iAOndZddlZddlZddlZddlmZmZddl m Z dZ dZ d d Z Gd d e ZdS)u HELANAL --- analysis of protein helices ======================================= :Author: Lily Wang :Year: 2020 :Copyright: Lesser GNU Public License v2.1+ .. versionadded:: 2.0.0 This module contains code to analyse protein helices using the HELANAL_ algorithm ([Bansal2000]_ , [Sugeta1967]_ ). HELANAL_ quantifies the geometry of helices in proteins on the basis of their Cα atoms. It can determine local structural features such as the local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. .. _HELANAL: https://pubmed.ncbi.nlm.nih.gov/10798526/ .. [Sugeta1967] Sugeta, H. and Miyazawa, T. 1967. General method for calculating helical parameters of polymer chains from bond lengths, bond angles and internal rotation angles. *Biopolymers* 5 673 - 679 .. [Bansal2000] Bansal M, Kumar S, Velavan R. 2000. HELANAL - A program to characterise helix geometry in proteins. *J Biomol Struct Dyn.* 17(5):811-819. Example use ----------- You can pass in a single selection:: import MDAnalysis as mda from MDAnalysis.tests.datafiles import PSF, DCD from MDAnalysis.analysis import helix_analysis as hel u = mda.Universe(PSF, DCD) helanal = hel.HELANAL(u, select='name CA and resnum 161-187') helanal.run() All computed properties are available in ``.results``:: print(helanal.results.summary) Alternatively, you can analyse several helices at once by passing in multiple selection strings:: helanal2 = hel.HELANAL(u, select=('name CA and resnum 100-160', 'name CA and resnum 200-230')) The :func:`helix_analysis` function will carry out helix analysis on atom positions, treating each row of coordinates as an alpha-carbon equivalent:: hel_xyz = hel.helix_analysis(u.atoms.positions, ref_axis=[0, 0, 1]) Classes ------- .. autoclass:: HELANAL Functions --------- .. autofunction:: helix_analysis .. autofunction:: vector_of_best_fit .. autofunction:: local_screw_angles N)utilmdamath) AnalysisBasec(||dz }tj|j|}tj|\}}}|d}t j|d|}|tjdz kr|dz}|S)a Fit vector through the centered coordinates, pointing to the first coordinate (i.e. upside-down). Parameters ---------- coordinates : :class:`numpy.ndarray` of shape (N, 3) Returns ------- :class:`numpy.ndarray` of shape (3,) Vector of best fit. raxisr) meannpmatmulTlinalgsvdranglepi) coordinatescenteredMt_Musvhvectorrs l/srv/www/vhosts/g4struct/public_html/venv/lib/python3.11/site-packages/MDAnalysis/analysis/helix_analysis.pyvector_of_best_fitrms[--1-555H 9XZ * *Dy}}T""HAq" UF M(1+v . .E ruqy"  Mctj|}tj||}tj|s[gdgdg}tj|s?|r=tj||}tj|s|=tj| |}tj||}tj||j|z }|dd|ddz}||z } tj ||g} tj tj | tj | x} \} } tj| | j| z x}\}}tj tj|dd\}}d|| dk<||dkxxdzcc<tj||tj k<tj|S)a Cylindrical azimuth angles between the local direction vectors, as projected onto the cross-section of the helix, from (-pi, pi]. The origin (angle=0) is set to the plane of global_axis and ref_axis. Parameters ---------- global_axis : :class:`numpy.ndarray` of shape (3,) Vector of best fit. Screw angles are calculated perpendicular to this axis. ref_axis : :class:`numpy.ndarray` of shape (3,) Reference length-wise axis. One of the reference vectors is orthogonal to this axis. helix_directions : :class:`numpy.ndarray` of shape (N, 3) array of vectors representing the local direction of each helix window. Returns ------- :class:`numpy.ndarray` of shape (N,) Array of screw angles. )rrrrrrr rr)r asarraycrossanypopdotrrreshapearrayouterrpnormarccoscliprrad2deg) global_axisref_axishelix_directionsperpnew_reforthonorm_global_sqmag_gproj_g proj_planerefsnorms_ ortho_normcoscos_perp cos_orthoto_perpto_orthos rlocal_screw_anglesr?s.*[))K 8Hk * *D 6$<<899iii(&,, 87 88GKKMM;77D&,, 87 8 HdUK ( (EVK55N Ik#3#5 6 6 GE ]]2q ! !K$7$72$>$> >F!F*J 8T5M " "DH dW]:66EMAz!# $ = = EEC (I "'#r1"5"566GX !HZ1_ X\b #%5HX"%  :h  rrc |dd|ddz }|dd|ddz }tj|}|dd|ddz}tj|dd|dd|z }tj|dd}tj|}tj|}dtjz|z } tj|dd|dd} | j tj| z j } tj | } tj tj | dt| dfj } tj| | j } tj| | j z| d} tjtjtj| dd}tj|d}|dzdd |z zz }tj|dk||dzdz }tjtj|dd| }|j |z j }|dd}|ddxx||ddj zj zcc<|dxx|d|dzzcc<t'|}t)|tj||}|| | |||||||d }|S) aL Calculate helix properties from atomic coordinates. Each property is calculated from a sliding window of 4 atoms, from i to i+3. Any property whose name begins with 'local' is a property of a sliding window. Parameters ---------- positions : :class:`numpy.ndarray` of shape (N, 3) Atomic coordinates. ref_axis : array-like of length 3, optional The reference axis used to calculate the tilt of the vector of best fit, and the local screw angles. Returns ------- dict with the following keys: local_twists : array, shape (N-3,) local twist angle from atom i+1 to i+2 local_nres_per_turn : array, shape (N-3,) number of residues per turn, based on local_twist local_axes : array, shape (N-3, 3) the length-wise helix axis of the local window local_bends : array, shape (N-6,) the angles between local helix angles, 3 windows apart local_heights : array, shape (N-3,) the rise of each local helix local_helix_directions : array, shape (N-2, 3) the unit vector from each local origin to atom i+1 local_origins : array, shape (N-2, 3) the projected origin for each helix all_bends : array, shape (N-3, N-3) angles between each local axis global_axis : array, shape (3,) vector of best fit through origins, pointing at the first origin. local_screw_angles : array, shape (N-2,) cylindrical azimuth angle to plane of global_axis and ref_axis rNr rr )offset??) local_twistslocal_nres_per_turn local_axes local_bends local_heightslocal_helix_directions local_origins all_bendsr,r?)rr(pdotr r*r)r+rr!r nan_to_numtiler"lenrwherediagonalabscopyrr?r ) positionsr-vectors bisectorsbimags adjacent_mag cos_thetatwistsrErFcross_birG zero_vectors bend_theta bend_matrixrHradiiheightsrJorigins helix_axesscrewresultss rhelix_analysisrfsvmin,G wqrr{*I ]9 % %F#2#;+L Yss^Yqrr];;lJI 2q))I Yy ! !F:f%%Lbe)f,x #2# !"" 66H*w}X6669Jz**J726*1555J7KLLNL:z|44J|~%z1J*RYrwz2q'A'ABBCCK+k!444K3 1i#8 9E HY!^U\3->!,C D DEfW\'!B$-<<==G'kF25"o""$$G CRCLLLU3CRC8::==LLL BKKK595b999KKK#G,,J BJx((*@  E %2 " "8  !#  G Nrc deZdZdZdddddddddZ dfd ZddZdZdZdZ dZ xZ S)HELANALa Perform HELANAL helix analysis on your trajectory. Parameters ---------- universe : Universe or AtomGroup The Universe or AtomGroup to apply the analysis to. select : str or iterable of str, optional The selection string to create an atom selection that the HELANAL analysis is applied to. Note that HELANAL is designed to work on the alpha-carbon atoms of protein residues. If you pass in multiple selections, the selections will be analysed separately. ref_axis : array-like of length 3, optional The reference axis used to calculate the tilt of the vector of best fit, and the local screw angles. flatten_single_helix : bool, optional Whether to flatten results if only one selection is passed. split_residue_sequences : bool, optional Whether to split the residue sequence into individual helices. This keyword only applies if a residue gap is present in the AtomGroup generated by a ``select`` string. If ``False``, the residues will be analysed as a single helix. If ``True``, each group of consecutive residues will be treated as a separate helix. verbose : bool, optional Turn on more logging and debugging. Attributes ---------- results.local_twists : array or list of arrays The local twist angle from atom i+1 to i+2. Each array has shape (n_frames, n_residues-3) results.local_nres_per_turn : array or list of arrays Number of residues per turn, based on local_twist. Each array has shape (n_frames, n_residues-3) results.local_axes : array or list of arrays The length-wise helix axis of the local window. Each array has shape (n_frames, n_residues-3, 3) results.local_heights : array or list of arrays The rise of each local helix. Each array has shape (n_frames, n_residues-3) results.local_helix_directions : array or list of arrays The unit vector from each local origin to atom i+1. Each array has shape (n_frames, n_residues-2, 3) results.local_origins :array or list of arrays The projected origin for each helix. Each array has shape (n_frames, n_residues-2, 3) results.local_screw_angles : array or list of arrays The local screw angle for each helix. Each array has shape (n_frames, n_residues-2) results.local_bends : array or list of arrays The angles between local helix axes, 3 windows apart. Each array has shape (n_frames, n_residues-6) results.all_bends : array or list of arrays The angles between local helix axes. Each array has shape (n_frames, n_residues-3, n_residues-3) results.global_axis : array or list of arrays The length-wise axis for the overall helix. This points at the first helix window in the helix, so it runs opposite to the direction of the residue numbers. Each array has shape (n_frames, 3) results.global_tilts : array or list of arrays The angle between the global axis and the reference axis. Each array has shape (n_frames,) results.summary : dict or list of dicts Summary of stats for each property: the mean, the sample standard deviation, and the mean absolute deviation. ))i)rA)rirA)rj)rErHrIrFrKrGrJr?name CArFTc ,tt|jj|t j|}fd|D}g} t||D]\} } t j| j } d} t| dkrYd | }|r&|d t| z }n| j g} tj || D]}t|}| |z } |dkr)tj d | |Etj|d \}}tj|dkrZd t%t&||dk}tj d | || | | |z | | |_tj||_||_dS) N)verbosec:g|]}|S) select_atoms).0runiverses r z$HELANAL.__init__..s'CCC1h++A..CCCrrrz+Your selection {} has gaps in the residues.z Splitting into {} helices. uFewer than 9 atoms found for helix in selection {} with these resindices: {}. This sequence will be skipped. HELANAL is designed to work on at sequences of ≥9 residues.T) return_countsz, zYour selection {} includes multiple atoms for residues with these resindices: {}.HELANAL is designed to work on one alpha-carbon per residue.)superrh__init__rr trajectoryr asiterablezip"group_same_or_consecutive_integers resindicesrPformatwarningswarnr uniquer"joinmapstrappend atomgroupsr r-_flatten)selfrrselectr-rmflatten_single_helixsplit_residue_sequences selectionsr consecutiveraggroupscountermsggngidscountsdup __class__s ` rrwzHELANAL.__init__s" gt%%   (' &   _V,, CCCC CCC  Z00" ?" ?EAr>> V6&1*%%))CS!_$=$=>>CM./5fQnn ""2glW&<#=>>>>/ ?2& 8,, , rrc|d|z}|j|f|ddz}tj|tjS)z.s333RR333rc>g|]}|S))rr)rqnrrs rrsz$HELANAL._prepare..s,OOOAT**4Q*??OOOrc:g|]}dS)rArrqrrs rrsz$HELANAL._prepare..s'#O#O#OAD$9$9$$?$?#O#O#OrcJg|]}|dz |dz f Srrrs rrsz$HELANAL._prepare..s@" " " 67D ! !1q5!a%. 1 1" " " r)r attr_shapesitemsrer,rL)rn_reskeyemptyrs` @r_preparezHELANAL._prepares334?333)//11 & &ICOOOOOOOOE %DL  #O#O#O#O#O#O#O  " " " " ;@" " "  rc|j}t|jD]R\}}t|j|j}|D]\}}|j|}||||<SdS)N)r-) _frame_index enumeraterrfrUr-rre)r_firrervalueattrs r _single_framezHELANAL._single_frames  t// $ $EAr$R\DMJJJG%mmoo $ $ U|C(#Q  $ $ $rcgx|j_}|jdzdz}|jjD]}t j|j|jtj ||zz }t j |dd}| t j t j |gd}t|j|z}g|j_t%t'|jD]}i}|D]} |j| } | |d} t j| || z } | | |dd | dd || <|jj |t'|jdkr-|jr(|d gzD]#} |j| } | d|j| < dSdSdS) NrrCgrD)r, global_tiltsrLrr r)r ddof)r sample_sdabs_devsummary)rerr-sumr,r rrrr(r*rr+r)listrkeysrrangerPrr rSstdr) rtiltsnorm_refaxesr: global_attrs attrnamesrstatsnamerr devs r _concludezHELANAL._concludes,.. !EM1$))++s2L, 5 5D)DM4622 d##h.C'#tS))C LLBIcNN33 4 4 4 4CCC )..0011L@ ! s4?++,, / /AE!  |D)Aw|||++fT!Wt^,, !%a!!!rs0KKZ25 5 5 pxxxxvggggglgggggr