Complex Folding Research Articles

Structure and development of the Valmiera–Lokno Uplift – a highly elevated basement block with a strongly deformed and eroded platform cover in the East European Craton interior around the Estonian–Latvian–Russian borderland

Based on drillings, a number of geological cross-sections, and structure contour and isopach maps were composed to describe/analyse the structure and development of the Valmiera–Lokno Uplift (VLU), a basement block elevated up to 700 m with a heavily deformed and eroded platform cover in the East European Craton interior, along the regional Liepaja–Riga–Pskov Fault Zone (LRPFZ). Five isolated basement-cored anticlines (BCA), the Lokno, Haanja, Moniste, Valmiera and Smiltene uplifts, arise in the platform cover on the VLU, whereas the downthrown LRPFZ side defines a complex monoclinal fold. The anticlines, straddling or occurring near the monocline, merge with it and thus have highly asymmetrical shapes. Thickness changes of stratigraphic units across the VLU reveal its complex history, reflecting regional tectonic activation pulses that varied noticeably even between neighbouring BCAs. In all, the latest Precambrian–earliest Ordovician initiation epoch of the VLU was followed by modest tectonic activity or a standstill period in the Middle Ordovician–Early Silurian. Intensifying tectonic movements culminated again in the prime of the Caledonian Orogeny in latest Silurian–earliest Devonian time, and faded thereafter towards the end of Early Devonian. The VLU has been reactivated occasionally since the latest Devonian and emerges as a crustal weakness in the recent movement and seismicity patterns. To decipher the origin of the VLU, hitherto factually undiscussed topics, a more detailed study of the LRPFZ, analysis of its fault pattern and kinematics alongside the regional tectonic setting/history is needed. A cursory look hints to a substantial Early Paleozoic sinistral strike-slip along the LRPFZ, allowing interpreting the VLU as a possible restraining bend structure.

Structural evolution of salt-influenced fold-and-thrust belts: A synthesis and new insights from basins containing isolated salt diapirs

Lateral shortening is expressed in unique ways in salt basins, especially if pre-shortening diapirs are present. We present an overview of previously-published and new physical models and present new 3-D conceptual models that capture the evolution of shortening structures in salt provinces dominated by precursor isolated diapirs (termed isolated-diapir provinces). In such provinces, isolated diapirs form only a minor volumetric component of a sedimentary basin, however, due to the relative weakness of rock salt and their ability to localize strain, during shortening they have a disproportionately large influence on structural development.We find three key mechanical principles govern the processes and structural styles developed during shortening of isolated-diapir provinces. First, salt diapirs shorten before surrounding sedimentary rocks due to their relative weakness, and so form salients in the thrust front during early shortening. Second, diapirs tend to nucleate folds and faults, which radiate out from the diapirs. Third, as diapir walls converge, the roof must shorten. Extrusive salt sheets are expelled through thin roofs, but thicker roofs resist piercement and so tend to undergo complex folding and faulting.As a result of these principles, the first-order controls on the structural styles expressed across a shortened isolated-diapir province are the configuration the diapir array prior to shortening, the connectivity of these diapirs prior to shortening, total strain magnitude, and diapir roof thickness. Second-order controls include the initial cross-sectional and map-view geometry of diapirs, diapir size, and diapir orientation with respect to the shortening direction.

An integrated workflow for phenazine-modifying enzyme characterization.

Increasing availability of new genomes and putative biosynthetic gene clusters (BGCs) has extended the opportunity to access novel chemical diversity for agriculture, medicine, environmental and industrial purposes. However, functional characterization of BGCs through heterologous expression is limited because expression may require complex regulatory mechanisms, specific folding or activation. We developed an integrated workflow for BGC characterization that integrates pathway identification, modular design, DNA synthesis, assembly and characterization. This workflow was applied to characterize multiple phenazine-modifying enzymes. Phenazine pathways are useful for this workflow because all phenazines are derived from a core scaffold for modification by diverse modifying enzymes (PhzM, PhzS, PhzH, and PhzO) that produce characterized compounds. We expressed refactored synthetic modules of previously uncharacterized phenazine BGCs heterologously in Escherichia coli and were able to identify metabolic intermediates they produced, including a previously unidentified metabolite. These results demonstrate how this approach can accelerate functional characterization of BGCs.

Anisotropy of cell division and epithelial sheet bending via apical constriction shape the complex folding pattern of beetle horn primordia

Insects can dramatically change their outer morphology at molting. To prepare for this drastic transformation, insects generate new external organs as folded primordia under the old cuticle. At molting, these folded primordia are physically extended to form their final outer shape in a very short time. Beetle horns are a typical example. Horn primordia are derived from a flat head epithelial sheet, on which deep furrows are densely added to construct the complex folded structure. Because the 3D structure of the pupa horn is coded in the complex furrow pattern, it is indispensable to know how and where the furrows are set. Here, we studied the mechanism of furrow formation using dachsous (ds) gene knocked down beetles that have shorter and fatter adult horns. The global shape of the beetle horn primordia is mushroom like, with dense local furrows across its surface. Knockdown of ds by RNAi changed the global shape of the primordia, causing the stalk region become apparently thicker. The direction of cell division is biased in wildtype horns to make the stalk shape thin and tall. However, in ds knocked down beetles, it became random, resulting in the short and thick stalk shape. On the other hand, a fine and dense local furrow was not significantly affected by the ds knockdown. In developing wildtype horn primordia, we observed that, before the local furrow is formed, the apical constriction signal emerged at the position of the future furrow, suggesting the pre-pattern for the fine furrow pattern. According to the results, we propose that development of complex horn primordia can be roughly divided to two distinct processes, 1) development of global primordia shape by anisotropic cell division, and 2) local furrow formation via actin-myosin dependent apical constriction of specific cells.

Quantitative Theoretical Predictions and Qualitative Bonding Analysis of the Divinylborinium System and Its Al, Ga, In, and Tl Congeners.

A substituted divinylborinium cation was synthesized recently and characterized crystallographically as a gauche structure with a 153° C1-C2-C3-C4 dihedral angle. A full theoretical geometrical optimization of the bis(2-mesityl-1,2-diphenylvinyl)-borane cation shows excellent agreement with the crystal structure. However, for the parent unsubstituted divinylborinium cation, we predict a nearly 90° C1-C2-C3-C4 dihedral angle using the CCSD(T)/cc-pVTZ coupled cluster method. The cis and trans planar geometries (0° and 180° for the C1-C2-C3-C4 dihedral angle) proved to be transition states with energy barriers of 2.8 and 2.3 kcal/mol, respectively, with respect to unimolecular conversion to the gauche equilibrium. The structures of the heavier boron group cations (Al, Ga, In, and Tl) have also been investigated here, finding even lower energy barriers (0.3-0.7 kcal/mol). After the ZPVE corrections, the barriers are further decreased. The torsional angles for the unknown Al, Ga, In, and Tl dimesityl substituted compounds should be somewhat less than 153°. Many of these findings may be understood in terms of qualitative electronic structure theory. The torsional folding of borane complex, including cationic divinylborinium and elementary vinylborane (C2H3BH2) or chlorovinylborane (C2H3BHCl) precursors, are investigated with natural bond orbital (NBO) analysis to unveil the electronic origins of the torsional properties. The NBO-based descriptors are employed to systematically deconstruct complex torsional dependence into a balanced portrayal of hyperconjugative and steric effects.

A folded viral noncoding RNA blocks host cell exoribonucleases through a conformationally dynamic RNA structure

Folded RNA elements that block processive 5' → 3' cellular exoribonucleases (xrRNAs) to produce biologically active viral noncoding RNAs have been discovered in flaviviruses, potentially revealing a new mode of RNA maturation. However, whether this RNA structure-dependent mechanism exists elsewhere and, if so, whether a singular RNA fold is required, have been unclear. Here we demonstrate the existence of authentic RNA structure-dependent xrRNAs in dianthoviruses, plant-infecting viruses unrelated to animal-infecting flaviviruses. These xrRNAs have no sequence similarity to known xrRNAs; thus, we used a combination of biochemistry and virology to characterize their sequence requirements and mechanism of stopping exoribonucleases. By solving the structure of a dianthovirus xrRNA by X-ray crystallography, we reveal a complex fold that is very different from that of the flavivirus xrRNAs. However, both versions of xrRNAs contain a unique topological feature, a pseudoknot that creates a protective ring around the 5' end of the RNA structure; this may be a defining structural feature of xrRNAs. Single-molecule FRET experiments reveal that the dianthovirus xrRNAs undergo conformational changes and can use "codegradational remodeling," exploiting the exoribonucleases' degradation-linked helicase activity to help form their resistant structure; such a mechanism has not previously been reported. Convergent evolution has created RNA structure-dependent exoribonuclease resistance in different contexts, which establishes it as a general RNA maturation mechanism and defines xrRNAs as an authentic functional class of RNAs.

Axonal neurofilaments exhibit frequent and complex folding behaviors.

Neurofilaments are flexible cytoskeletal polymers that are capable of folding and unfolding between their bouts of bidirectional movement along axons. Here we present a detailed characterization of this behavior in cultured neurons using kymograph analysis with approximately 30 ms temporal resolution. We analyzed 781 filaments ranging from 0.6-42 µm in length. We observed complex behaviors including pinch folds, hairpin folds, orientation changes (flips), and occasional severing and annealing events. On average, the filaments spent approximately 40% of their time in some sort of folded configuration. A small proportion of filaments (4%) moved while folded, but most (96%) moved in an outstretched configuration. Collectively, our observations suggest that motors may interact with neurofilaments at multiple points along their length, but preferentially at their ends. In addition, the prevalence of neurofilament folding and the tendency of neurofilaments to straighten out when they move, suggest that an important function of the movement of these polymers in axons may be to maintain them in an outstretched and longitudinally co-aligned configuration. Thus, neurofilament movement may function as much to organize these polymers as to move them, and this could explain why they spend so much time engaged in apparently unproductive bidirectional movement.

Exploration of the folding dynamics of human telomeric G-quadruplex with a hybrid atomistic structure-based model.

Structure-based models or Gō-like models, which are built from one or multiple particular experimental structures, have been successfully applied to the folding of proteins and RNAs. Recently, a variant termed the hybrid atomistic model advances the description of backbone and side chain interactions of traditional structure-based models, by borrowing the description of local interactions from classical force fields. In this study, we assessed the validity of this model in the folding problem of human telomeric DNA G-quadruplex, where local dihedral terms play important roles. A two-state model was developed and a set of molecular dynamics simulations was conducted to study the folding dynamics of sequence Htel24, which was experimentally validated to adopt two different (3 + 1) hybrid G-quadruplex topologies in K+ solution. Consistent with the experimental observations, the hybrid-1 conformation was found to be more stable and the hybrid-2 conformation was kinetically more favored. The simulations revealed that the hybrid-2 conformation folded in a higher cooperative manner, which may be the reason why it was kinetically more accessible. Moreover, by building a Markov state model, a two-quartet G-quadruplex state and a misfolded state were identified as competing states to complicate the folding process of Htel24. Besides, the simulations also showed that the transition between hybrid-1 and hybrid-2 conformations may proceed an ensemble of hairpin structures. The hybrid atomistic structure-based model reproduced the kinetic partitioning folding dynamics of Htel24 between two different folds, and thus can be used to study the complex folding processes of other G-quadruplex structures.

An orientation based correction method for SfM-MVS point clouds—Implications for field geology

Advancements in computing capabilities over the last decade have allowed for the routine creation of Structure from Motion-Multiview Stereo (SfM-MVS) terrain models that can serve as base for high resolution geologic mapping. Outcrops models developed from these systems are high-resolution, photo-realistic 3D base providing unprecedented capability for geometric analysis. Yet, before this technology becomes a mainstay of field geology, the potential errors associated with it must be well understood. Here, we compare orientation measurements from multi-point analyses on the SfM-MVS point clouds to those taken in the field with the objective of resolving the geometry of complex folds within the outcrop. We also analyzed two point clouds of the same exposure created from different ground-based cameras to compare the ranges of error. We found that the point clouds produced from ground-based photos exhibited significant rigid-body rotation relative to the real world despite well distributed ground control, yet the models maintained a realistic scale and internal geometry. To correct the error the model values were rotated and the discrepancy reassessed. The two point clouds produced similar results, however, the Sony compact-digital-camera-based point cloud ultimately corresponded more closely to field values. We suggest that the primary cause of the error in the point clouds was GPS-based and was enhanced by the lack of significant topographic relief in our camera positions, allowing rigid-body rotations along the axis of the photographic array. This outcome suggests that care must be taken when GPS errors are a significant fraction of the outcrop size and relatively 2D outcrops imaged by a relatively 1D image array are subject to rotation errors that are difficult to remove without high-resolution ground control. Short of using a UAV and/or RTK-GPS we show how this can be resolved simply by collecting several known orientations in the field, which can then be used to orient the model more accurately, akin to ground control points. This addition is a key step if this method is to be used for more thorough analysis and is a general method that could be used to orient virtual outcrops with no geographic reference.

Sperm packaging in the seminal vesicles of Hygrophila (Gastropoda: Pulmonata)

Spermatozoa of freshwater pulmonates (Hygrophila) are morphologically complex cells that may reach significant lengths (up to 1 mm). This raises a question as to whether these cells are arranged or compacted in any specialized fashion as they move through the reproductive passages. The use of chemically unprocessed, rather than fixative-treated, material shows that the spermatozoa of Hygrophila found in the seminal vesicles, unlike other spermatozoa, are arranged in a compacted fashion implying that they undergo complex folding and unfolding processes on the way toward and from these organs. This study examined sperm packaging in the seminal vesicles of six hygrophilan families. The packaged spermatozoon forms a ring-shaped structure consisting of three domains. The first domain (the anterior portion of the spermatozoon) participates only in the formation of the outer coils of the ring. The second domain (a major portion of the sperm midpiece) is folded and twisted on itself and coiled into a ring. The third domain (the posterior portion of the spermatozoon) is coiled in a smaller ring that lies inside the first ring. The folding process is reconstructed as the inverse of the unfolding sequence observed in dry mounts and in the spermatozoa mounted in Berlese solution. The possible mechanism of the sperm-packaging process and phylogenetic implications are discussed.

Caustic Skeleton & Cosmic Web

We present a general formalism for identifying the caustic structure of a dynamically evolving mass distribution, in an arbitrary dimensional space. The identification of caustics in fluids with Hamiltonian dynamics, viewed in Lagrangian space, corresponds to the classification of singularities in Lagrangian catastrophe theory. On the basis of this formalism we develop a theoretical framework for the dynamics of the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. Given the collisionless nature of the gravitationally dominant dark matter component in the universe, the presented formalism entails an accurate description of the spatial organization of matter resulting from the gravitationally driven formation of cosmic structure. The present work represents a significant extension of the work by Arnol'd et al. [1], who classified the caustics that develop in one- and two-dimensional systems that evolve according to the Zel'dovich approximation. His seminal work established the defining role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. Involving a complex folding of the 6-D sheetlike phase-space distribution, it manifests itself in the appearance of infinite density caustic features. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. In this study we introduce an alternative and transparent proof for Lagrangian catastrophe theory. This facilitates the derivation of the caustic conditions for general Lagrangian fluids, with arbitrary dynamics. Most important in the present context is that it allows us to follow and describe the full three-dimensional geometric and topological complexity of the purely gravitationally evolving nonlinear cosmic matter field. While generic and statistical results can be based on the eigenvalue characteristics, one of our key findings is that of the significance of the eigenvector field of the deformation field for outlining the entire spatial structure of the caustic skeleton emerging from a primordial density field. In this paper we explicitly consider the caustic conditions for the three-dimensional Zel'dovich approximation, extending earlier work on those for one- and two-dimensional fluids towards the full spatial richness of the cosmic web. In an accompanying publication, we apply this towards a full three-dimensional study of caustics in the formation of the cosmic web and evaluate in how far it manages to outline and identify the intricate skeletal features in the corresponding N-body simulations.

Foldamer Tertiary Structure through Sequence-Guided Protein Backbone Alteration.

The prospect of recreating the complex structural hierarchy of protein folding in synthetic oligomers with backbones that are artificial in covalent structure ("foldamers") has long fascinated chemists. Foldamers offer complex functions from biostable scaffolds and have found widespread applications in fields from biomedical to materials science. Most precedent has focused on isolated secondary structures or their assemblies. In considering the goal of complex protein-like tertiary folding patterns, a key barrier became apparent. How does one design a backbone with covalent connectivity and a sequence of side-chain functional groups that will support defined intramolecular packing of multiple artificial secondary structures? Two developments were key to overcoming this challenge. First was the recognition of the power of blending α-amino acid residues with monomers differing in backbone connectivity to create "heterogeneous-backbone" foldamers. Second was the finding that replacing some of the natural α-residues in a biological sequence with artificial-backbone variants can result in a mimic that retains both the fold and function of the native sequence and, in some cases, gains advantageous characteristics. Taken together, these precedents lead to a view of a protein as chemical entity having two orthogonal sequences: a sequence of side-chain functional groups and a separate sequence of backbone units displaying those functional groups. In this Account, we describe our lab's work over the last ∼10 years to leverage the above concept of protein sequence duality in order to develop design principles for constructing heterogeneous-backbone foldamers that adopt complex protein-like tertiary folds. Fundamental to the approach is the utilization of a variety of artificial building blocks (e.g., d-α-residues, Cα-Me-α-residues, N-Me-α-residues, β-residues, γ-residues, δ-residues, polymer segments) in concert, replacing a fraction of α-residues in a given prototype sequence. We provide an overview of the state-of-the-art in terms of design principles for choosing substitutions based on consideration of local secondary structure and retention of key side-chain functional groups. We survey high-resolution structures of backbone-modified proteins to illustrate how diverse artificial moieties are accommodated in tertiary fold contexts. We detail efforts to elucidate how backbone alteration impacts folding thermodynamics and describe how such data informs the development of improved design rules. Collectively, a growing body of results by our lab and others spanning multiple protein systems suggests there is a great deal of plasticity with respect to the backbone chemical structures upon which sequence-encoded tertiary folds can manifest. Moreover, these efforts suggest sequence-guided backbone alteration as a broadly applicable strategy for generating foldamers with complex tertiary folding patterns. We conclude by offering some perspective regarding the near future of this field, in terms of unanswered questions, technological needs, and opportunities for new areas of inquiry.

Online Optimization of Total Acceptance in Hamiltonian Replica Exchange Simulations.

Replica exchange is a widely used sampling strategy in molecular simulation. While a variety of methods exist to optimize parameters for temperature replica exchange, less is known about how to optimize parameters for more general Hamiltonian replica exchange simulations. We present an algorithm for the online optimization of total acceptance for both temperature and Hamiltonian replica exchange simulations using stochastic gradient descent. We optimize the total acceptance, a heuristic objective function capturing the efficiency of replica exchange. Our approach is general and has several desirable properties, including: (1) it makes few assumptions about the system of interest, (2) optimization occurs online without the requirement of presimulation, and (3) most importantly, it readily generalizes to systems where there are multiple control parameters (e.g., temperatures, force constants, etc.) that determine the Hamiltonian of each replica. We explore some general properties of the algorithm on a simple harmonic oscillator system, and demonstrate its effectiveness on a more complex data-guided protein folding simulation.

A Self-Folding Dynamic Covalent Shape Memory Epoxy and Its Continuous Glass Fiber Composite

Continuous fiber reinforced thermoset composites are highly important in a variety of industrial applications because of their ultrahigh specific strength. However, conventional shaping techniques for such materials can hardly achieve very sophisticated shapes. In this paper, we present an unconventional method to enable complex shapes for continuous fiber reinforced thermoset epoxy composites that provided a capability of topology change due to the dynamic ester bonds. Thus, the corresponding composites providing largely enhanced mechanical strength can be endowed with complex permanent shapes via folding. At lower temperatures, the exchange reaction was frozen and the epoxy networks provided ideal shape memory behavior. Accordingly, the composites with complex permanent shapes enabled a self-folding shape recovery process. In addition, a laser half-cutting technique was applied to build controllable defects within the composites. As a result, more complex folding geometries which were extremely challeng...

Equilibrium and Non-equilibrium Studies of Protein G using High-Resolution Optical Trapping Unveil Heterogeneous Unfolding Pathways

Recent advances in spatial and temporal resolution of biophysical measurements have revealed ‘beyond two-state’ complexity in protein folding, even for small, single-domain proteins. In this work, the folding/unfolding kinetics of the B1 domain of inmmunoglobulin-binding protein G, a well-studied model system, was investigated using high-resolution optical traps. For non-equilibrium force ramp measurements, simple force-dependent folding distributions were observed. However, multiple peaks were seen in the unfolding force distribution, consistent with multiple parallel unfolding pathways or multiple folded states. We then performed long duration fixed trap measurements while slowly stepping the applied force. We were thereby able to directly measure folding and unfolding rate constants versus force under near equilibrium conditions. All molecules showed the same folding behavior, consistent with a simple two-state Bell's formula. However, these same molecules showed one of two unfolding behaviors at low forces, either ‘fast’ and force independent, or ‘slow’ and strongly force dependent. Equilibrium fixed trap observations of individual molecules for over tens of minutes show no switching between unfolding mechanisms amid hundreds of transitions. However, both unfolding mechanisms are observed for the same individual molecules using the force ramp method, indicating that out of equilibrium pulling may be necessary to switch individual molecule unfolding behavior. Taken together, these measurements indicate that protein G unfolds on a more complex energy landscape containing multiple pathways and intermediate states.

Probing Protein Folding Landscape by Using Combined Force Spectroscopy and Molecular Dynamics Simulations

Most proteins, even those with complex folding trajectories and rough energy landscapes, successfully navigate the funneled folding landscape to achieve the correct native conformations. However, some proteins misfold, sometimes resulting in some neurodegenerative diseases and cancers. Such misfolding is thought to occur via partially folded high-energy structures accessible from the native state or during the folding process. Structural and energetic characterization of such high-energy species is important but experimentally challenging due to their rare and transient nature under native conditions. Single-molecule force spectroscopy allows investigation of the force dependent movement of the transition state ensemble and detection of high-energy intermediates, which may be populated at high force. Molecular dynamics simulations allow atomistic characterization of structures and multiple folding pathways on the energy landscape. Here, we probe important protein sub-states and folding pathways of the second PDZ domain of PTP-BL by using a combination of single molecule optical tweezers experiments and molecular dynamics simulations.

Hybrid Particle-Field Model for Conformational Dynamics of Peptide Chains.

We propose the first model of a polypeptide chain based on a hybrid-particle field approach. The intramolecular potential is built on a two-bead coarse grain mapping for each amino acid. We employ a combined potential for the bending and the torsional degrees of freedom that ensures the stabilization of secondary structure elements in the conformational space of the polypeptide. The electrostatic dipoles associated with the peptide bonds of the main chain are reconstructed by a topological procedure. The intermolecular interactions comprising both the solute and the explicit solvent are treated by a density functional-based mean-field potential. Molecular dynamics simulations on a series of test systems show how the model here introduced is able to capture all the main features of polypeptides. In particular, homopolymers of different lengths yield a complex folding phase diagram, covering from the collapsed to swollen state. Moreover, simulations on models of a four-helix bundle and of an alpha + beta peptide evidence how the collapse of the hydrophobic core drives the appearance of both folded motifs and the stabilization of tertiary or quaternary assemblies. Finally, the polypeptide model is able to structurally respond to the environmental changes caused by the presence of a lipid bilayer.

The Trifold Universe

This paper studies a new concept called universal folding. The visible universe is the result of a complex invisible folding series. There are three major folds (Trifold): from the Plank length, to the radius of an electron, and finally, to the radius of universe. Each of the three-major folds follows the same folding formula. Our findings help us understand the grand architecture of the universe. The ideal average human height, city block size, city size, diameter of the continents, the diameter of the Sun, the distance between the Earth and the Sun, the radius of the solar system, the radius of the Milky Way galaxy, the average diameter of the filament of the universe, and the radius of the universe are important resonance lengths in the formula. This paper helps scientists study everything from a new angle and become aware of the architectural design of the universe.

Effect of ligand binding on a protein with a complex folding landscape.

Ligand binding to a protein can stabilize it significantly against unfolding. The variation of the folding free energy, ΔΔG0, due to ligand binding can be derived from a simple reaction scheme involving exclusive binding to the native state. One obtains the following expression: , where Kd is the ligand dissociation constant and L is its concentration, R is the universal gas constant and T is the temperature. This expression has been shown to correctly describe experimental results on multiple proteins. In the current work we studied the effect of ligand binding on the stability of the multi-domain protein adenylate kinase from E. coli (AKE). Unfolding experiments were conducted using single-molecule FRET spectroscopy, which allowed us to directly obtain the fraction of unfolded protein in a model-free way from FRET efficiency histograms. Surprisingly, it was found that the effect of two inhibitors (Ap5A and AMPPNP) and a substrate (AMP) on the stability of AKE was much smaller than expected based on Kd values obtained independently using microscale thermophoresis. To shed light on this issue, we measured the Kd for Ap5A over a range of chemical denaturant concentrations where the protein is still folded. It was found that Kd increases dramatically over this range, likely due to the population of folding intermediates, whose binding to the ligand is much weaker than that of the native state. We propose that binding to folding intermediates may dominate the effect of ligands on the stability of multi-domain proteins, and could therefore have a strong impact on protein homeostasis in vivo.

A physical multifield model predicts the development of volume and structure in the human brain

The prenatal development of the human brain is characterized by a rapid increase in brain volume and a development of a highly folded cortex. At the cellular level, these events are enabled by symmetric and asymmetric cell division in the ventricular regions of the brain followed by an outwards cell migration towards the peripheral regions. The role of mechanics during brain development has been suggested and acknowledged in past decades, but remains insufficiently understood. Here we propose a mechanistic model that couples cell division, cell migration, and brain volume growth to accurately model the developing brain between weeks 10 and 29 of gestation. Our model accurately predicts a 160-fold volume increase from 1.5 cm3 at week 10 to 235 cm3 at week 29 of gestation. In agreement with human brain development, the cortex begins to form around week 22 and accounts for about 30% of the total brain volume at week 29. Our results show that cell division and coupling between cell density and volume growth are essential to accurately model brain volume development, whereas cell migration and diffusion contribute mainly to the development of the cortex. We demonstrate that complex folding patterns, including sinusoidal folds and creases, emerge naturally as the cortex develops, even for low stiffness contrasts between the cortex and subcortex.