Flexibility between domains of proteins is often critical for function. These motions and proteins with large scale flexibility in general are often not readily amenable to conventional structural analysis such as X-ray crystallography, nuclear magnetic resonance spectroscopy (NMR) or electron microscopy. A common evolution of a crystallography project, once a high resolution structure has been determined, is to postulate possible sights of flexibility. Here we describe an analysis tool using relatively inexpensive small angle X-ray scattering (SAXS) measurements to identify flexibility and validate a constructed minimal ensemble of models, which represent highly populated conformations in solution. The resolution of these results is sufficient to address the questions being asked: what kinds of conformations do the domains sample in solution? In our rigid body modeling strategy BILBOMD, molecular dynamics (MD) simulations are used to explore conformational space. A common strategy is to perform the MD simulation on the domains connections at very high temperature, where the additional kinetic energy prevents the molecule from becoming trapped in a local minimum. The MD simulations provide an ensemble of molecular models from which a SAXS curve is calculated and compared to the experimental curve. A genetic algorithm is used to identify the minimal ensemble (minimal ensemble search, MES) required to best fit the experimental data. We demonstrate the use of MES in several model and in four experimental examples.

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DNA double strand break (DSB) repair by non-homologous end joining (NHEJ) is initiated by DSB detection by Ku70/80 (Ku) and DNA-dependent protein kinase catalytic subunit (DNA-PKcs) recruitment, which promotes pathway progression through poorly defined mechanisms. Here, Ku and DNA-PKcs solution structures alone and in complex with DNA, defined by x-ray scattering, reveal major structural reorganizations that choreograph NHEJ initiation. The Ku80 C-terminal region forms a flexible arm that extends from the DNA-binding core to recruit and retain DNA-PKcs at DSBs. Furthermore, Ku- and DNA-promoted assembly of a DNA-PKcs dimer facilitates trans-autophosphorylation at the DSB. The resulting site-specific autophosphorylation induces a large conformational change that opens DNA-PKcs and promotes its release from DNA ends. These results show how protein and DNA interactions initiate large Ku and DNA-PKcs rearrangements to control DNA-PK biological functions as a macromolecular machine orchestrating assembly and disassembly of the initial NHEJ complex on DNA.

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This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. The BOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

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This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions, but also for estimating their fitness. The results indicate that fitness inheritance is a promising concept in BOA, because population-sizing requirements for building appropriate models of promising solutions lead to good fitness estimates even if only a small proportion of candidate solutions is evaluated using the actual fitness function. This can lead to a reduction of the number of actual fitness evaluations by a factor of 30 or more.

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