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Abstract Understanding and controlling protein motion at atomic resolution is a hallmark challenge for structural biologists and protein engineers because conformational dynamics are essential for complex functions such as enzyme catalysis and allosteric regulation. Time-resolved crystallography offers a window into protein motions, yet without a universal perturbation to initiate conformational changes the method has been limited in scope. Here we couple a solvent-based temperature jump with time-resolved crystallography to visualize structural motions in lysozyme, a dynamic enzyme. We observed widespread atomic vibrations on the nanosecond timescale, which evolve on the submillisecond timescale into localized structural fluctuations that are coupled to the active site. An orthogonal perturbation to the enzyme, inhibitor binding, altered these dynamics by blocking key motions that allow energy to dissipate from vibrations into functional movements linked to the catalytic cycle. Because temperature jump is a universal method for perturbing molecular motion, the method demonstrated here is broadly applicable for studying protein dynamics. 

In the classical Steiner tree problem, given an undirected, connected graph G =( V , E ) with non-negative edge costs and a set of terminals T ⊆ V , the objective is to find a minimum-cost tree E &prime ⊆ E that spans the terminals. The problem is APX-hard; the best-known approximation algorithm has a ratio of ρ = ln (4)+ε < 1.39. In this article, we study a natural generalization, the multi-level Steiner tree (MLST) problem: Given a nested sequence of terminals T ℓ ⊂ … ⊂ T 1 ⊆ V , compute nested trees E ℓ ⊆ … ⊆ E 1 ⊆ E that span the corresponding terminal sets with minimum total cost. The MLST problem and variants thereof have been studied under various names, including Multi-level Network Design, Quality-of-Service Multicast tree, Grade-of-Service Steiner tree, and Multi-tier tree. Several approximation results are known. We first present two simple O (ℓ)-approximation heuristics. Based on these, we introduce a rudimentary composite algorithm that generalizes the above heuristics, and determine its approximation ratio by solving a linear program. We then present a method that guarantees the same approximation ratio using at most 2ℓ Steiner tree computations. We compare these heuristics experimentally on various instances of up to 500 vertices using three different network generation models. We also present several integer linear programming formulations for the MLST problem and compare their running times on these instances. To our knowledge, the composite algorithm achieves the best approximation ratio for up to ℓ = 100 levels, which is sufficient for most applications, such as network visualization or designing multi-level infrastructure. 

Innovative new crystallographic methods are facilitating structural studies from ever smaller crystals of biological macromolecules. In particular, serial X-ray crystallography and microcrystal electron diffraction (MicroED) have emerged as useful methods for obtaining structural information from crystals on the nanometre to micrometre scale. Despite the utility of these methods, their implementation can often be difficult, as they present many challenges that are not encountered in traditional macromolecular crystallography experiments. Here, XFEL serial crystallography experiments and MicroED experiments using batch-grown microcrystals of the enzyme cyclophilin A are described. The results provide a roadmap for researchers hoping to design macromolecular microcrystallography experiments, and they highlight the strengths and weaknesses of the two methods. Specifically, we focus on how the different physical conditions imposed by the sample-preparation and delivery methods required for each type of experiment affect the crystal structure of the enzyme.