prompt.diffusion

29 - def __init__(self, relax):

30 # Help. 31 self.__relax_help__ = \ 32 """Class for manipulating the diffusion tensor.""" 33 34 # Add the generic help string. 35 self.__relax_help__ = self.__relax_help__ + "\n" + help.relax_class_help 36 37 # Place relax in the class namespace. 38 self.__relax__ = relax

39 40

41 - def copy(self, run1=None, run2=None):

42 """Function for copying diffusion tensor data from run1 to run2. 43 44 Keyword Arguments 45 ~~~~~~~~~~~~~~~~~ 46 47 run1: The name of the run to copy the sequence from. 48 49 run2: The name of the run to copy the sequence to. 50 51 52 Description 53 ~~~~~~~~~~~ 54 55 This function will copy the diffusion tensor data from 'run1' to 'run2'. 'run2' must not 56 contain any diffusion tensor data. 57 58 59 Examples 60 ~~~~~~~~ 61 62 To copy the diffusion tensor from run 'm1' to run 'm2', type: 63 64 relax> diffusion_tensor.copy('m1', 'm2') 65 """ 66 67 # Function intro text. 68 if self.__relax__.interpreter.intro: 69 text = sys.ps3 + "diffusion_tensor.copy(" 70 text = text + "run1=" + `run1` 71 text = text + ", run2=" + `run2` + ")" 72 print text 73 74 # The run1 argument. 75 if type(run1) != str: 76 raise RelaxStrError, ('run1', run1) 77 78 # The run2 argument. 79 if type(run2) != str: 80 raise RelaxStrError, ('run2', run2) 81 82 # Execute the functional code. 83 self.__relax__.generic.diffusion_tensor.copy(run1=run1, run2=run2)

84 85

86 - def delete(self, run=None):

87 """Function for deleting diffusion tensor data. 88 89 Keyword Arguments 90 ~~~~~~~~~~~~~~~~~ 91 92 run: The name of the run. 93 94 95 96 Description 97 ~~~~~~~~~~~ 98 99 This function will delete all diffusion tensor data for the given run. 100 """ 101 102 # Function intro text. 103 if self.__relax__.interpreter.intro: 104 text = sys.ps3 + "diffusion_tensor.delete(" 105 text = text + "run=" + `run` + ")" 106 print text 107 108 # The run argument. 109 if type(run) != str: 110 raise RelaxStrError, ('run', run) 111 112 # Execute the functional code. 113 self.__relax__.generic.diffusion_tensor.delete(run=run)

114 115

116 - def display(self, run=None):

117 """Function for displaying the diffusion tensor. 118 119 Keyword Arguments 120 ~~~~~~~~~~~~~~~~~ 121 122 run: The name of the run. 123 """ 124 125 # Function intro text. 126 if self.__relax__.interpreter.intro: 127 text = sys.ps3 + "diffusion_tensor.display(" 128 text = text + "run=" + `run` + ")" 129 print text 130 131 # The run argument. 132 if type(run) != str: 133 raise RelaxStrError, ('run', run) 134 135 # Execute the functional code. 136 self.__relax__.generic.diffusion_tensor.display(run=run)

137 138

139 - def init(self, run=None, params=None, time_scale=1.0, d_scale=1.0, angle_units='deg', param_types=0, spheroid_type=None, fixed=1):

140 """Function for initialising the diffusion tensor. 141 142 Keyword Arguments 143 ~~~~~~~~~~~~~~~~~ 144 145 run: The name of the run to assign the data to. 146 147 params: The diffusion tensor data. 148 149 time_scale: The correlation time scaling value. 150 151 d_scale: The diffusion tensor eigenvalue scaling value. 152 153 angle_units: The units for the angle parameters. 154 155 param_types: A flag to select different parameter combinations. 156 157 spheroid_type: A string which, if supplied together with spheroid parameters, will restrict 158 the tensor to either being 'oblate' or 'prolate'. 159 160 fixed: A flag specifying whether the diffusion tensor is fixed or can be optimised. 161 162 163 The sphere (isotropic diffusion) 164 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 165 166 When the molecule diffuses as a sphere, all three eigenvalues of the diffusion tensor are 167 equal, Dx = Dy = Dz. In this case, the orientation of the XH bond vector within the 168 diffusion frame is inconsequential to relaxation, hence, the spherical or Euler angles are 169 undefined. Therefore solely a single geometric parameter, either tm or Diso, can fully and 170 sufficiently parameterise the diffusion tensor. The correlation function for the global 171 rotational diffusion is 172 173 ----- 174 1 - tau / tm 175 C(tau) = - e , 176 5 177 ----- 178 179 To select isotropic diffusion, the parameters argument should be a single floating point 180 number. The number is the value of the isotropic global correlation time, tm, in seconds. 181 To specify the time in nanoseconds, set the 'time_scale' argument to 1e-9. Alternative 182 parameters can be used by changing the 'param_types' flag to the following integers 183 184 0: tm (Default), 185 1: Diso, 186 187 where 188 189 1 / tm = 6Diso. 190 191 192 The spheroid (axially symmetric diffusion) 193 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 194 195 When two of the three eigenvalues of the diffusion tensor are equal, the molecule diffuses 196 as a spheroid. Four pieces of information are required to specify this tensor, the two 197 geometric parameters, Diso and Da, and the two orientational parameters, the polar angle 198 theta and the azimuthal angle phi describing the orientation of the axis of symmetry. The 199 correlation function of the global diffusion is 200 201 ----- 202 _1_ 203 1 \ - tau / tau_i 204 C(tau) = - > ci . e , 205 5 /__ 206 i=-1 207 ----- 208 209 where 210 211 c-1 = 1/4 (3 dz^2 - 1)^2, 212 c0 = 3 dz^2 (1 - dz^2), 213 c1 = 3/4 (dz^2 - 1)^2, 214 215 and 216 217 1 / tau -1 = 6Diso - 2Da, 218 1 / tau 0 = 6Diso - Da, 219 1 / tau 1 = 6Diso + 2Da. 220 221 The direction cosine dz is defined as the cosine of the angle alpha between the XH bond 222 vector and the unique axis of the diffusion tensor. 223 224 To select axially symmetric anisotropic diffusion, the parameters argument should be a tuple 225 of floating point numbers of length four. A tuple is a type of data structure enclosed in 226 round brackets, the elements of which are separated by commas. Alternative sets of 227 parameters, 'param_types', are 228 229 0: (tm, Da, theta, phi) (Default), 230 1: (Diso, Da, theta, phi), 231 2: (tm, Dratio, theta, phi), 232 3: (Dpar, Dper, theta, phi), 233 4: (Diso, Dratio, theta, phi), 234 235 where 236 237 tm = 1 / 6Diso, 238 Diso = 1/3 (Dpar + 2Dper), 239 Da = Dpar - Dper, 240 Dratio = Dpar / Dper. 241 242 The spherical angles {theta, phi} orienting the unique axis of the diffusion tensor within 243 the PDB frame are defined between 244 245 0 <= theta <= pi, 246 0 <= phi <= 2pi, 247 248 while the angle alpha which is the angle between this axis and the given XH bond vector is 249 defined between 250 251 0 <= alpha <= 2pi. 252 253 The 'spheroid_type' argument should be 'oblate', 'prolate', or None. The argument will be 254 ignored if the diffusion tensor is not axially symmetric. If 'oblate' is given, then the 255 constraint Da <= 0 is used while if 'prolate' is given, then the constraint Da >= 0 is 256 used. If nothing is supplied, then Da will be allowed to have any values. To prevent 257 minimisation of diffusion tensor parameters in a space with two minima, it is recommended 258 to specify which tensor is to be minimised, thereby partitioning the two minima into the two 259 subspaces along the boundry Da = 0. 260 261 262 The ellipsoid (rhombic diffusion) 263 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 264 265 When all three eigenvalues of the diffusion tensor are different, the molecule diffuses as 266 an ellipsoid. This diffusion is also known as fully anisotropic, asymmetric, or rhombic. 267 The full tensor is specified by six pieces of information, the three geometric parameters 268 Diso, Da, and Dr representing the isotropic, anisotropic, and rhombic components of the 269 tensor, and the three Euler angles alpha, beta, and gamma orienting the tensor within the 270 PDB frame. The correlation function is 271 272 273 ----- 274 _2_ 275 1 \ - tau / tau_i 276 C(tau) = - > ci . e , 277 5 /__ 278 i=-2 279 ----- 280 281 where the weights on the exponentials are 282 283 c-2 = 1/4 (d + e), 284 c-1 = 3 dy^2 dz^2, 285 c0 = 3 dx^2 dz^2, 286 c1 = 3 dx^2 dy^2, 287 c2 = 1/4 (d + e). 288 289 Let 290 291 R = sqrt(1 + 3Dr), 292 293 then 294 295 d = 3 (dx^4 + dy^4 + dz^4) - 1, 296 e = - 1 / R ((1 + 3Dr)(dx^4 + 2dy^2 dz^2) + (1 - 3Dr)(dy^4 + 2dx^2 dz^2) - 2(dz^4 + 2dx^2 dy^2)). 297 298 The correlation times are 299 300 1 / tau -2 = 6Diso - 2Da . R, 301 1 / tau -1 = 6Diso - Da (1 + 3Dr), 302 1 / tau 0 = 6Diso - Da (1 - 3Dr), 303 1 / tau 1 = 6Diso + 2Da, 304 1 / tau 1 = 6Diso + 2Da . R. 305 306 The three direction cosines dx, dy, and dz are the coordinates of a unit vector parallel to 307 the XH bond vector. Hence the unit vector is [dx, dy, dz]. 308 309 To select fully anisotropic diffusion, the parameters argument should be a tuple of length 310 six. A tuple is a type of data structure enclosed in round brackets, the elements of which 311 are separated by commas. Alternative sets of parameters, 'param_types', are 312 313 0: (tm, Da, Dr, alpha, beta, gamma) (Default), 314 1: (Diso, Da, Dr, alpha, beta, gamma), 315 2: (Dx, Dy, Dz, alpha, beta, gamma), 316 317 where 318 319 tm = 1 / 6Diso, 320 Diso = 1/3 (Dx + Dy + Dz), 321 Da = Dz - (Dx + Dy)/2, 322 Dr = (Dy - Dx)/2Da. 323 324 The angles alpha, beta, and gamma are the Euler angles describing the diffusion tensor 325 within the PDB frame. These angles are defined using the z-y-z axis rotation notation where 326 alpha is the initial rotation angle around the z-axis, beta is the rotation angle around the 327 y-axis, and gamma is the final rotation around the z-axis again. The angles are defined 328 between 329 330 0 <= alpha <= 2pi, 331 0 <= beta <= pi, 332 0 <= gamma <= 2pi. 333 334 Within the PDB frame, the XH bond vector is described using the spherical angles theta and 335 phi where theta is the polar angle and phi is the azimuthal angle defined between 336 337 0 <= theta <= pi, 338 0 <= phi <= 2pi. 339 340 341 Units 342 ~~~~~ 343 344 The 'time_scale' argument should be a floating point number. The only parameter affected by 345 this value is tm. 346 347 The 'd_scale' argument should also be a floating point number. Parameters affected by this 348 value are Diso, Dpar, Dper, Da, Dx, Dy, and Dz. Significantly, Dr is not affected. 349 350 The 'angle_units' argument should either be the string 'deg' or 'rad'. Parameters affected 351 are theta, phi, alpha, beta, and gamma. 352 353 354 355 Examples 356 ~~~~~~~~ 357 358 To set an isotropic diffusion tensor with a correlation time of 10 ns, assigning it to the 359 run 'm1', type: 360 361 relax> diffusion_tensor('m1', 10e-9) 362 relax> diffusion_tensor(run='m1', params=10e-9) 363 relax> diffusion_tensor('m1', 10.0, 1e-9) 364 relax> diffusion_tensor(run='m1', params=10.0, time_scale=1e-9, fixed=1) 365 366 367 To select axially symmetric diffusion with a tm value of 8.5 ns, Dratio of 1.1, theta value 368 of 20 degrees, and phi value of 20 degrees, and assign it to the run 'm8', type: 369 370 relax> diffusion_tensor('m8', (8.5e-9, 1.1, 20.0, 20.0), param_types=1) 371 372 373 To select a spheroid diffusion tensor with a Dpar value of 1.698e7, Dper value of 1.417e7, 374 theta value of 67.174 degrees, and phi value of -83.718 degrees, and assign it to the run 375 'spheroid', type one of: 376 377 relax> diffusion_tensor('spheroid', (1.698e7, 1.417e7, 67.174, -83.718), param_types=1) 378 relax> diffusion_tensor(run='spheroid', params=(1.698e7, 1.417e7, 67.174, -83.718), 379 param_types=1) 380 relax> diffusion_tensor('spheroid', (1.698e-1, 1.417e-1, 67.174, -83.718), param_types=1, 381 d_scale=1e8) 382 relax> diffusion_tensor(run='spheroid', params=(1.698e-1, 1.417e-1, 67.174, -83.718), 383 param_types=1, d_scale=1e8) 384 relax> diffusion_tensor('spheroid', (1.698e-1, 1.417e-1, 1.1724, -1.4612), param_types=1, 385 d_scale=1e8, angle_units='rad') 386 relax> diffusion_tensor(run='spheroid', params=(1.698e-1, 1.417e-1, 1.1724, -1.4612), 387 param_types=1, d_scale=1e8, angle_units='rad', fixed=1) 388 389 390 To select ellipsoidal diffusion, type: 391 392 relax> diffusion_tensor('m5', (1.340e7, 1.516e7, 1.691e7, -82.027, -80.573, 65.568), 393 param_types=2) 394 395 396 To select and minimise a spherical diffusion tensor, type (followed by a minimisation 397 command): 398 399 relax> diffusion_tensor('diff', 10e-9, fixed=0) 400 """ 401 402 # Function intro text. 403 if self.__relax__.interpreter.intro: 404 text = sys.ps3 + "diffusion_tensor.init(" 405 text = text + "run=" + `run` 406 text = text + ", params=" + `params` 407 text = text + ", time_scale=" + `time_scale` 408 text = text + ", d_scale=" + `d_scale` 409 text = text + ", angle_units=" + `angle_units` 410 text = text + ", param_types=" + `param_types` 411 text = text + ", spheroid_type=" + `spheroid_type` 412 text = text + ", fixed=" + `fixed` + ")" 413 print text 414 415 # The name of the run. 416 if type(run) != str: 417 raise RelaxStrError, ('run', run) 418 419 # Parameter argument. 420 if type(params) != int and type(params) != float and type(params) != tuple: 421 raise RelaxNumTupleError, ('diffusion parameters', params) 422 if type(params) == tuple: 423 if len(params) != 4 and len(params) != 6: 424 raise RelaxError, "The diffusion parameters argument must either be a number or a tuple of numbers of length 4 or 6." 425 for i in xrange(len(params)): 426 if type(params[i]) != float and type(params[i]) != int: 427 raise RelaxNumTupleError, ('diffusion parameters', params) 428 429 # Time scale argument. 430 if type(time_scale) != float: 431 raise RelaxFloatError, ('time scale', time_scale) 432 433 # D scale argument. 434 if type(d_scale) != float: 435 raise RelaxFloatError, ('D scale', d_scale) 436 437 # Angle scale units argument. 438 if type(angle_units) != str: 439 raise RelaxStrError, ('angle units', angle_units) 440 441 # Parameter types argument. 442 if type(param_types) != int: 443 raise RelaxIntError, ('parameter types', param_types) 444 445 # Spheroid type argument. 446 if spheroid_type != None and type(spheroid_type) != str: 447 raise RelaxNoneStrError, ('spheroid type', spheroid_type) 448 449 # The fixed flag. 450 if type(fixed) != int or (fixed != 0 and fixed != 1): 451 raise RelaxBinError, ('fixed flag', fixed) 452 453 # Execute the functional code. 454 self.__relax__.generic.diffusion_tensor.init(run=run, params=params, time_scale=time_scale, d_scale=d_scale, angle_units=angle_units, param_types=param_types, spheroid_type=spheroid_type, fixed=fixed)

Source Code for Module prompt.diffusion_tensor