The missing link: covalent linkages in structural models

Covalent linkages between constituent blocks of macromolecules and ligands have been subject to inconsistent treatment during the model-building, refinement and deposition process. This may stem from a number of sources, including difficulties with initially detecting the covalent linkage, identifying the correct chemistry, obtaining an appropriate restraint dictionary and ensuring its correct application. The analysis presented herein assesses the extent of problems involving covalent linkages in the Protein Data Bank (PDB). Not only will this facilitate the remediation of existing models, but also, more importantly, it will inform and thus improve the quality of future linkages. By considering linkages of known type in the CCP4 Monomer Library (CCP4-ML), failure to model a covalent linkage is identified to result in inaccurate (systematically longer) interatomic distances. Scanning the PDB for proximal atom pairs that do not have a corresponding type in the CCP4-ML reveals a large number of commonly occurring types of unannotated potential linkages; in general, these may or may not be covalently linked. Manual consideration of the most commonly occurring cases identifies a number of genuine classes of covalent linkages. The recent expansion of the CCP4-ML is discussed, which has involved the addition of over 16 000 and the replacement of over 11 000 component dictionaries using AceDRG. As part of this effort, the CCP4-ML has also been extended using AceDRG link dictionaries for the aforementioned linkage types identified in this analysis. This will facilitate the identification of such linkage types in future modelling efforts, whilst concurrently easing the process involved in their application. The need for a universal standard for maintaining link records corresponding to covalent linkages, and references to the associated dictionaries used during modelling and refinement, following deposition to the PDB is emphasized. The importance of correctly modelling covalent linkages is demonstrated using a case study, which involves the covalent linkage of an inhibitor to the main protease in various viral species, including SARS-CoV-2. This example demonstrates the importance of properly modelling covalent linkages using a comprehensive restraint dictionary, as opposed to just using a single interatomic distance restraint or failing to model the covalent linkage at all.

CBCR: A Curriculum Based Strategy For Chromosome Reconstruction

In this paper, we introduce a novel algorithm that aims to estimate chromosomes’ structure from their Hi-C contact data, called Curriculum Based Chromosome Reconstruction (CBCR). Specifically, our method performs this three dimensional reconstruction using cis-chromosomal interactions from Hi-C data. CBCR takes intra-chromosomal Hi-C interaction frequencies as an input and outputs a set of xyz coordinates that estimate the chromosome’s three dimensional structure in the form of a .pdb file. The algorithm relies on progressively training a distance-restraint-based algorithm with a strategy we refer to as curriculum learning. Curriculum learning divides the Hi-C data into classes based on contact frequency and progressively re-trains the distance-restraint algorithm based on the assumed importance of each curriculum in predicting the underlying chromosome structure. The distance-restraint algorithm relies on a modification of a Gaussian maximum likelihood function that scales probabilities based on the importance of features. We evaluate the performance of CBCR on both simulated and actual Hi-C data and perform validation on FISH, HiChIP, and ChIA-PET data as well. We also compare the performance of CBCR to several current methods. Our analysis shows that the use of curricula affects the rate of convergence of the optimization while decreasing the computational cost of our distance-restraint algorithm. Also, CBCR is more robust to increases in data resolution and therefore yields superior reconstruction accuracy of higher resolution data than all other methods in our comparison.

Adaptive Cartesian and torsional restraints for interactive model rebuilding

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows beyond that range. In each current implementation the rate at which the potential flattens at large deviations follows a fixed form, although the form chosen varies among implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here, two new such potentials are described: a Cartesian distance restraint derived from a recent generalization of common loss functions and a periodic torsion restraint based on a renormalization of the von Mises distribution. Further, their implementation as user-adjustable/switchable restraints in ISOLDE is described and their use in some real-world examples is demonstrated.

Improving integrative 3D modeling into low- to medium- resolution EM structures with evolutionary couplings

Electron microscopy (EM) continues to provide near-atomic resolution structures for well-behaved proteins and protein complexes. Unfortunately, structures of some complexes are limited to low- to medium-resolution due to biochemical or conformational heterogeneity. Thus, the application of unbiased systematic methods for fitting individual structures into EM maps is important. A method that employs co-evolutionary information obtained solely from sequence data could prove invaluable for quick, confident localization of subunits within these structures. Here, we incorporate the co-evolution of intermolecular amino acids as a new type of distance restraint in the Integrative Modeling Platform (IMP) in order to build three-dimensional models of atomic structures into EM maps ranging from 10-14 Å in resolution. We validate this method using four complexes of known structure, where we highlight the conservation of intermolecular couplings despite dynamic conformational changes using the BAM complex. Finally, we use this method to assemble the subunits of the bacterial holo-translocon into a model that agrees with previous biochemical data. The use of evolutionary couplings in integrative modeling improves systematic, unbiased fitting of atomic models into medium- to low-resolution EM maps, providing additional information to integrative models lacking in spatial data.

Adaptive conformational restraints for interactive model rebuilding in Cartesian and torsion space

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain its conformation to that of a higher-resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of “top-out” potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows larger than a defined transition point. In each current implementation, the rate at which the potential flattens beyond the transition region follows a fixed form – although the form chosen varies between implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here we describe two new such potentials: a Cartesian distance restraint derived from a recent generalisation of common loss functions, and a periodic torsion restraint based on a renormalisation of the von Mises distribution. Further, we describe their implementation as user-adjustable/switchable restraints in ISOLDE, and demonstrate their use in some real-world examples.SynopsisNew forms of adaptive or top-out distance and torsion restraints are described, suitable for restraining a model to match a reference structure during interactive rebuilding. In addition, their implementation in ISOLDE is described along with some illustrative example applications.

Molecular Dynamics Simulations of the “Breathing” Phase Transformation of MOF Nanocrystallites

One of the intriguing features of certain metal-organic frameworks (MOFs) is the large volume change upon external stimuli like pressure or guest molecule adsorption, referred to as “breathing”. This displacive phase transformation from an open to a closed pore has been investigated intensively by theoretical simulations within periodic boundary conditions (PBC). However, the actual free energy barriers for the transformation under real conditions and the impact of surface effects on it can only be studied beyond PBC for nanocrystallites. In this work, we used the first-principles parameterized forcefield MOF-FF to investigate the thermal- and pressure induced transformations for nanocrystallites of the pillared-layer DMOF-1 (Zn<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(bdc)<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(dabco); bdc: 1,4-benzenedicarboxylate; dabco: 1,4-diazabicyclo[2.2.2]octane) as a model system. By heating of prepared closed pore nanocrystallites of different size, a spontaneous opening is observed within a few tenth of picoseconds with an interface between the closed and open pore phase moving with a velocity of several 100 m/s<math><mrow><mrow><mi></mi> </mrow><mrow><mi></mi> </mrow> </mrow></math> through the system. The critical nucleation temperature for the opening transition raises with size. On the other hand, by forcing the closing transition with a distance restraint between paddle-wheel units placed on opposite edges of the crystallite, the free energy barrier can be determined by umbrella sampling. As expected, this barrier is substantially lower than the one determined for a concerted process under PBC. Interestingly, the barrier reduces with the size of the crystallite, indicating a hindering surface effect. The results demonstrate the need consider domain boundaries and surfaces, for example by simulations that go beyond PBC and to large system sizes in order to properly predict and describe first order phase transitions in MOFs.<div> </div>

Molecular Dynamics Simulations of the “Breathing” Phase Transformation of MOF Nanocrystallites

One of the intriguing features of certain metal-organic frameworks (MOFs) is the large volume change upon external stimuli like pressure or guest molecule adsorption, referred to as “breathing”. This displacive phase transformation from an open to a closed pore has been investigated intensively by theoretical simulations within periodic boundary conditions (PBC). However, the actual free energy barriers for the transformation under real conditions and the impact of surface effects on it can only be studied beyond PBC for nanocrystallites. In this work, we used the first-principles parameterized forcefield MOF-FF to investigate the thermal- and pressure induced transformations for nanocrystallites of the pillared-layer DMOF-1 (Zn<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(bdc)<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(dabco); bdc: 1,4-benzenedicarboxylate; dabco: 1,4-diazabicyclo[2.2.2]octane) as a model system. By heating of prepared closed pore nanocrystallites of different size, a spontaneous opening is observed within a few tenth of picoseconds with an interface between the closed and open pore phase moving with a velocity of several 100 m/s<math><mrow><mrow><mi></mi> </mrow><mrow><mi></mi> </mrow> </mrow></math> through the system. The critical nucleation temperature for the opening transition raises with size. On the other hand, by forcing the closing transition with a distance restraint between paddle-wheel units placed on opposite edges of the crystallite, the free energy barrier can be determined by umbrella sampling. As expected, this barrier is substantially lower than the one determined for a concerted process under PBC. Interestingly, the barrier reduces with the size of the crystallite, indicating a hindering surface effect. The results demonstrate the need consider domain boundaries and surfaces, for example by simulations that go beyond PBC and to large system sizes in order to properly predict and describe first order phase transitions in MOFs.<div> </div>