Rotamer libraries

Concept

As previously established in MMM, site-directed labeling is modelled in MMMx based on pre-computed rotamer libraries of the label side groups. Such libraries can be generated with classical atomic force fields via molecular dynamics simulations or Monte Carlo sampling of conformation space. Briefly, the label side group is represented by a moderate number, typically between 100 and 10000, of rotameric states and their associated reference populations for a state that is non-interacting with the protein. Upon attachment to a labelling site, interaction with the protein is computed for a static (ensemble) structure of the latter assuming only non-bonded interaction via a Lennard-Jones potential parametrized in the Universal Force Field (UFF). Flexibility of the protein as well as of the label beyond rotameric states is roughly modelled by an f-factor () that scales van-der-Waals radii of atoms in the underlying force field. A few libraries use an enhanced attraction term, i.e., the attractive part of the Lennard-Jones potential is multiplied by the f-factor and an enhancement factor . The default f-factor is 0.5 and the default enhancement factor is 1.0.

Attachment results in rotation and translation of the rotamer coordinates and in reweighting of populations, assuming a Boltzmann distribution at 298 K. Distributions of properties can then be computed by population-weighted averaging.

A number of features in MMM were used only in method development and have not been in use anymore for years. These features are deprecated in MMMx. The concept of a “library temperature” has been deprecated as well, as libraries computed for the glass transition temperature of the medium have been found to perform worse than those computed for ambient temperature (298 K).

Implementation

The labeling concept is implemented by providing a set of rotamer libraries, a package for generating additional libraries for new labels, and by a function get_label for retrieving attributes of labels, such as distributions of label position and orientation.

Labelling is dynamic and virtual. Dynamic labeling means that a label L at residue R is computed at the time when the user of an entity first tries to retrieve attributes of this label at this particular site. The label attributes are then stored at residue level, whereas no atomic coordinates are generated at entity level (virtual labeling). Explicit coordinates of all atoms are generated only for clash tests, for saving label rotamers to a PDB file, for visualizing the label in all-atom graphics, or when requested. Once computed, the explicit coordinates are stored in the atom coordinate array of the entity, while their indices are stored in the labels field of the labelled residue.

The following chemical modifications are implicit (d on need to be performed before labeling):

• mutation of any amino acid to cysteine or an unnatural amino acid for labeling

• conversion of uracil to 4-thiouracil

• conversion of phosphates to thiophosphates

The get_label function

Use this function if you want to label a residue with a particular label or want to retrieve attributes of a previously computed label.

argsout = get_label(entity,label,attributes)
[argsout,exceptions] = get_label(entity,label,attributes)
argsout = get_label(entity,label,attributes,address)
[argsout,exceptions] = get_label(entity,label,attributes,address)

Parameters

• entity - entity in MMMx:atomic format

• label - label name

• attributes - either a string (see table below) or a cell array of strings

• address - MMMx residue address

Returns

• argsout - output arguments (M-element cell array for a single attribute)

• exceptions - error message (1-element cell array)

Either a rotamer library for label must be registered with MMMx (see below) or the label name must be atom.<atname>, where <atname> is an existing atom name for this residue.

Requesting several attributes for the same site (residue) simultaneously can lead to a significant speedup in large entitities. The gain in speed may be very large if the labels were already precomputed. To do this, arrange all attributes in a cell of strings and split the output cell array:

site = sprintf('{%i}%s',conformer_number,residue);
[argsout,entity,exceptions] = get_label(entity,label,{'positions','populations'},site);
positions = argsout{1}{1};
populations = argsout{2}{1};

Attributes

Variable	Explanation	Type
info	rotamer library information	struct
info.tlc	MMMx internal three-letter code	string
info.class	label class, for instance nitroxide	string
info.smiles	SMILES string representing label structure	string
info.f_factor	f-factor and attraction enhancement factor	(1,2) double
info.ref_pop	reference populations for R rotamers	(R,1) double
info.site	site address	string
part_fun	attachment partitition function	double
potentials	attachment potentials (J/mol)	(R,1) double
torsion	T sidechain torsions for R rotamers	(R,T) double
orientations	Euler angles of molecular frame	(R,3) double
populations	populations for R rotamers	(R,1) double
positions	positions for R rotamers	(R,3) double
numbers	numbers of the rotamers in the library	(R,1) int
coor	full atom coordinates of R rotamers	(R,1) cell
affine	affine matrix that transforms from the standard frame to the site frame	(4,4) double

Note that SMILES strings for nitroxides tend to be interpreted as the corresponding hydroxylamines by some programs, notably by ChemDraw. For libraries that contain several stereoisomers, the SMILES string refers to only one of them.

The attribute orientations can be used for simulating orientation selection in pulsed dipolar spectroscopy for spin labels or averaging for FRET chromophores. In order to compute unit vectors along the axes of the label molecular frame in the entity frame (direction cosine matrix DCM, the unit vectors are matrix rows) for rotamer , use the code (example):

entity = get_pdb('2lzm'); % load structure of T4 Lysozyme with ID 2lzm from PDB server
[argout,exceptions] = get_label(entity,'mtsl','orientations','(A)131'); % get MTSL label orientation at residue 13
orientations = argout{1}; % extract from cell output
r = 1;
DCM = Euler2DCM(orientations(r,:)); % compute direction cosine matrix

Set of libraries

MMMx uses a single type of rotamer libraries, built by hierarchical clustering of Monte-Carlo generated conformer ensembles. Ensemble generation assumes torsion potentials and the non-bonded interaction potential of UFF.

For the following labels, rotamer libraries are provided with MMMx:

Label	Synonyms	Class	Attachment	Rotamers
R1A	mtsl, mtssl	nitroxide	cysteine	216	1
R7A	br-mtsl, br-mtssl	nitroxide	cysteine	216	1
V1A	v1	nitroxide	cysteine	72	1
IA1	ia-proxyl	nitroxide	cysteine	108	1
BAS	basl	nitroxide	cysteine	240	1
MA1	ma-proxyl	nitroxide	cysteine	108	2.0
DZD	dzd	nitroxide	cysteine	216	1
DZC	dzc	nitroxide	cysteine	216	1
GDI	iag	nitroxide	cysteine	2461	2.0
GDM	mag	nitroxide	cysteine	1367	2.0
TUP	iap-4tu, iap-thiouracil	nitroxide	4-thiouracil	72	1
TUM	mts-4tu, mts-thiouracil	nitroxide	4-thiouracil	192	1
RTT	r5-tpt	nitroxide	5’-thiophosphate	576	1
R5T	r5-tp	nitroxide	thiophosphate	360	1
R5P	r5p	nitroxide	5’-thiophosphate	2048	1
R3P	r3p	nitroxide	3’-thiophosphate	512	1
K1H	HF-K1	nitroxide	unnatural aa	288	1
HO4	HO4451	nitroxide	unnatural aa	1024	1
HO5	HO5223	nitroxide	unnatural aa	1024	1
NC1	cNox@Tyr	nitroxide	tyrosine	128	1
NX1	lNox@Tyr	nitroxide	tyrosine	256	1
CNR	CNC-NO	nitroxide	cofactor	144	1
GMO	dota-gd	gadolinium	cysteine	648	1
GTO	dtpa-gd	gadolinium	cysteine	2430	1
GBH	br-py-do3a	gadolinium	cysteine	180	1
GBM	br-py-do3ma	gadolinium	cysteine	180	1
M8D	m8-dota-gd	gadolinium	cysteine	1944	1
GPM	gpymi-MTA	gadolinium	cysteine	432	1
TMT	tormyshev-trityl	trityl	cysteine	3888	1
A55	AlexaFluor555, AF555	chromophore	cysteine	1024	1
A64	AlexaFluor647, AF647	chromophore	cysteine	1024	1
HCU	dHis-Cu	histidine	any amino acid	12	1

Label names (three-letter codes) and synonyms are case-insensitive. Note that gadolinium labels are sufficiently good approximations for other lanthanide labels with the same ligand, for instance, for pseudo-contact shift (PCS) and paramagnetic relaxation enhncement (PRE) computations.

---

Rotamer library format

Rotamer libraries are stored in a binary Matlab format as a struct variable rot_lib. The fields are defined as follows:

Field	Content	Type
tlc	three-letter code	string
synonyms	S synonyms for the label name	(1,*S*) cell string
SMILES	SMILES string defining the structure	string
rotamers	information on R rotamers (index r)	(1,*R*) struct
rotamers(r).coor	Cartesian coordinates of A atoms/rotamer	(A,3) double
rotamers(k).torsion	values of T torsion angles for R rotamers	(R,T) double
elements	atomic numbers for A atoms	(A,1) uint8
populations	R populations for the non-attached rotamers	(R,1) double
position	P atom numbers and densities that define the label position	(P,2) double
attachment	structure element to which the label can be attached, for instance peptide	string
side_chain	first side chain atom numer, for instance 9 for a CB atom in position 9	ìnt
f_factor	“forgive” factor and attraction enhancement	(1,2) double
atom_tags	A atom names	(1,*A*) cell string
std_frame	atoms that define the standard frame for attachment: origin, atom on x axis, atom in xy plane	(1,3) int
std_frame_atoms	atom types of the standard frame	(1,3) cell string
mol_frame	atoms that define the label molecular frame: origin, atom on x axis, atom in xy plane	(1,3) int
mol_frame_atoms	atom types of the standard frame	(1,3) cell string
class	label class, for instance nitroxide	string
chi_def	definition of T torsion angles	(T,4) int
connect	bonding information for up to B bonds for A atoms	(A,B) int
attach_forcefield	force field for protein attachment, usually UFF_Towhee	string
B_factors	pseudo-temperature factors for N atoms in R rotamers	(N,R) double
method	method for library generation. for instance MMM_Monte_Carlo	string
gen_forcefield	force field used in library generation for instance UFF_Towhee	string
types	A atom type numbers for the used force field	(A,1) uint16
solvation	solvation assumed in library generation, usually none	string
prerun	number of trials in a prerun of the MMMx native UFF Monte Carlo rotamer library generator	int
suppress_H	true if hydrogen atoms were neglected in library generation, not recommended	boolean
threshold	thresholds for confermer acceptance in the MMMx native generator	double
min_strain	minimum strain energy (kcal/mol) encountered	double
maxdist	maximum distance of the label position from the backbone (CA atom or origin of attachment) frame	double
color	RGB color triplet (fraction) for display	(1,3) double
radius	sphere radius (Angstroem) corresponding to 100% rotamer population for display	double
ff	force field parameters for attachment	struct
ff.LJ_r	van-der-Waals radii for attachment indexed by atomic number	(1,103) double
ff.LJ_D	Lennard-Jones potentials for attachment indexed by atomic number	(1,103) double
ff.types	atom type tags for force field	string

The pseudo-temperature factors relate to the variation of atom positions within the cluster of conformers that was projected onto a single rotamer.