MOTIVATION: Collagen fibrils are the primary load-bearing units of connective tissues. However, generating atomistic, simulation-ready models remains challenging due to collagen's hierarchical organization and the diversity of its crosslinking network across tissues, ages, and metabolic states. Notably, non-enzymatic advanced glycation end-product (AGE) crosslinks-central to aging and diabetic complications-are largely absent from current atomistic fibril modelling workflows. RESULTS: Here, we present an extension of the ColBuilder framework to generate atomistic collagen fibril models that incorporate three representative AGE-derived crosslinks (glucosepane, pentosidine, and MOLD) alongside enzymatic crosslinks. Amber99-compatible parameters are provided and assessed against QM-optimized reference geometries using all-atom molecular dynamics (MD) simulations. As proof-of-concept, we examine the mechanical response of single D-period collagen microfibrils featuring enzymatic-only, AGE-only, and mixed crosslink patterns in molecular dynamics simulations under force, and observe that AGE crosslinks differently impact the fibril structure compared to enzymatic crosslinks. The extension to ColBuilder can aid future structure-based research on collagen aging. AVAILABILITY AND IMPLEMENTATION: ColBuilder is available as an open-source Python command-line package at https://github.com/graeter-group/colbuilder.

Recent advances in geometric deep learning and generative modeling have enabled the design of novel proteins with a wide range of desired properties. However, current state-of-the-art approaches are typically restricted to generating proteins with only static target properties, such as motifs and symmetries. In this work, we take a step towards overcoming this limitation by proposing a framework to condition structure generation on flexibility, which is crucial for key functionalities such as catalysis or molecular recognition. We first introduce BackFlip, an equivariant neural network for predicting per-residue flexibility from an input backbone structure. Relying on BackFlip, we propose FliPS, an SE(3)-equivariant conditional flow matching model that solves the inverse problem, that is, generating backbones that display a target flexibility profile. In our experiments, we show that FliPS is able to generate novel and diverse protein backbones with the desired flexibility, verified by Molecular Dynamics (MD) simulations. FliPS and BackFlip are available at https://github.com/graeter-group/flips.

Deep generative models have recently been proposed for sampling protein conformations from the Boltzmann distribution, as an alternative to often prohibitively expensive Molecular Dynamics simulations. However, current state-of-the-art approaches rely on fine-tuning pre-trained folding models and evolutionary sequence information, limiting their applicability and efficiency, and introducing potential biases. In this work, we propose a flow matching model for sampling protein conformations based solely on backbone geometry - BBFlow. We introduce a geometric encoding of the backbone equilibrium structure as input and propose to condition not only the flow but also the prior distribution on the respective equilibrium structure, eliminating the need for evolutionary information. The resulting model is orders of magnitudes faster than current state-of-the-art approaches at comparable accuracy, is transferable to multi-chain proteins, and can be trained from scratch in a few GPU days. In our experiments, we demonstrate that the proposed model achieves competitive performance with reduced inference time, across not only an established benchmark of naturally occurring proteins but also de novo proteins, for which evolutionary information is scarce or absent. BBFlow is available at https://github.com/graeter-group/bbflow.

MOTIVATION: Collagen fibrils are fundamental building blocks of connective tissues, yet generating accurate molecular models of their structure remains challenging due to their hierarchical organization and complex crosslinking patterns. RESULTS: ColBuilder has been developed to automate the generation of atomistic models of crosslinked collagen fibrils and facilitate the setup of molecular simulations. The tool integrates homology modeling, higher order structure generation and optimization to build complete fibril structures with precise control over sequence composition, crosslinking patterns, and dimensions. Users can explore different collagen sequences, manipulate crosslink chemistry through mixed ratios and densities, and generate fibrils of varying diameter and length. All-atom molecular dynamics simulations of 335nm-long fibrils validate the generated structures, showing excellent agreement with experimental measurements of D-band periodicity and force-extension behavior. AVAILABILITY AND IMPLEMENTATION: ColBuilder is available both as an open-source command-line application and through a web interface at https://colbuilder.mpip-mainz.mpg.de.

We introduce a generative model for protein backbone design utilizing geometric products and higher order message passing. In particular, we propose Clifford Frame Attention (CFA), an extension of the invariant point attention (IPA) architecture from AlphaFold2, in which the backbone residue frames and geometric features are represented in the projective geometric algebra. This enables to construct geometrically expressive messages between residues, including higher order terms, using the bilinear operations of the algebra. We evaluate our architecture by incorporating it into the framework of FrameFlow, a state-of-the-art flow matching model for protein backbone generation. The proposed model achieves high designability, diversity and novelty, while also sampling protein backbones that follow the statistical distribution of secondary structure elements found in naturally occurring proteins, a property so far only insufficiently achieved by many state-of-the-art generative models.

Plasmodium falciparum (Pf) is responsible for the most lethal form of malaria. VAR2CSA is an adhesin protein expressed by this parasite at the membrane of infected erythrocytes for attachment to the placenta, leading to pregnancy-associated malaria. VAR2CSA is a large 355 kDa multidomain protein composed of nine extracellular domains, a transmembrane helix, and an intracellular domain. VAR2CSA binds to Chondroitin Sulphate A (CSA) of the proteoglycan matrix of the placenta. Shear flow, as the one occurring in blood, has been shown to enhance the (VAR2CSA-mediated) adhesion of Pf-infected erythrocytes on the CSA-matrix. However, the underlying molecular mechanism governing this enhancement has remained elusive. Here, we address this question by using equilibrium, force-probe, and docking-based molecular dynamics simulations. We subjected the VAR2CSA protein-CSA sugar complex to a force mimicking the tensile force exerted on this system due to the shear of the flowing blood. We show that upon this force exertion, VAR2CSA undergoes a large opening conformational transition before the CSA sugar chain dissociates from its main binding site. This preferential order of events is caused by the orientation of the molecule during elongation, as well as the strong electrostatic attraction of the sugar to the main protein binding site. Upon opening, two additional cryptic CSA binding sites get exposed and a functional dodecameric CSA molecule can be stably accommodated at these force-exposed positions. Thus, our results suggest that mechanical forces increase the avidity of VAR2CSA by turning it from a monovalent to a multivalent state. We propose this to be the molecular cause of the observed shear-enhanced adherence. Mechanical control of the valency of VAR2CSA is an intriguing hypothesis that can be tested experimentally and which is of relevance for the understanding of the malaria infection and for the development of anti placental-malaria vaccines targeting VAR2CSA.

Phosphorylation of intrinsically disordered proteins (IDPs) can produce changes in structural and dynamical properties and thereby mediate critical biological functions. How phosphorylation effects intrinsically disordered proteins has been studied for an increasing number of IDPs, but a systematic understanding is still lacking. Here, we compare the collapse propensity of four disordered proteins, Ash1, the C-terminal domain of RNA polymerase (CTD2'), the cytosolic domain of E-Cadherin, and a fragment of the p130Cas, in unphosphorylated and phosphorylated forms using extensive all-atom molecular dynamics (MD) simulations. We find all proteins to show V-shape changes in their collapse propensity upon multi-site phosphorylation according to their initial net charge: phosphorylation expands neutral or overall negatively charged IDPs and shrinks positively charged IDPs. However, force fields including those tailored towards and commonly used for IDPs overestimate these changes. We find quantitative agreement of MD results with SAXS and NMR data for Ash1 and CTD2' only when attenuating protein electrostatic interactions by using a higher salt concentration (e.g. 350 mM), highlighting the overstabilization of salt bridges in current force fields. We show that phosphorylation of IDPs also has a strong impact on the solvation of the protein, a factor that in addition to the actual collapse or expansion of the IDP should be considered when analyzing SAXS data. Compared to the overall mild change in global IDP dimension, the exposure of active sites can change significantly upon phosphorylation, underlining the large susceptibility of IDP ensembles to regulation through post-translational modifications.

The Catabolite Activator Protein (CAP) is a showcase example for entropic allostery. For full activation and DNA binding, the homodimeric protein requires the binding of two cyclic AMP (cAMP) molecules in an anti-cooperative manner, the source of which appears to be largely of entropic nature according to previous experimental studies. We here study at atomic detail the allosteric regulation of CAP with Molecular dynamics (MD) simulations. We recover the experimentally observed entropic penalty for the second cAMP binding event with our recently developed force covariance entropy estimator and reveal allosteric communication pathways with Force Distribution Analyses (FDA). Our observations show that CAP binding results in characteristic changes in the interaction pathways connecting the two cAMP allosteric binding sites with each other, as well as with the DNA binding domains. We identified crucial relays in the mostly symmetric allosteric activation network, and suggest point mutants to test this mechanism. Our study suggests inter-residue forces, as opposed to coordinates, as a highly sensitive measure for structural adaptations that, even though minute, can very effectively propagate allosteric signals.

Mechanosensing at focal adhesions regulates vital cellular processes. Here, we present results from molecular dynamics (MD) and mechano-biochemical network simulations that suggest a direct role of Focal Adhesion Kinase (FAK) as a mechano-sensor. Tensile forces, propagating from the membrane through the PIP2 binding site of the FERM domain and from the cytoskeleton-anchored FAT domain, activate FAK by unlocking its central phosphorylation site (Tyr576/577) from the autoinhibitory FERM domain. Varying loading rates, pulling directions, and membrane PIP2 concentrations corroborate the specific opening of the FERM-kinase domain interface, due to its remarkably lower mechanical stability compared to the individual alpha-helical domains and the PIP2-FERM link. Analyzing downstream signaling networks provides further evidence for an intrinsic mechano-signaling role of FAK in broadcasting force signals through Ras to the nucleus. This distinguishes FAK from hitherto identified focal adhesion mechano-responsive molecules, allowing a new interpretation of cell stretching experiments.

3-Phosphogycerate kinase (PGK) is a two domain enzyme, which transfers a phosphate group between its two substrates, 1,3-bisphosphoglycerate bound to the N-domain and ADP bound to the C-domain. Indispensable for the phosphoryl transfer reaction is a large conformational change from an inactive open to an active closed conformation via a hinge motion that should bring substrates into close proximity. The allosteric pathway resulting in the active closed conformation has only been partially uncovered. Using Molecular Dynamics simulations combined with Force Distribution Analysis (FDA), we describe an allosteric pathway, which connects the substrate binding sites to the interdomain hinge region. Glu192 of alpha-helix 7 and Gly394 of loop L14 act as hinge points, at which these two secondary structure elements straighten, thereby moving the substrate-binding domains towards each other. The long-range allosteric pathway regulating hPGK catalytic activity, which is partially validated and can be further tested by mutagenesis, highlights the virtue of monitoring internal forces to reveal signal propagation, even if only minor conformational distortions, such as helix bending, initiate the large functional rearrangement of the macromolecule.

Nature has shaped the make up of proteins since their appearance, [Formula: see text]3.8 billion years ago. However, the fundamental drivers of structural change responsible for the extraordinary diversity of proteins have yet to be elucidated. Here we explore if protein evolution affects folding speed. We estimated folding times for the present-day catalog of protein domains directly from their size-modified contact order. These values were mapped onto an evolutionary timeline of domain appearance derived from a phylogenomic analysis of protein domains in 989 fully-sequenced genomes. Our results show a clear overall increase of folding speed during evolution, with known ultra-fast downhill folders appearing rather late in the timeline. Remarkably, folding optimization depends on secondary structure. While alpha-folds showed a tendency to fold faster throughout evolution, beta-folds exhibited a trend of folding time increase during the last [Formula: see text]1.5 billion years that began during the "big bang" of domain combinations. As a consequence, these domain structures are on average slow folders today. Our results suggest that fast and efficient folding of domains shaped the universe of protein structure. This finding supports the hypothesis that optimization of the kinetic and thermodynamic accessibility of the native fold reduces protein aggregation propensities that hamper cellular functions.

A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.

BACKGROUND: The way mechanical stress is distributed inside and propagated by proteins and other biopolymers largely defines their function. Yet, determining the network of interactions propagating internal strain remains a challenge for both, experiment and theory. Based on molecular dynamics simulations, we developed force distribution analysis (FDA), a method that allows visualizing strain propagation in macromolecules. RESULTS: To be immediately applicable to a wide range of systems, FDA was implemented as an extension to Gromacs, a commonly used package for molecular simulations. The FDA code comes with an easy-to-use command line interface and can directly be applied to every system built using Gromacs. We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data. CONCLUSIONS: Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers. By elucidating propagation of internal strain upon ligand binding, we previously also successfully revealed the functionality of a stiff allosteric protein. FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

The role of mechanical force in cellular processes is increasingly revealed by single molecule experiments and simulations of force-induced transitions in proteins. How the applied force propagates within proteins determines their mechanical behavior yet remains largely unknown. We present a new method based on molecular dynamics simulations to disclose the distribution of strain in protein structures, here for the newly determined high-resolution crystal structure of I27, a titin immunoglobulin (IG) domain. We obtain a sparse, spatially connected, and highly anisotropic mechanical network. This allows us to detect load-bearing motifs composed of interstrand hydrogen bonds and hydrophobic core interactions, including parts distal to the site to which force was applied. The role of the force distribution pattern for mechanical stability is tested by in silico unfolding of I27 mutants. We then compare the observed force pattern to the sparse network of coevolved residues found in this family. We find a remarkable overlap, suggesting the force distribution to reflect constraints for the evolutionary design of mechanical resistance in the IG family. The force distribution analysis provides a molecular interpretation of coevolution and opens the road to the study of the mechanism of signal propagation in proteins in general.

Many fundamental cellular processes such as gene expression are tightly regulated by protein allostery. Allosteric signal propagation from the regulatory to the active site requires long-range communication, the molecular mechanism of which remains a matter of debate. A classical example for long-range allostery is the activation of the methionine repressor MetJ, a transcription factor. Binding of its co-repressor SAM increases its affinity for DNA several-fold, but has no visible conformational effect on its DNA binding interface. Our molecular dynamics simulations indicate correlated domain motions within MetJ, and quenching of these dynamics upon SAM binding entropically favors DNA binding. From monitoring conformational fluctuations alone, it is not obvious how the presence of SAM is communicated through the largely rigid core of MetJ and how SAM thereby is able to regulate MetJ dynamics. We here directly monitored the propagation of internal forces through the MetJ structure, instead of relying on conformational changes as conventionally done. Our force distribution analysis successfully revealed the molecular network for strain propagation, which connects collective domain motions through the protein core. Parts of the network are directly affected by SAM binding, giving rise to the observed quenching of fluctuations. Our results are in good agreement with experimental data. The force distribution analysis suggests itself as a valuable tool to gain insight into the molecular function of a whole class of allosteric proteins.