Restricted Mesh Annealing (RMA)

Restricted Mesh Annealing (RMA) is a constrained subtomogram alignment algorithm that was introduced in our work. It imposes longitudinal and lateral constraints between molecules and optimize the alignment score using simulated annealing.

As an example of using RMA, see the case study.

For the longitudinal and lateral distance ranges, you can use the variable d to specify the distances. d is a numpy.ndarray of shape (N,), where N is the number of molecules. For example, d.mean() is the mean distance between laterally neighboring molecules if d is used in the lateral constraint.

Run RMA on a Landscape

API: run_rma_on_landscape

GUI: Subtomogram Averaging > Landscape > Run annealing (RMA)

List of Parameters

1. Select the landscape in the "landscape layer" combobox.
2. "Longitudinal range (nm)" is the constrant of the longitudinal distance between neighboring molecules.
3. "Lateral range (nm)" is the constrant of the lateral distance between neighboring molecules.
4. "Maximum angle (deg)" is the another constraint. It is the maximum allowed angle between the spline tangent and the vector connecting the two molecules.
5. "temperature time const" is the time constant of the simulated annealing. Larger value means slower annealing. 1.0 is usually a good value.
6. "LJ const" is the constant of the Lennard-Jones-like potential. If greater than 0, the annealing will use a Lennard-Jones-like potential to allow molecules to separate further apart than the cutoff distance.
7. "num trials" and "seed" are the parameters for random initialization. RMA will be run multiple times with different random initializations, and the result with the best score will be selected. You can increase the number of trials to get better results at the cost of longer computation time.
8. You can preview the distribution of the longitudinal/lateral distances by clicking the "Preview molecule network" button.

Run RMA without Constructing a Landscape

API: align_all_rma

GUI: Subtomogram Averaging > Alignment > Simulated Annealing

Energy Potential in RMA

In RMA, negative cross-correlation scores are interpreted as the internal energy of the system, and the neighboring molecules are constrained by the "binding energy". Minimization of the total energy is the goal of the simulated annealing.

Modeling the binding energy is not simple. To avoid complicating the outcome, RMA does not model the physical binding energy, but instead uses step-wise potentials: trapozoidal potential and Lennard-Jones-like potential.

The trapozoidal potential can be interpreted as a hard constraint, with which the inter-molecular distances are not allowed to exceed the minimum and maximum cutoff distances. For example, if a microtubule is a complete cylinder, this potential gives good alignment results.

The Lennard-Jones-like potential allows the inter-molecular distances to exceed the maximum cutoff distance, but with an energy penalty \(E_{\infty}\). Therefore, molecules will be put close to each other as much as possible, but separating them further apart does not make the entire system unstable. This potential is useful when the microtubule is broken or flared.

Energy potentials change over time so that the binding energy outside the allowed distance range is differentiable. This is important for the optimization process, although simulated annealing does not strictly require the energy to be differentiable.