Biomedical Engineering Reference
In-Depth Information
biomolecules [3, 4], high-throughput data acquisition is within reach. Since SAXS data
only describes the spherical averaging of the electron density of the average conforma-
tion of the ensemble, additional information is needed to assist structural interpretation.
Typical
in silico
protein structure determination methods, such as ones based on
Markov chain Monte Carlo (MCMC) simulations, propose plausible structural confor-
mations, and compute their associated simulated data by means of a forward model.
Then, the simulated and the experimental data are compared using an error model of
the experiment. For this procedure to be successful, an efficient method for both sam-
pling protein structures and calculating the simulated data is required.
One approach for the calculation of a SAXS curve from a given structure makes use
of the Debye formula [5], which is calculated from a set of spherical scatterers [6-9].
Another, more recent approach, is based on spherical harmonics expansions [10]. This
approach is faster, but becomes problematic for certain structures, such as those with
internal cavities [11]. Here, we present an efficient application of the Debye formula,
based on a simplified representation of protein structure and the computational power
provided by Graphics Processor Units (GPUs).
In recent publications, our group developed probabilistic models for the proposal
of protein-like conformations, in full atomic detail, for both backbone and side chains
[12, 13]. These models were used for the inference of protein structure from NMR
data [14]. We also developed a forward model of the scattering profile evaluation, that
includes the experimental error associated with SAXS data [15]. The forward model
consists of a coarse-grained computation based on the Debye formula. Our main aim is
the study of proteins consisting of multiple domains connected by flexible linkers. Such
proteins play a major role in the regulation of gene expression, cell growth, cell cycle,
metabolic pathways, signal transduction, protein folding and transport [16, 17]. With
this aim, a computationally efficient forward model for the calculation of SAXS curves
is paramount.
We ported our original implementation of the Debye formula to General Purpose
computing on Graphics Processing Units (GPGPU). GPUs are parallel computing en-
gines that can offer great advantages in terms of cost-efficiency and low power con-
sumption [18]. One of the emerging standards of choice for their programming is the
Open Computing Language (OpenCL), an open standard that provides an abstraction
layer over multi- and many-core computational hardware [19]. The OpenCL Debye im-
plementation was utilized as a likelihood term in an MCMC simulation, providing the
basis for efficient protein structure determination from low-resolution SAXS data.
2
Methods
2.1
Forward SAXS Computation
The observed data in a SAXS experiment is a one-dimensional intensity curve,
I
(
q
)
,
measured at discretized scattering momenta
q
=4
π
sin(
θ
)
/λ
, with
λ
the wavelength of
the incoming radiation, and
2
θ
the angle between this beam and the scattered rays. The
calculation of a theoretical SAXS profile from a given atomic structure is based on the
well-known Debye formula [5]:
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