Christian Andreetta

Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances – so-called “potentials of mean force” (PMFs) – have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state – a necessary component of these potentials – is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities “reference ratio distributions” deriving from the application of the “reference ratio method.” This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

Calculation of accurate small angle X-ray scattering curves from coarse-grained protein models

BackgroundGenome sequencing projects have expanded the gap between the amount of known protein sequences and structures. The limitations of current high resolution structure determination methods make it unlikely that this gap will disappear in the near future. Small angle X-ray scattering (SAXS) is an established low resolution method for routinely determining the structure of proteins in solution. The purpose of this study is to develop a method for the efficient calculation of accurate SAXS curves from coarse-grained protein models. Such a method can for example be used to construct a likelihood function, which is paramount for structure determination based on statistical inference.ResultsWe present a method for the efficient calculation of accurate SAXS curves based on the Debye formula and a set of scattering form factors for dummy atom representations of amino acids. Such a method avoids the computationally costly iteration over all atoms. We estimated the form factors using generated data from a set of high quality protein structures. No ad hoc scaling or correction factors are applied in the calculation of the curves. Two coarse-grained representations of protein structure were investigated; two scattering bodies per amino acid led to significantly better results than a single scattering body.ConclusionWe show that the obtained point estimates allow the calculation of accurate SAXS curves from coarse-grained protein models. The resulting curves are on par with the current state-of-the-art program CRYSOL, which requires full atomic detail. Our method was also comparable to CRYSOL in recognizing native structures among native-like decoys. As a proof-of-concept, we combined the coarse-grained Debye calculation with a previously described probabilistic model of protein structure, TorusDBN. This resulted in a significant improvement in the decoy recognition performance. In conclusion, the presented method shows great promise for use in statistical inference of protein structures from SAXS data.

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure.

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Subtle Monte Carlo Updates in Dense Molecular Systems

Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions.

Financial software on GPUs: between Haskell and Fortran

This paper presents a real-world pricing kernel for financial derivatives and evaluates the language and compiler tool chain that would allow expressive, hardware-neutral algorithm implementation and efficient execution on graphics-processing units (GPU). The language issues refer to preserving algorithmic invariants, e.g., inherent parallelism made explicit by map-reduce-scan functional combinators. Efficient execution is achieved by manually; applying a series of generally-applicable compiler transformations that allows the generated-OpenCL code to yield speedups as high as 70x and 540x on a commodity mobile and desktop GPU, respectively. Apart from the concrete speed-ups attained, our contributions are twofold: First, from a language perspective;, we illustrate that even state-of-the-art auto-parallelization techniques are incapable of discovering all the requisite data parallelism when rendering the functional code in Fortran-style imperative array processing form. Second, from a performance perspective;, we study which compiler transformations are necessary to map the high-level functional code to hand-optimized OpenCL code for GPU execution. We discover a rich optimization space with nontrivial trade-offs and cost models. Memory reuse in map-reduce patterns, strength reduction, branch divergence optimization, and memory access coalescing, exhibit significant impact individually. When combined, they enable essentially full utilization of all GPU cores. Functional programming has played a crucial double role in our case study: Capturing the naturally data-parallel structure of the pricing algorithm in a transparent, reusable and entirely hardware-independent fashion; and supporting the correctness of the subsequent compiler transformations to a hardware-oriented target language by a rich class of universally valid equational properties. Given the observed difficulty of automatically parallelizing imperative sequential code and the inherent labor of porting hardware-oriented and -optimized programs, our case study suggests that functional programming technology can facilitate high-level; expression of leading-edge performant portable; high-performance systems for massively parallel hardware architectures.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a proteins nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well‐justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications. Proteins 2014; 82:288–299.

FinPar: A Parallel Financial Benchmark

Commodity many-core hardware is now mainstream, but parallel programming models are still lagging behind in efficiently utilizing the application parallelism. There are (at least) two principal reasons for this. First, real-world programs often take the form of a deeply nested composition of parallel operators, but mapping the available parallelism to the hardware requires a set of transformations that are tedious to do by hand and beyond the capability of the common user. Second, the best optimization strategy, such as what to parallelize and what to efficiently sequentialize, is often sensitive to the input dataset and therefore requires multiple code versions that are optimized differently, which also raises maintainability problems. This article presents three array-based applications from the financial domain that are suitable for gpgpu execution. Common benchmark-design practice has been to provide the same code for the sequential and parallel versions that are optimized for only one class of datasets. In comparison, we document (1) all available parallelism via nested map-reduce functional combinators, in a simple Haskell implementation that closely resembles the original code structure, (2) the invariants and code transformations that govern the main trade-offs of a data-sensitive optimization space, and (3) report target cpu and multiversion gpgpu code together with an evaluation that demonstrates optimization trade-offs and other difficulties. We believe that this work provides useful insight into the language constructs and compiler infrastructure capable of expressing and optimizing such applications, and we report in-progress work in this direction.

Parallel GPGPU Evaluation of Small Angle X-Ray Scattering Profiles in a Markov Chain Monte Carlo Framework

Inference of protein structure from experimental data is of crucial interest in science, medicine and biotechnology. Low-resolution methods, such as small angle X-ray scattering (SAXS), play a major role in investigating important biological questions regarding the structure of proteins in solution.