Homework Assignment - 00
CS267 - Spring 2006
I am a third year student in the Biophysics Graduate Group, working in the the laboratory of Prof. George Oster. I am currently working on modeling ring-shaped ATPase molecular motors. Rho helicase and other ATPases containing a RecA-like catalytic site are important components of the cellular machinery and provide a paradigm of how enzymes use the energy of nucleotide binding and hydrolysis to perform mechanical work. Early on in my graduate studies I became fascinated by the fact that although the common structure of RecA-like motors ATP binding site indicates that these enzymes share a common mechanism, experimental evidence suggests that the coupling of hydrolysis to mechanical work is dependent on the oligomeric arrangement of these multi-subunit proteins. Such systems exhibit a combinatorial explosion. The simplest posited catalytic cycle of a single subunit has 10 states giving 10^6 distinct chemical states for the whole hexameric enzyme (thus requiring a rate matrix of 10^12 elements). Thus even kinetic simulations are limited by the discrepancy between the computing resources and the computational load of the ideal calculations. In taking CS267, I am hoping to learn how to develop efficient algorithms and for tackling this class of problems.
Background
Single-particle electron cryomicroscopy represents an important technique in imaging large macromolecular complexes at high resolution. Samples are frozen in vitrious-ice and many individual particles are imaged by collecting information on the elastic scattering of electrons interacting with the specimen. In this brief review I will focus on what are termed 'zero-tilt' techniques in which the random orientations of the molecules trapped in the sample are exploited to construct a three-dimensional model of the complex.
The Computational Problem
So you have several thousand images of the 2D projection of a particle, oriented randomly in space. In order to reconstitute the 3D structure of your favorite molecule, you need to determine the Euler angles and translational offset of each image in space and then align all of the properly oriented images. Multireference Alignment (MRA) is a commonly used projection matching method, used to determine and refine the parameters defining a given image's position and orientation in space. Sander, et al [1], describe a rough example of the scaling issues associated with tackling such a computational task: a standard reconstruction requires ~250,000 raw images (128 x 128 pixels) that are aligned against a set of ~4500 reference images. On their 4-processor Compaq Alpha EV6 500 Mhz, running the IMAGIC-5 image processing software package, a single iteration of the MRA would take on the order of 2 years.
The MRA Procedure [2]
Filtering
Band-pass filtering of images to suppress low frequency noise that corrupts the alignment. High-frequency noise is sometimes excluded in initial alignments, but reintroduced at later stages of the reconstruction.
Correlation Based Alignment
Pertinent translation parameters are extracted from correlations between images. Sander, et al describe two distinct techniques (i) Direct Alignment (DA) - Translation alignment computed using a Cross-Correlation Function (CCF) and the rotation angles via a rotational correlation function in a separate step. (ii) Exhaustive Alignment - evaluate all possible positions of an image within some range. This is much slower than DA.
Figures from [2]
Improving the MRA [1]
Sander, et al propose an improvement to the MRA which saves data about the correlations and creates a interpolation between them to then restrict subsequent searches of the space. This operation can be implemented for a parallel computing cluster.
Testing System - AMD Athlon 2000+ MP cluster with 1-64 processors, running Windows 2000 Professional, and NT-MPICH
Test Data - 20,000 images (128x128 pixels) aligned against 1650 reference images.
Scaling - Four processors run MRA in 5h 57 min, while 64 processors require 23 min. Below is a plot of reciprocal computing time for varying numbers of processors:
Other examples of cryo-EM reconstruction on parallel computing cluster
Another discussion of computer architecture as applied to particle reconstruction is described by Zhou, et al [3], where they apply the resources of a large shared memory parallel machine to refine the structure of the Herpesvirus B-Capsid structure.
Conclusions
The correlation interpolation method appears to be easily transferable into a parallel computing environment with dramatic scalability. The algorithm appears to sucessfully compare against other alignment methods while using less reference images (and thus carries less of a computational burden). The referenced papers did not note how much computational power (in MFlops) they were getting compared to the best possible perfomance of their machine.
References
[1] Sander, B., et al (2003) Corrim-based alignment for improved speed in single-particle image processing, Journal of Struct. Biol 143, 219-228.
[2] van Heel, et al (2000) Single-particle electron cryo-microscopy: towards atomic resolution, Q. Rev Biophys 33, 307-369.
[3] Zhou, Z.H., et al (1998) Refinement of Herpesvirus B-capsid Structure on Parallel Supercomputers, Biophys Journal 74, 576-588.