sspre

Overview

sspre provides tools for computing synthetic paramagnetic relaxation enhancement (PRE) profiles from MD simulation ensembles and comparing them to experimental NMR data. The module exposes a single class, SSPRE, which wraps an SSProtein object together with the experimental parameters of the PRE measurement.

What PRE profiles measure. In a PRE experiment, a nitroxide spin label (typically a MTSL-labelled cysteine) is introduced at a specific sequence position. The unpaired electron of the spin label accelerates the relaxation of nearby backbone amide protons, reducing their observed NMR signal intensity. The key observables are:

  • Intensity ratio \(I_\text{para} / I_\text{dia}\) — ratio of signal intensities in the paramagnetic vs. diamagnetic sample, ranging from 0 (near the label) to 1 (far away).

  • Transverse relaxation rate \(\Gamma_2\) — the spin-label-induced relaxation rate enhancement (in Hz), a complementary observable.

Physical model. The calculation uses the Solomon–Bloembergen framework: for each residue, the \(r^{-6}\)-weighted mean distance to the spin-label atom is averaged over all frames of the trajectory. This ensemble averaging correctly captures the non-linear distance dependence of PRE relaxation and is the approach validated in the references below.

Workflow. An SSPRE object is created by supplying an SSProtein and the four experimental parameters: effective correlation time \(\tau_c\) (ns), INEPT delay \(t_\text{delay}\) (ms), diamagnetic transverse relaxation rate \(R_{2D}\) (Hz), and proton Larmor frequency \(\omega_H\) (Hz). generate_PRE_profile then computes the full-length intensity ratio and \(\Gamma_2\) profiles for a given label position:

from soursop.sstrajectory import SSTrajectory
from soursop.sspre import SSPRE

TrajOb = SSTrajectory('traj.xtc', 'start.pdb')
protein = TrajOb.proteinTrajectoryList[0]

# 600 MHz magnet, tau_c = 5 ns, t_delay = 16 ms, R_2D = 10 Hz
pre = SSPRE(protein, tau_c=5, t_delay=16, R_2D=10, W_H=600000000)

# spin label at residue 42 (CB atom by default)
intensity_ratio, gamma2 = pre.generate_PRE_profile(label_position=42)

Key references. The methodology is described in the supplementary information of:

  • Meng, W., Lyle, N., Luan, B., Raleigh, D.P., and Pappu, R.V. (2013). Proc. Natl. Acad. Sci. U. S. A. 110, 2123–2128.

  • Das, R.K., Huang, Y., Phillips, A.H., Kriwacki, R.W., and Pappu, R.V. (2016). Proc. Natl. Acad. Sci. U. S. A. 113, 5616–5621.

  • Peran, I., Holehouse, A. S., Carrico, I. S., Pappu, R. V., Bilsel, O., & Raleigh, D. P. (2019). Proc. Natl. Acad. Sci. U. S. A. 116(25), 12301–12310.

class soursop.sspre.SSPRE(SSProteinObject, tau_c, t_delay, R_2D, W_H)[source]

Synthetic paramagnetic relaxation enhancement (PRE) calculations.

Wraps an SSProtein ensemble and computes intramolecular PRE intensity ratios and the associated transverse relaxation enhancement (gamma) profiles for a nitroxide spin label placed at an arbitrary sequence position. The model follows the approach used by Meng & Lyle (PNAS 2013), Das et al. (PNAS 2016) and Peran & Holehouse (PNAS 2019), and is fast enough to apply to large (multi-thousand frame) disordered-protein ensembles.

A typical workflow is to extract an SSProtein from an SSTrajectory, construct an SSPRE object with the relevant experimental parameters (effective correlation time, INEPT delay, diamagnetic transverse relaxation rate and proton Larmor frequency) and then call generate_PRE_profile for one or more label positions. The bound SSProtein is treated as read-only and is not modified.

Example

>>> P = traj.proteinTrajectoryList[0]
>>> spre = SSPRE(P, tau_c=5.0, t_delay=10.0, R_2D=10.0, W_H=600000000)
>>> profile, gamma = spre.generate_PRE_profile(label_position=42)
__init__(SSProteinObject, tau_c, t_delay, R_2D, W_H)[source]

Build an SSPRE object bound to a single-chain protein ensemble.

Stores the bound SSProtein and the experimental parameters, runs physiological sanity checks on the inputs (emitting an SSWarning for values far outside their normal range without blocking analysis) and precomputes the spectral-density prefactor used by generate_PRE_profile. The resulting object can then be used to calculate PRE profiles from the underlying ensemble; the calculation is extremely fast.

Parameters:

  • SSProteinObject (soursop.ssprotein.SSProtein) – SSProtein object extracted from an SSTrajectory. This is the main object over which protein-centric analysis is performed in SOURSOP. It is treated as read-only.

  • tau_c (float) – Effective rotational correlation time in nanoseconds, typically between 1 and 30.

  • t_delay (float) – Total duration of the INEPT delays in the PRE experiment, in milliseconds. Depends on the pulse sequence but is typically ~1-30 ms for an HSQC.

  • R_2D (float) – Transverse relaxation rate of the backbone amide protons in the diamagnetic form of the protein, in Hz (per second). A value of around 10 is typical.

  • W_H (float) – Proton Larmor frequency of the magnet, in Hz - i.e. the nominal “MHz” rating of the magnet expressed in Hz (a 600 MHz magnet uses 600000000). The proton Larmor frequency at 1 Tesla is 267530000 per second per Tesla.

Raises:

soursop.ssexceptions.SSException – If SSProteinObject is not an SSProtein instance.

Example

>>> P = traj.proteinTrajectoryList[0]
>>> spre = SSPRE(P, tau_c=5.0, t_delay=10.0, R_2D=10.0, W_H=600000000)
generate_PRE_profile(label_position, spin_label_atom='CB', target_relaxation_atom='N')[source]

Compute the PRE intensity ratio and gamma profile for a spin label.

Places a nitroxide spin label on the spin_label_atom of residue label_position and, for every residue that has a cached CA atom, computes the spin-label-induced transverse relaxation enhancement (the gamma profile) and the corresponding paramagnetic/diamagnetic intensity ratio (the PRE profile). By default the label is on CB and relaxation is assessed from the CB-to-backbone-N distances, matching the parameterisation used by Meng, Lyle, Luan, Raleigh & Pappu (PNAS 2013, 110:2123-2128), Das, Huang, Phillips, Kriwacki & Pappu (PNAS 2016, 113:5616-5621) and Peran, Holehouse, Carrico, Pappu, Bilsel & Raleigh (PNAS 2019, 116:12301-12310).

The PRE profile is the intensity ratio (Iparamagnetic / Idiamagnetic) and typically lies between 0 and 1: a ratio near 0 means the spin label dominates relaxation (the residue is, on average, close to the label) while a ratio near 1 means relaxation is dominated by non-spin-label mechanisms (the residue is far from the label). The gamma profile is the spin-label-induced amide-proton relaxation rate in per-second units, a second observable directly comparable with experiment.

The r^-6 distance dependence is averaged after the per-frame relaxation is computed (not by averaging distances first), because the distance-to-relaxation mapping is non-linear. This routine is extremely fast (sub-10 s on a ~6000-frame ensemble).

Parameters:

  • label_position (int) – Sequence position at which the spin label is located. Should contain a CB atom (i.e. not be glycine) unless spin_label_atom is changed to 'CA' (see below).

  • spin_label_atom (str, optional) – Name of the atom on which the spin label sits. Should be 'CB' but may be changed if the labelled residue lacks a CB (e.g. a glycine in place of the cysteine nitroxide site). Default 'CB'.

  • target_relaxation_atom (str, optional) – Name of the atom at which relaxation is evaluated. This should be 'N' (backbone amide), as that is how the approach is parameterised; an atom of this name is searched for in every residue. Changing it is strongly discouraged. Default 'N'.

Returns:

A 2-tuple (profile, gamma) where profile is the PRE intensity ratio and gamma is the spin-label-induced amide proton relaxation rate (per second), each with one entry per CA-containing residue (in ascending residue order).

Return type:

tuple of (list of float, list of float)

Example

>>> profile, gamma = spre.generate_PRE_profile(label_position=42)
>>> len(profile) == len(gamma)
True