MatchMaps: non-isomorphous difference maps for X-ray crystallography.

Conformational change mediates the biological functions of macromolecules. Crystallographic measurements can map these changes with extraordinary sensitivity as a function of mutations, ligands and time. A popular method for detecting structural differences between crystallographic data sets is the isomorphous difference map. These maps combine the phases of a chosen reference state with the observed changes in structure factor amplitudes to yield a map of changes in electron density. Such maps are much more sensitive to conformational change than structure refinement is, and are unbiased in the sense that observed differences do not depend on refinement of the perturbed state. However, even modest changes in unit-cell properties can render isomorphous difference maps useless. This is unnecessary. Described here is a generalized procedure for calculating observed difference maps that retains the high sensitivity to conformational change and avoids structure refinement of the perturbed state. This procedure is implemented in an open-source Python package, MatchMaps, that can be run in any software environment supporting PHENIX [Liebschner et al. (2019). Acta Cryst. D75, 861-877] and CCP4 [Agirre et al. (2023). Acta Cryst. D79, 449-461]. Worked examples show that MatchMaps 'rescues' observed difference electron-density maps for poorly isomorphous crystals, corrects artifacts in nominally isomorphous difference maps, and extends to detecting differences across copies within the asymmetric unit or across altogether different crystal forms.

Perturbative diffraction methods resolve a conformational switch that facilitates a two-step enzymatic mechanism.

Enzymes catalyze biochemical reactions through precise positioning of substrates, cofactors, and amino acids to modulate the transition-state free energy. However, the role of conformational dynamics remains poorly understood due to poor experimental access. This shortcoming is evident with Escherichia coli dihydrofolate reductase (DHFR), a model system for the role of protein dynamics in catalysis, for which it is unknown how the enzyme regulates the different active site environments required to facilitate proton and hydride transfer. Here, we describe ligand-, temperature-, and electric-field-based perturbations during X-ray diffraction experiments to map the conformational dynamics of the Michaelis complex of DHFR. We resolve coupled global and local motions and find that these motions are engaged by the protonated substrate to promote efficient catalysis. This result suggests a fundamental design principle for multistep enzymes in which pre-existing dynamics enable intermediates to drive rapid electrostatic reorganization to facilitate subsequent chemical steps.

MatchMaps: Non-isomorphous difference maps for X-ray crystallography.

Conformational change mediates the biological functions of macromolecules. Crystallographic measurements can map these changes with extraordinary sensitivity as a function of mutations, ligands, and time. The isomorphous difference map remains the gold standard for detecting structural differences between datasets. Isomorphous difference maps combine the phases of a chosen reference state with the observed changes in structure factor amplitudes to yield a map of changes in electron density. Such maps are much more sensitive to conformational change than structure refinement is, and are unbiased in the sense that observed differences do not depend on refinement of the perturbed state. However, even minute changes in unit cell properties can render isomorphous difference maps useless. This is unnecessary. Here we describe a generalized procedure for calculating observed difference maps that retains the high sensitivity to conformational change and avoids structure refinement of the perturbed state. We have implemented this procedure in an open-source python package, MatchMaps, that can be run in any software environment supporting PHENIX and CCP4. Through examples, we show that MatchMaps "rescues" observed difference electron density maps for poorly-isomorphous crystals, corrects artifacts in nominally isomorphous difference maps, and extends to detecting differences across copies within the asymmetric unit, or across altogether different crystal forms.

Correcting systematic errors in diffraction data with modern scaling algorithms.

X-ray diffraction enables the routine determination of the atomic structure of materials. Key to its success are data-processing algorithms that allow experimenters to determine the electron density of a sample from its diffraction pattern. Scaling, the estimation and correction of systematic errors in diffraction intensities, is an essential step in this process. These errors arise from sample heterogeneity, radiation damage, instrument limitations and other aspects of the experiment. New X-ray sources and sample-delivery methods, along with new experiments focused on changes in structure as a function of perturbations, have led to new demands on scaling algorithms. Classically, scaling algorithms use least-squares optimization to fit a model of common error sources to the observed diffraction intensities to force these intensities onto the same empirical scale. Recently, an alternative approach has been demonstrated which uses a Bayesian optimization method, variational inference, to simultaneously infer merged data along with corrections, or scale factors, for the systematic errors. Owing to its flexibility, this approach proves to be advantageous in certain scenarios. This perspective briefly reviews the history of scaling algorithms and contrasts them with variational inference. Finally, appropriate use cases are identified for the first such algorithm, Careless, guidance is offered on its use and some speculations are made about future variational scaling methods.

Resolving conformational changes that mediate a two-step catalytic mechanism in a model enzyme.

Enzymes catalyze biochemical reactions through precise positioning of substrates, cofactors, and amino acids to modulate the transition-state free energy. However, the role of conformational dynamics remains poorly understood due to lack of experimental access. This shortcoming is evident with E. coli dihydrofolate reductase (DHFR), a model system for the role of protein dynamics in catalysis, for which it is unknown how the enzyme regulates the different active site environments required to facilitate proton and hydride transfer. Here, we present ligand-, temperature-, and electric-field-based perturbations during X-ray diffraction experiments that enable identification of coupled conformational changes in DHFR. We identify a global hinge motion and local networks of structural rearrangements that are engaged by substrate protonation to regulate solvent access and promote efficient catalysis. The resulting mechanism shows that DHFR's two-step catalytic mechanism is guided by a dynamic free energy landscape responsive to the state of the substrate.

Emerging Time-Resolved X-Ray Diffraction Approaches for Protein Dynamics.

Proteins guide the flows of information, energy, and matter that make life possible by accelerating transport and chemical reactions, by allosterically modulating these reactions, and by forming dynamic supramolecular assemblies. In these roles, conformational change underlies functional transitions. Time-resolved X-ray diffraction methods characterize these transitions either by directly triggering sequences of functionally important motions or, more broadly, by capturing the motions of which proteins are capable. To date, most successful have been experiments in which conformational change is triggered in light-dependent proteins. In this review, I emphasize emerging techniques that probe the dynamic basis of function in proteins lacking natively light-dependent transitions and speculate about extensions and further possibilities. In addition, I review how the weaker and more distributed signals in these data push the limits of the capabilities of analytical methods. Taken together, these new methods are beginning to establish a powerful paradigm for the study of the physics of protein function.

A unifying Bayesian framework for merging X-ray diffraction data.

Novel X-ray methods are transforming the study of the functional dynamics of biomolecules. Key to this revolution is detection of often subtle conformational changes from diffraction data. Diffraction data contain patterns of bright spots known as reflections. To compute the electron density of a molecule, the intensity of each reflection must be estimated, and redundant observations reduced to consensus intensities. Systematic effects, however, lead to the measurement of equivalent reflections on different scales, corrupting observation of changes in electron density. Here, we present a modern Bayesian solution to this problem, which uses deep learning and variational inference to simultaneously rescale and merge reflection observations. We successfully apply this method to monochromatic and polychromatic single-crystal diffraction data, as well as serial femtosecond crystallography data. We find that this approach is applicable to the analysis of many types of diffraction experiments, while accurately and sensitively detecting subtle dynamics and anomalous scattering.

Native SAD phasing at room temperature.

Single-wavelength anomalous diffraction (SAD) is a routine method for overcoming the phase problem when solving macromolecular structures. This technique requires the accurate measurement of intensities to determine differences between Bijvoet pairs. Although SAD experiments are commonly conducted at cryogenic temperatures to mitigate the effects of radiation damage, such temperatures can alter the conformational ensemble of the protein and may impede the merging of data from multiple crystals due to non-uniform freezing. Here, a strategy is presented to obtain high-quality data from room-temperature, single-crystal experiments. To illustrate the strengths of this approach, native SAD phasing at 6.55 keV was used to solve four structures of three model systems at 295 K. The resulting data sets allow automatic phasing and model building, and reveal alternate conformations that reflect the structure of proteins at room temperature.

reciprocalspaceship: a Python library for crystallographic data analysis.

Crystallography uses the diffraction of X-rays, electrons or neutrons by crystals to provide invaluable data on the atomic structure of matter, from single atoms to ribosomes. Much of crystallography's success is due to the software packages developed to enable automated processing of diffraction data. However, the analysis of unconventional diffraction experiments can still pose significant challenges - many existing programs are closed source, sparsely documented, or challenging to integrate with modern libraries for scientific computing and machine learning. Described here is reciprocalspaceship, a Python library for exploring reciprocal space. It provides a tabular representation for reflection data from diffraction experiments that extends the widely used pandas library with built-in methods for handling space groups, unit cells and symmetry-based operations. As is illustrated, this library facilitates new modes of exploratory data analysis while supporting the prototyping, development and release of new methods.

Polymeric peptide pigments with sequence-encoded properties.

Melanins are a family of heterogeneous polymeric pigments that provide ultraviolet (UV) light protection, structural support, coloration, and free radical scavenging. Formed by oxidative oligomerization of catecholic small molecules, the physical properties of melanins are influenced by covalent and noncovalent disorder. We report the use of tyrosine-containing tripeptides as tunable precursors for polymeric pigments. In these structures, phenols are presented in a (supra-)molecular context dictated by the positions of the amino acids in the peptide sequence. Oxidative polymerization can be tuned in a sequence-dependent manner, resulting in peptide sequence-encoded properties such as UV absorbance, morphology, coloration, and electrochemical properties over a considerable range. Short peptides have low barriers to application and can be easily scaled, suggesting near-term applications in cosmetics and biomedicine.

Electric-field-stimulated protein mechanics.

The internal mechanics of proteins-the coordinated motions of amino acids and the pattern of forces constraining these motions-connects protein structure to function. Here we describe a new method combining the application of strong electric field pulses to protein crystals with time-resolved X-ray crystallography to observe conformational changes in spatial and temporal detail. Using a human PDZ domain (LNX2PDZ2) as a model system, we show that protein crystals tolerate electric field pulses strong enough to drive concerted motions on the sub-microsecond timescale. The induced motions are subtle, involve diverse physical mechanisms, and occur throughout the protein structure. The global pattern of electric-field-induced motions is consistent with both local and allosteric conformational changes naturally induced by ligand binding, including at conserved functional sites in the PDZ domain family. This work lays the foundation for comprehensive experimental study of the mechanical basis of protein function.

Evolvability as a function of purifying selection in TEM-1 ß-lactamase.

Evolvability­the capacity to generate beneficial heritable variation­is a central property of biological systems. However, its origins and modulation by environmental factors have not been examined systematically. Here, we analyze the fitness effects of all single mutations in TEM-1 ß-lactamase (4,997 variants) under selection for the wild-type function (ampicillin resistance) and for a new function (cefotaxime resistance). Tolerance to mutation in this enzyme is bimodal and dependent on the strength of purifying selection in vivo, a result that derives from a steep non-linear ampicillin-dependent relationship between biochemical activity and fitness. Interestingly, cefotaxime resistance emerges from mutations that are neutral at low levels of ampicillin but deleterious at high levels; thus the capacity to evolve new function also depends on the strength of selection. The key property controlling evolvability is an excess of enzymatic activity relative to the strength of selection, suggesting that fluctuating environments might select for high-activity enzymes.

Trend and fluctuations: analysis and design of population dynamics measurements in replicate ecosystems.

The dynamical evolution of complex systems is often intrinsically stochastic and subject to external random forces. In order to study the resulting variability in dynamics, it is essential to make measurements on replicate systems and to separate arbitrary variation of the average dynamics of these replicates from fluctuations around the average dynamics. Here we do so for population time-series data from replicate ecosystems sharing a common average dynamics or common trend. We explain how model parameters, including the effective interactions between species and dynamical noise, can be estimated from the data and how replication reduces errors in these estimates. For this, it is essential that the model can fit a variety of average dynamics. We then show how one can judge the quality of a model, compare alternate models, and determine which combinations of parameters are poorly determined by the data. In addition we show how replicate population dynamics experiments could be designed to optimize the acquired information of interest about the systems. Our approach is illustrated on a set of time series gathered from replicate microbial closed ecosystems.

Contingency and statistical laws in replicate microbial closed ecosystems.

Contingency, the persistent influence of past random events, pervades biology. To what extent, then, is each course of ecological or evolutionary dynamics unique, and to what extent are these dynamics subject to a common statistical structure? Addressing this question requires replicate measurements to search for emergent statistical laws. We establish a readily replicated microbial closed ecosystem (CES), sustaining its three species for years. We precisely measure the local population density of each species in many CES replicates, started from the same initial conditions and kept under constant light and temperature. The covariation among replicates of the three species densities acquires a stable structure, which could be decomposed into discrete eigenvectors, or "ecomodes." The largest ecomode dominates population density fluctuations around the replicate-average dynamics. These fluctuations follow simple power laws consistent with a geometric random walk. Thus, variability in ecological dynamics can be studied with CES replicates and described by simple statistical laws.

Genome-wide analysis of mRNA abundance in two life-cycle stages of Trypanosoma brucei and identification of splicing and polyadenylation sites.

Transcription of protein-coding genes in trypanosomes is polycistronic and gene expression is primarily regulated by post-transcriptional mechanisms. Sequence motifs in the untranslated regions regulate mRNA trans-splicing and RNA stability, yet where UTRs begin and end is known for very few genes. We used high-throughput RNA-sequencing to determine the genome-wide steady-state mRNA levels ('transcriptomes') for approximately 90% of the genome in two stages of the Trypanosoma brucei life cycle cultured in vitro. Almost 6% of genes were differentially expressed between the two life-cycle stages. We identified 5' splice-acceptor sites (SAS) and polyadenylation sites (PAS) for 6959 and 5948 genes, respectively. Most genes have between one and three alternative SAS, but PAS are more dispersed. For 488 genes, SAS were identified downstream of the originally assigned initiator ATG, so a subsequent in-frame ATG presumably designates the start of the true coding sequence. In some cases, alternative SAS would give rise to mRNAs encoding proteins with different N-terminal sequences. We could identify the introns in two genes known to contain them, but found no additional genes with introns. Our study demonstrates the usefulness of the RNA-seq technology to study the transcriptional landscape of an organism whose genome has not been fully annotated.

Four histone variants mark the boundaries of polycistronic transcription units in Trypanosoma brucei.

Unusually for a eukaryote, genes transcribed by RNA polymerase II (pol II) in Trypanosoma brucei are arranged in polycistronic transcription units. With one exception, no pol II promoter motifs have been identified, and how transcription is initiated remains an enigma. T. brucei has four histone variants: H2AZ, H2BV, H3V, and H4V. Using chromatin immunoprecipitation (ChIP) and sequencing (ChIP-seq) to examine the genome-wide distribution of chromatin components, we show that histones H4K10ac, H2AZ, H2BV, and the bromodomain factor BDF3 are enriched up to 300-fold at probable pol II transcription start sites (TSSs). We also show that nucleosomes containing H2AZ and H2BV are less stable than canonical nucleosomes. Our analysis also identifies >60 unexpected TSS candidates and reveals the presence of long guanine runs at probable TSSs. Apparently unique to trypanosomes, additional histone variants H3V and H4V are enriched at probable pol II transcription termination sites. Our findings suggest that histone modifications and histone variants play crucial roles in transcription initiation and termination in trypanosomes and that destabilization of nucleosomes by histone variants is an evolutionarily ancient and general mechanism of transcription initiation, demonstrated in an organism in which general pol II transcription factors have been elusive.

Analysis of the Trypanosoma brucei cell cycle by quantitative DAPI imaging.

Trypanosoma brucei has two DNA compartments: the nucleus and the kinetoplast. DNA replication of these two compartments only partially coincides. Woodward and Gull [Woodward R, Gull K. Timing of nuclear and kinetoplast DNA replication and early morphological events in the cell cycle of Trypanosoma brucei. J Cell Sci 1990;95:49-57] comprehensively studied the relative timing of the replication and segregation of nuclear DNA (nDNA) and kinetoplast DNA (kDNA). Others have since assumed the consistency of morphological indicators of cell-cycle stage among strains and conditions. We report the use of quantitative DAPI imaging to determine the cell-cycle stage of individual procyclic cells. Using this approach, we found that kinetoplast elongation occurs mainly during nuclear S phase and not during G2, as previously assumed. We confirmed this finding by sorting cells by DNA content, followed by fluorescence microscopy. In addition, simultaneous quantitative imaging at two wavelengths can be used to determine the abundance of cell-cycle-regulated proteins during the cell cycle. We demonstrate this technique by co-staining for the non-acetylated state of lysine 4 of histone H4 (H4K4), which is enriched during nuclear S phase.