Parallel GPGPU Evaluation of Small Angle X-Ray Scattering Profiles in a Markov Chain Monte Carlo Framework - Biomedical Engineering Systems and Technologies - page 208

We measured the divergence between the SP and DP executions, and no signifi-
cant differences arise between the results. Therefore, the SP implementation is used by
default.

2.6 Monte Carlo Simulation

PHAISTOS is a software framework for protein structure prediction, inference and sim-
ulation based on Bayesian principles [23]. PHAISTOS samples protein structures X
given the experimental data I exp from a Bayesian posterior distribution P ( X I exp ) us-

ing an MCMC procedure, similar to [14]. The posterior is given by the formula:

|

P ( X | I exp ) ∝ P ( I exp | X ) P ( X ) (2)

and consists of a prior P ( X ) that includes probabilistic models of the main and side
chains in proteins [12, 13], while the likelihood P ( I exp | X ) brings in the SAXS data.

The likelihood essentially expresses the correspondence between the experimental data
and the data calculated from a given structure using the forward model.
For the calculation of the likelihood, we used the error model given in [15]. The
resulting likelihood is:

X )= P ( I exp |

q N

( I exp ( q ) | I calc ( q ) ,σ ( q )) , (3)

where ) is the normal distribution with mean I calc ( q ) and standard deviation σ ( q ) ,

controlled by scaling parameters α and β :

N ( ·

σ ( q )= I exp ( q ) · ( q + α ) · β (4)

The prior P ( X ) is brought in indirectly by sampling from the proposal distribution for
protein conformations [14].
The majority of time dedicated to each simulation step is spent on computing the
energy function for the proposed structure. The GPGPU SAXS algorithm directly re-
duces this time. Furthermore, at each MCMC step, PHAISTOS performs local moves
on a portion of the protein, which allows the Page-Tile algorithm to use the fast tile
recalculation path.

2.7 Performance Test Configuration

Performance was measured on a system with a Core i7-920 CPU (4 cores / 8 hardware
threads), 12GB of DDR3 RAM and a NVIDIA GeForce GTX 560 Ti GPU with 1GB
of GDDR5 RAM. The GTX 560 Ti has 8 compute units with 32 processing elements
each, comprising 384 processing elements, with 32KB 32-bit registers and 48KB of
local memory for each compute unit.