t j||||f|jj|jddf<dS) NF)inplacei,i->g?rrr )box)rn dimensions positionsr rsqrteinsumarccosmaxminarctan2cossinarraydot concatenaterrvrwrrxrryrsrupirr _frame_index)rQp0p1p2v01v21r01r12a012ephithetacpspctstRzpos2omega root_basedrJanglesr7shifts r _single_framezBAT._single_frames : (:/LRRR%dj%@@@LRR2g2ggbic2233gbic2233y IgsC00g '344)GS#667      #Ij1qt$$ !A$ VC[[ VC[[ VE]] VE]] X2grBw $sBlR"Wb2gr4J K  vvb2g 47DG,,^R#ueS#t)L$MNN  I !4$):N    I  I  I  $     " I  I  I  I  $    6769d23E%!be)4=13  12 2  *AAA-...rc~td||j|||tdt j||j_|jjj|j d|j j zfkrYd|jjjdd|jjjdd|j d|j j zfd }t||jjdd df|j djkrtd |S) aLoads the bat trajectory from a file in numpy binary format Parameters ---------- filename : str name of numpy binary file start : int, optional start frame of analysis stop : int, optional stop frame of analysis step : int, optional number of frames to skip between each analysed frame See Also -------- save: Saves the bat trajectory in a file in numpy binary format zChoosing framesz Loading filerLz%Dimensions of array in loaded file, (r,rz'), differ from required dimensions of ()NzXPosition of initial atom in file inconsistent with current trajectory in starting frame.)loggerinfo _setup_frames _trajectoryrrzrrshaperrOrmr5rnpositionany)rQr{startstopsteperrmsgs rrzzBAT.loadsN$  %&&& 4+UD$??? N###78,,  <  !dmQ9I5I%J J JGL$*1-GG<#)!,GG#'-483C1C!DGGG  V$$ $ L QU #tz!}'= = B B D D L  rcDtj||jjdS)zSaves the bat trajectory in a file in numpy binary format See Also -------- load: Loads the bat trajectory from a file in numpy binary format N)rsaverr)rQr{s rrzBAT.saves! $,*+++++rc $|dd}|dd\}}}|dd\}}}|jjdz } |d| dz} || dzd| zdz} tj|d| zdzd} | |j} d| |j<| | z } | t jzdt jzzt jz } t jgd}t jdd|g}t j|t j |zd||t j |zz g}t j |}t j |}t j|| dg||dggd g}| |}t j |}t j |}t j |}t j |}t j||z| ||zg||z|||zg| d|gg}| |}| |}||z }||z }||z }t j |jjdf}|||j d<|||j d <|||j d<t|j| | | D]b\\}}}}}}}||}||} ||}t j |}!t j |}"t j |}#t j |}$||z }%|%t jt jd |%|%z}%|| z }&|&t jt jd |&|&z}&t j|&|%}'t jd |%|&}(t't jd |(|(zz d })|'|)z }'t j|'|%}*|||*|!z|$z|'|!z|#zz|%|"zz zz||<d|S)a<Conversion of a single frame from BAT to Cartesian coordinates One application of this function is to determine the new Cartesian coordinates after modifying a specific torsion angle. Parameters ---------- bat_frame : numpy.ndarray an array with dimensions (3N,) with external then internal degrees of freedom based on the root atoms, followed by the bond, angle, and (proper and improper) torsion coordinates. Returns ------- XYZ : numpy.ndarray an array with dimensions (N,3) with Cartesian coordinates. The first dimension has the same ordering as the AtomGroup used to initialize the class. The molecule will be whole opposed to wrapped around a periodic boundary. NrL r r)rrrr)rrrrrrg|=)rOrmcopydeepcopyrsrurrrrrrrrpziprqrrcrossr)+rQ bat_frameoriginrrrrrr n_torsionsrJrr7rrrrcosoRomegarrrrReXYZr%r'r;r=angletorsionp3sn_angcs_angsn_torcs_torrv32vpcssnvus+ r Cartesianz BAT.Cartesians,2A2'!neU$QqS>c4X%) !j1n,-:>A NQ,>>?=1z>A+=+?+?!@AA6769d23E%!be)4=Xooo & & XsCo & & XsRVD\\)3cBF4LL6H0HI J JVE]] VE]]BQ<"b!iii@AA ZZ^^ VC[[ VC[[ VE]] VE]] X2gsBG $rBwBG&<sArl K  VVBZZ VVBZZ f  f  f h(!,--&(D  "#&(D  "#&(D  "#69  "E686 6    1 RRc5'RBRBRBVE]]FVE]]FVG__FVG__Fr'C 2729Wc37788 8Cr'C 2729Wc37788 8C#s##B7C--BRWS27]++\::BbB"c""B3V f$rF{V';;cFlJCGG rc|jS)z=The atomgroup for which BAT are computed (read-only property)rNrs rrz BAT.atomsqs xrc:tdtjiS)Nr)lookup)rndarray_vstackrs r_get_aggregatorzBAT._get_aggregatorvsE<+F#GHHHHr)NN)NNN)__name__ __module__ __qualname____doc__%_analysis_algorithm_is_parallelizable classmethodrFr dciter rgrrrzrrpropertyrr __classcell__)rs@rr@r@s/  -1)  [ SY    C * j j j j j  j X   I I I V''''R,,,aaaFXIIIIIIIrr@)F)rloggingwarningsnumpyrr MDAnalysisr2baserrMDAnalysis.lib.distancesrrrMDAnalysis.lib.mdamathr r r getLoggerrrrr>r@rrrrs).HHR ,,,,,,,,LLLLLLLLLL------  8 $ $KKKK(<<<~sIsIsIsIsI,sIsIsIsIsIr