GenCoords Models
The following parametric models are defined for use with the GenCoords program. The parameters listed here are specified at run time as param1, param2, ..., paramNp in an Ellipsoid.model file.
frenetHelix: Each building block consists of nS helical stacks of nL ellipsoids. Each set of nL ellipsoids is arranged on its own helical space curve defined by pitchlength L and R. The same L and R are used for all the stacks. The resulting nS helical groups are each rotated about the common helical axis (z-axis) to be phi degrees apart. In addition, each of the helical stacks is helically translated relative to their neighbours, which corresponds to a displacement sReg along the helical space curve.
The spacing of the ellipsoids is uniform and is controlled by the parameter spacer which multiplies a standard constant.
Multiple copies of the building blocks are then stacked along the vertical axis. Each is rotated about the vertical axis such that the corresponding ellipsoids lie on the same helical space curve. The net result is that each ellipsoid is pointing towards the helical axis along the radial vector, which means that each ellipsoid is parallel to the radial vector of the frenet frame for it's helical space curve.
The handedness is defined by chirality +1 = right handed, -1 = left handed. The attractive and repulsive potential around each site is defined by aa, ab, ac and ra, rb, rc respectively. The parameters in order are: aa, ab, ac, ra, rb, rc, L, R, sReg, phi, Chirality, nS, nL, spacer
displacement: An ellipsoid is placed at the origin and a second is placed at a vector R defined in the basis of the principle axis of the first ellipsoid. The second ellipsoid is then rotated by three euler angles (alpha, beta and gamma). This uses the ZYZ convention so alpha about Z axis, Beta' about the Y axis and then gamma about the Z axis again. The resulting pair of ellipsoids are then stacked vertically space by an amount V until there are nE/2 pairs in a rigid cluster. Then the rigid clusters are spaced vertically with a displacement of nE * V/2. Parameter order: aa, ab, ac, ra, rb, rc, R_x, R_y, R_z, alpha, beta, gamma, V
verticalHelix: This is the same as the frenetHelix, except that once the building block has been defined, they are spaced vertically with no rotation. The parameter order is: spacer, aa, ab, ac, ra, rb, rc, L, R, sReg, phi, Chirality, nS, nL
distance: One ellipsoid is placed at the origin and the other a distance d away. The ellipsoids are then oriented so that their point of closest approach of the b vectors of their body frames are a distance s apart and a distance U1 from the first ellipsoid and U2 from the second. Each ellipsoid is then rotated about it's b-axis by an angle gamma1 and gamma2. Each cluster is then stacked along it's Z axis by an amount V with no additional rotations. Parameter order: aa, ab, ac, ra, rb, rc, d, s, U1, U2, gamma1, gamma2, V
angle: One ellipsoid is placed at the origin with its b-vector pointing along the y axis. It is rotated about a vertical axis by beta1 and about its b-axis by an amount gamma1. The second ellipsoid is placed at the point d on the x-axis. It is rotated by an angle beta2 about the z-axis, and angle alpha about it's a-axis and by an angle gamma2 about it's b-axis. beta2 and gamma2 are defined using db and dg respectively where db = beta2-beta1 and the same for gamma. This makes it more obvious what the shape will be E.g. can set db to be -beta1 to get symmetries and so on. The building blocks are stacked vertically spaced by a distance V. Parameter order: ab, ac, ra, rb, rc, d, alpha, beta1, db, gamma1, dg, spacer, V
anglerot: The same as angle except that the entire building block is rotated as it is stacked using the euler angles calpha, cbeta and cgamma. Parameter order: ab, ac, ra, rb, rc, d, alpha, beta1, db, gamma1, dg, spacer, V, calpha,cbeta,cgamma.
angleNudge: The same as angle except that each building block is offset by an amount nudgeX, nudgeY, nudgeZ in the x,y and z directions in units of ac, ab and aa respectively. The further up the stack the building block, the greater the nudge. Parameter order: ab, ac, ra, rb, rc, d, alpha, beta1, db, gamma1, dg, spacer, V, nudgeX, nudgeY, nudgeZ.
pdb: The same as angle except the building blocks are placed at the positions indicated in the file coords.in. Each building block is rotated by the angle-axis vector also defined in coords.in. The distances between the closest points of approach of each body-axis vector are output. Parameter order: ab, ac, ra, rb, rc, d, alpha, beta1, db, gamma1, dg, spacer, V
coordsModel: Identical to pdb except that the distances are output.
figureGenerator: Same as angle except that the building blocks are placed on a helical curve with vertical twist per block of b radians and radius R, with z-axis rotation phi and a corkscrew displacement of sReg. There are nF filaments of building blocks produced. PArameter order: ab, ac, ra, rb, rc, d, alpha, beta1, db, gamma1, dgamma, dT, R, b, phi, sReg, nF