Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy.

Understanding and controlling ultrafast charge carrier dynamics is of fundamental importance in diverse fields of (quantum) science and technology. Here, we create a three-dimensional hot electron gas through two-photon photoemission from a copper surface in vacuum. We employ an ultrafast electron microscope to record movies of the subsequent electron dynamics on the picosecond-nanosecond time scale. After a prompt Coulomb explosion, the subsequent dynamics is characterized by a rapid oblate-to-prolate shape transformation of the electron gas, and periodic and long-lived electron cyclotron oscillations inside the magnetic field of the objective lens. In this regime, the collective behavior of the oscillating electrons causes a transient, mean-field lensing effect and pronounced distortions in the images. We derive an analytical expression for the time-dependent focal length of the electron-gas lens, and perform numerical electron dynamics and probe image simulations to determine the role of Coulomb self-fields and image charges. This work inspires the visualization of cyclotron dynamics inside two-dimensional electron-gas materials and enables the elucidation of electron/plasma dynamics and properties that could benefit the development of high-brightness electron and X-ray sources.

Protein-protein docking by fast generalized Fourier transforms on 5D rotational manifolds.

Energy evaluation using fast Fourier transforms (FFTs) enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods, efficient acceleration is achieved only in either the translational or the rotational subspace. Developing an efficient and accurate docking method that expands FFT-based sampling to five rotational coordinates is an extensively studied but still unsolved problem. The algorithm presented here retains the accuracy of earlier methods but yields at least 10-fold speedup. The improvement is due to two innovations. First, the search space is treated as the product manifold [Formula: see text], where [Formula: see text] is the rotation group representing the space of the rotating ligand, and [Formula: see text] is the space spanned by the two Euler angles that define the orientation of the vector from the center of the fixed receptor toward the center of the ligand. This representation enables the use of efficient FFT methods developed for [Formula: see text] Second, we select the centers of highly populated clusters of docked structures, rather than the lowest energy conformations, as predictions of the complex, and hence there is no need for very high accuracy in energy evaluation. Therefore, it is sufficient to use a limited number of spherical basis functions in the Fourier space, which increases the efficiency of sampling while retaining the accuracy of docking results. A major advantage of the method is that, in contrast to classical approaches, increasing the number of correlation function terms is computationally inexpensive, which enables using complex energy functions for scoring.

Comprehensive experimental and computational analysis of binding energy hot spots at the NF-κB essential modulator/IKKß protein-protein interface.

We report a comprehensive analysis of binding energy hot spots at the protein-protein interaction (PPI) interface between nuclear factor kappa B (NF-κB) essential modulator (NEMO) and IκB kinase subunit ß (IKKß), an interaction that is critical for NF-κB pathway signaling, using experimental alanine scanning mutagenesis and also the FTMap method for computational fragment screening. The experimental results confirm that the previously identified NEMO binding domain (NBD) region of IKKß contains the highest concentration of hot-spot residues, the strongest of which are W739, W741, and L742 (ΔΔG = 4.3, 3.5, and 3.2 kcal/mol, respectively). The region occupied by these residues defines a potentially druggable binding site on NEMO that extends for ~16 Å to additionally include the regions that bind IKKß L737 and F734. NBD residues D738 and S740 are also important for binding but do not make direct contact with NEMO, instead likely acting to stabilize the active conformation of surrounding residues. We additionally found two previously unknown hot-spot regions centered on IKKß residues L708/V709 and L719/I723. The computational approach successfully identified all three hot-spot regions on IKKß. Moreover, the method was able to accurately quantify the energetic importance of all hot-spot residues involving direct contact with NEMO. Our results provide new information to guide the discovery of small-molecule inhibitors that target the NEMO/IKKß interaction. They additionally clarify the structural and energetic complementarity between "pocket-forming" and "pocket-occupying" hot-spot residues, and further validate computational fragment mapping as a method for identifying hot spots at PPI interfaces.

Relationship between hot spot residues and ligand binding hot spots in protein-protein interfaces.

In the context of protein-protein interactions, the term "hot spot" refers to a residue or cluster of residues that makes a major contribution to the binding free energy, as determined by alanine scanning mutagenesis. In contrast, in pharmaceutical research, a hot spot is a site on a target protein that has high propensity for ligand binding and hence is potentially important for drug discovery. Here we examine the relationship between these two hot spot concepts by comparing alanine scanning data for a set of 15 proteins with results from mapping the protein surfaces for sites that can bind fragment-sized small molecules. We find the two types of hot spots are largely complementary; the residues protruding into hot spot regions identified by computational mapping or experimental fragment screening are almost always themselves hot spot residues as defined by alanine scanning experiments. Conversely, a residue that is found by alanine scanning to contribute little to binding rarely interacts with hot spot regions on the partner protein identified by fragment mapping. In spite of the strong correlation between the two hot spot concepts, they fundamentally differ, however. In particular, while identification of a hot spot by alanine scanning establishes the potential to generate substantial interaction energy with a binding partner, there are additional topological requirements to be a hot spot for small molecule binding. Hence, only a minority of hot spots identified by alanine scanning represent sites that are potentially useful for small inhibitor binding, and it is this subset that is identified by experimental or computational fragment screening.

Hot spot analysis for driving the development of hits into leads in fragment-based drug discovery.

Fragment-based drug design (FBDD) starts with finding fragment-sized compounds that are highly ligand efficient and can serve as a core moiety for developing high-affinity leads. Although the core-bound structure of a protein facilitates the construction of leads, effective design is far from straightforward. We show that protein mapping, a computational method developed to find binding hot spots and implemented as the FTMap server, provides information that complements the fragment screening results and can drive the evolution of core fragments into larger leads with a minimal loss or, in some cases, even a gain in ligand efficiency. The method places small molecular probes, the size of organic solvents, on a dense grid around the protein and identifies the hot spots as consensus clusters formed by clusters of several probes. The hot spots are ranked based on the number of probe clusters, which predicts the binding propensity of the subsites and hence their importance for drug design. Accordingly, with a single exception the main hot spot identified by FTMap binds the core compound found by fragment screening. The most useful information is provided by the neighboring secondary hot spots, indicating the regions where the core can be extended to increase its affinity. To quantify this information, we calculate the density of probes from mapping, which describes the binding propensity at each point, and show that the change in the correlation between a ligand position and the probe density upon extending or repositioning the core moiety predicts the expected change in ligand efficiency.

Domain motion and interdomain hot spots in a multidomain enzyme.

The aim of this article is to analyze conformational changes by comparing 10 different structures of Pseudomonas aeruginosa phosphomannomutase/phosphoglucomutase (PMM/PGM), a four-domain enzyme in which both substrate binding and catalysis require substantial movement of the C-terminal domain. We focus on changes in interdomain and active site crevices using a method called computational solvent mapping rather than superimposing the structures. The method places molecular probes (i.e., small organic molecules containing various functional groups) around the protein to find hot spots. One of the most important hot spots is in the active site, consistent with the ability of the enzyme to bind both glucose and mannose phosphosugar substrates. The protein has eight additional hot spots at domain-domain interfaces and hinge regions. The locations and nature of six of these hot spots vary between the open, half-open, and closed conformers of the enzyme, in good agreement with the ligand-induced conformational changes. In the closed structures the number of probe clusters at the hinge region significantly depends on the position of the phosphorylated oxygen in the substrate (e.g., glucose 1-phosphate versus glucose 6-phosphate), but the protein remains almost unchanged in terms of the overall RMSD, indicating that computational solvent mapping is a more sensitive approach to detect changes in binding sites and interdomain crevices. Focusing on multidomain proteins we show that the subresolution conformational differences revealed by the mapping are in fact significant, and present a general statistical method of analysis to determine the significance of rigid body domain movements in X-ray structures.