FRET based conformational sampling

FRET-based conformational sampling

Overview

ChiSurf can be used to sample the conformational space of proteins in agreement with experimental FRET data. For that, proteins are represented using the dihedral angles of the peptide backbone as internal coordinates. For the peptide backbone, an atomistic representation is used. The peptide backbone is represented by N, C, O, and Cα atoms in addition to the H atoms that bridge the O and the N atoms to form beta-sheets and alpha helices as secondary structure elements. The side-chains are represented by a single centroid that is positioned at the side-chains center of mass.

The proteins conformational space is sampled in a Monte-Carlo (MC) scheme. In the MC scheme, the dihedral angles of the previous conformation are randomly perturbed to yield a conformation for the following MC step. In each MC step, a set of AA is randomly chosen, and their dihedral angles are randomly perturbed. These AAs are chosen at each iteration from a user-specified “move-map”. The move-map specifies for all AA in the peptide chain the probability for being selected in a random perturbation (move). Following a perturbation, the cartesian coordinates of the atoms and the side-chain centroids are calculated. Next, for the new set of dihedral angles, an user-specified energy function is evaluated. The energy function is created by a weighted linear combination of a set of predefined energy functions and may consider statistical potentials, excluded volumes, physics-based potentials, or experimental potentials in a joint energy term. The new value of the energy function, E_{i+1}, is compared to Ei the previous value of the energy function. A move is accepted if E_{i+1} is smaller than E_i or if:

$$exp((E_{struct,i}-E_{struct,i}+1)/kT)\$\$ > r$$

where r is a random number in the range [0,1), and kT is a scaling factor analogous to temperature.

FRET is a low-resolution technique. Hence, FRET measurements are relatively insensitive to small structural changes. Moreover, the comparison of a structural model to the experimental data is computationally expensive, as, for an accurate comparison, the positional distribution of the fluorophores around their attachment point needs to be simulated. Hence, in ChiSurf, the agreement of the sampled conformations with the FRET experiments is evaluated in a second MC scheme in addition to the MC scheme used to sample the conformational space of the protein. The second MC scheme biases the structural sampling towards configurations that are in agreement with the experiments. The first (structure) MC sampling scheme accumulates structural changes. Next, the second FRET MC evaluates the accumulated changes and accepts these changes if changes improve the agreement with the experimental data or if

$$exp((E_{FRET,i}-E_{FRET,i}+1)/kT)\$\$ > r$$

where r is a random number in the range [0,1), and kT_FRET is a scaling factor, E_{FRET,i} quantifies the disagreement with the experimental data of the previously accepted structural model, and E_{FRET,i+1} is the disagreement with the experimental data of the proposed structural model.

By default, E_{FRET,i} corresponds to the sum of a error-weighted sum of squared deviations between the experimentally determined distances and the simulated distances. This disagreement, chi^2, is calculated by:

$$chi^2 = 1/(N-1) \sum_i^N ( (d_{exp,i} – d_{sim,i})/(err_{exp_i}^2))^2$$

Where N corresponds to the number of experimental distances d_{exp,i} is an experimental distance with associated experimental error err_{exp,i} and d_{sim,i} correspond to a simulated distance for a structural model.

File formats

Outputs

The structure sampling of ChiSurf uses JSON files to save configurations and parameters. ChiSurf saves MC trajectories as HDF5 files in the MDTraj format (http://mdtraj.org). The values of the FRET bias potential can be saved in ChiSurf as comma-separated files.

Inputs

The experimental FRET constrains are https://github.com/Fluorescence-Tools/Olga/blob/master/doc/JSON Types%20and%20Parameters.docx The user interface

User interface

Command line

Two provides a user interface and an

This is achieved using the FRET positioning system (FPS) as a forward model for sampled by simulating fluorescence observables using. and sampling the conformational space of the studied protein.

where the backbone is represented by is represented by an atomistic representation of the backbone is

The internal coordinates are converted to cartesian coordinates to

To evaluate the

Moreover, the protein representation considers
The conformational space is sampled

For that, ChiSurf represents and samples using the the protein backbone. the conformational space.

protein is represented in internal coordinates of the protein.