Pincus blob elasticity in an intrinsically disordered protein.

Understanding the dynamic structure of intrinsically disordered proteins (IDPs) is important to deciphering their biological functions. Here, we exploit precision entropic elasticity measurements to infer the conformational behavior of a model IDP construct formed from the disordered tail of the neurofilament low molecular weight protein. The IDP construct notably displays a low-force power-law elastic regime, consistent with the Pincus blob model, which allows direct extraction of the Flory exponent, [Formula: see text], from the force-extension relationship. We find [Formula: see text] increases with added denaturant, transitioning from a nearly ideal chain to a swollen chain in a manner quantitatively consistent with measurements of IDP dimensions from other experimental techniques. We suggest that measurements of entropic elasticity could be broadly useful in the study of IDP structure.

Glassy Dynamics and Memory Effects in an Intrinsically Disordered Protein Construct.

Glassy, nonexponential relaxations in globular proteins are typically attributed to conformational behaviors that are missing from intrinsically disordered proteins. Yet, we show that single molecules of a disordered-protein construct display two signatures of glassy dynamics, logarithmic relaxations and a Kovacs memory effect, in response to changes in applied tension. We attribute this to the presence of multiple independent local structures in the chain, which we corroborate with a model that correctly predicts the force dependence of the relaxation. The mechanism established here likely applies to other disordered proteins.

Nanoparticle Mobility over a Surface as a Probe for Weak Transient Disordered Peptide-Peptide Interactions.

Weak interactions form the core basis of a vast number of biological processes, in particular, those involving intrinsically disordered proteins. Here, we establish a new technique capable of probing these weak interactions between synthetic unfolded polypeptides using a convenient yet efficient, quantitative method based on single particle tracking of peptide-coated gold nanoparticles over peptide-coated surfaces. We demonstrate that our technique is sensitive enough to observe the influence of a single amino acid mutation on the transient peptide-peptide interactions. Furthermore, the effects of buffer salinity, which are expected to alter weak electrostatic interactions, are also readily detected and examined in detail. The method presented here has the potential to evaluate, in a high-throughput manner, weak interactions for a wide range of disordered proteins, polypeptides, and other biomolecules.

Universal and Accessible Entropy Estimation Using a Compression Algorithm.

Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug design. Current techniques suffer from being model specific, requiring abundant computation resources and simulation at conditions far from the studied realization. Here, we present a universal scheme to calculate entropy using lossless-compression algorithms and validate it on simulated systems of increasing complexity. Our results show accurate entropy values compared to benchmark calculations while being computationally effective. In molecular-dynamics simulations of protein folding, we exhibit unmatched detection capability of the folded states by measuring previously undetectable entropy fluctuations along the simulation timeline. Such entropy evaluation opens a new window onto the dynamics of complex systems and allows efficient free-energy calculations.

Molecular Precision and Enzymatic Degradation: From Readily to Undegradable Polymeric Micelles by Minor Structural Changes.

Studying the enzymatic degradation of synthetic polymers is crucial for the design of suitable materials for biomedical applications ranging from advanced drug delivery systems to tissue engineering. One of the key parameters that governs enzymatic activity is the limited accessibility of the enzyme to its substrates that may be collapsed inside hydrophobic domains. PEG-dendron amphiphiles can serve as powerful tools for the study of enzymatic hydrolysis of polymeric amphiphiles due to the monodispersity and symmetry of the hydrophobic dendritic block, which significantly simplifies kinetic analyses. Using these hybrids, we demonstrate how precise, minor changes in the hydrophobic block are manifested into tremendous changes in the stability of the assembled micelles toward enzymatic degradation. The obtained results emphasize the extreme sensitivity of self-assembly and its great importance in regulating the accessibility of enzymes to their substrates. Furthermore, the demonstration that the structural differences between readily degradable and undegradable micelles are rather minor, points to the critical roles that self-assembly and polydispersity play in designing biodegradable materials.

Reversible Dimerization of Polymeric Amphiphiles Acts as a Molecular Switch of Enzymatic Degradability.

Enzyme-responsive polymeric micelles have great potential as drug delivery systems due to the high selectivity and overexpression of disease-associated enzymes, which could be utilized to trigger the release of active drugs only at the target site. We previously demonstrated that enzymatic degradation rates of amphiphilic PEG-dendron hybrids could be precisely tuned by gradually increasing the hydrophobic to hydrophilic ratio. However, with the increase in hydrophobicity, the micelles rapidly became too stable and could not be degraded, as often encountered for many other amphiphilic assemblies. Here we address the challenge to balance between stability and reactivity of enzymatically degradable assemblies by utilizing reversible dimerization of diblock polymeric amphiphiles to yield jemini amphiphiles. This molecular transformation serves as a tool to control the critical micelle concentration of the amphiphiles in order to tune their micellar stability and enzymatic degradability. To demonstrate this approach, we show that simple dimerization of two polymeric amphiphiles through a single reversible disulfide bond significantly increased the stability of their micellar assemblies toward enzymatic degradation, although the hydrophilic to hydrophobic ratio was not changed. Reduction of the disulfide bond led to dedimerization of the polymeric hybrids and allowed their degradation by the activating enzyme. The generality of the approach is demonstrated by designing both esterase- and amidase-responsive micellar systems. This new molecular design can serve as a simple tool to increase the stability of polymeric micelles without impairing their enzymatic degradability.

Structural Effects of Single Mutations in a Filamentous Viral Capsid Across Multiple Length Scales.

Filamentous bacteriophage (phage) are single-stranded DNA viruses that infect bacteria. Single-site mutants of fd phage have been studied by magic-angle spinning nuclear magnetic resonance and by small-angle X-ray scattering. Detailed analysis has been performed that provides insight into structural variations on three length scales. The results, analyzed in conjunction with existing literature data, suggest that a single charge mutation on the capsid surface affects direct interviral interactions but not the structure of individual particles or the macroscale organization. On the other hand, a single hydrophobic mutation located at the hydrophobic interface that stabilizes capsid assembly alters the atomic structure of the phage, mainly affecting intersubunit interactions, affects its macroscale organization, that is, the pitch of the cholesteric liquid crystal formed by the particles, but skips the nanoscale hence does not affect direct interparticle interactions. An X-ray scattering under osmotic pressure assay provides the effective linear charge density of the phage and we obtain values of 0.6 Å-1 and 0.4 Å-1 for fd and M13 phage, respectively. These values agree with a simple consideration of a single cylinder with protein and DNA charges spread according to the most recent atomic-resolution models of the phage.

Structural Transition in Myelin Membrane as Initiator of Multiple Sclerosis.

In demyelinating diseases such as multiple sclerosis, disrupted myelin structures impair the functional role of the sheath as an insulating layer for proper nerve conduction. Though the etiology and recovery pathways remain unclear, in vivo studies show alterations in the lipid and the adhesive protein (myelin basic protein, MBP) composition. We find that in vitro cytoplasmic myelin membranes with modified lipid composition and low MBP concentration, as in demyelinating disease, show structural instabilities and pathological phase transition from a lamellar to inverted hexagonal, which involve enhanced local curvature. Similar curvatures are also found in vivo in diseased myelin sheaths. In addition, MBP dimers form a correlated mesh-like network within the inner membrane space, only in the vicinity of native lipid composition. These findings delineate the distinct functional roles of dominant constituents in cytoplasmic myelin sheaths, and shed new light on mechanisms disrupting lipid-protein complexes in the diseased state.

Probing the interactions of intrinsically disordered proteins using nanoparticle tags.

The structural plasticity of intrinsically disordered proteins serves as a rich area for scientific inquiry. Such proteins lack a fix three-dimensional structure but can interact with multiple partners through numerous weak bonds. Nevertheless, this intrinsic plasticity possesses a challenging hurdle in their characterization. We underpin the intermolecular interactions between intrinsically disordered neurofilaments in various hydrated conditions, using grafted gold nanoparticle (NP) tags. Beyond its biological significance, this approach can be applied to modify the surface interaction of NPs for the creation of future tunable "smart" hybrid biomaterials.

Encapsulation and covalent binding of molecular payload in enzymatically activated micellar nanocarriers.

The high selectivity and often-observed overexpression of specific disease-associated enzymes make them extremely attractive for triggering the release of hydrophobic drug or probe molecules from stimuli-responsive micellar nanocarriers. Here we utilized highly modular amphiphilic polymeric hybrids, composed of a linear hydrophilic polyethylene glycol (PEG) and an esterase-responsive hydrophobic dendron, to prepare and study two diverse strategies for loading of enzyme-responsive micelles. In the first type of micelles, hydrophobic coumarin-derived dyes were encapsulated noncovalently inside the hydrophobic core of the micelle, which was composed of lipophilic enzyme-responsive dendrons. In the second type of micellar nanocarrier the hydrophobic molecular cargo was covalently linked to the end-groups of the dendron through enzyme-cleavable bonds. These amphiphilic hybrids self-assembled into micellar nanocarriers with their cargo covalently encapsulated within the hydrophobic core. Both types of micelles were highly responsive toward the activating enzyme and released their molecular cargo upon enzymatic stimulus. Importantly, while faster release was observed with noncovalent encapsulation, higher loading capacity and slower release rate were achieved with covalent encapsulation. Our results clearly indicate the great potential of enzyme-responsive micellar delivery platforms due to the ability to tune their payload capacities and release rates by adjusting the loading strategy.

Structural flexibility of CaV1.2 and CaV2.2 I-II proximal linker fragments in solution.

Voltage-dependent calcium channels (CaV) enable the inward flow of calcium currents for a wide range of cells. CaV1 and CaV2 subtype α1 subunits form the conducting pore using four repeated membrane domains connected by intracellular linkers. The domain I-II linker connects to the membrane gate (IS6), forming an α-helix, and is bound to the CaVß subunit. Previous studies indicated that this region may or may not form a continuous helix depending on the CaV subtype, thereby modulating channel activation and inactivation properties. Here, we used small-angle x-ray scattering and ensemble modeling analysis to investigate the solution structure of these linkers, extending from the membrane domain and including the CaVß-binding site, called the proximal linker (PL). The results demonstrate that the CaV1.2 PL is more flexible than the CaV2.2 PL, the flexibility is intrinsic and not dependent on CaVß binding, and the flexibility can be most easily explained by the presence of conserved glycines. Our analysis also provides a robust example of investigating protein domains in which flexibility plays an essential role.

Agitated ants: regulation and self-organization of incipient nest excavation via collisional cues.

Ants are millimetres in scale yet collectively create metre-scale nests in diverse substrates. To discover principles by which ant collectives self-organize to excavate crowded, narrow tunnels, we studied incipient excavation in small groups of fire ants in quasi-two-dimensional arenas. Excavation rates displayed three stages: initially excavation occurred at a constant rate, followed by a rapid decay, and finally a slower decay scaling in time as t-1/2. We used a cellular automata model to understand such scaling and motivate how rate modulation emerges without global control. In the model, ants estimated their collision frequency with other ants, but otherwise did not communicate. To capture early excavation rates, we introduced the concept of 'agitation'-a tendency of individuals to avoid rest if collisions are frequent. The model reproduced the observed multi-stage excavation dynamics; analysis revealed how parameters affected features of multi-stage progression. Moreover, a scaling argument without ant-ant interactions captures tunnel growth power-law at long times. Our study demonstrates how individual ants may use local collisional cues to achieve functional global self-organization. Such contact-based decisions could be leveraged by other living and non-living collectives to perform tasks in confined and crowded environments.

A generic coalescent-based framework for the selection of a reference panel for imputation.

An important component in the analysis of genome-wide association studies involves the imputation of genotypes that have not been measured directly in the studied samples. The imputation procedure uses the linkage disequilibrium (LD) structure in the population to infer the genotype of an unobserved single nucleotide polymorphism. The LD structure is normally learned from a dense genotype map of a reference population that matches the studied population. In many instances there is no reference population that exactly matches the studied population, and a natural question arises as to how to choose the reference population for the imputation. Here we present a Coalescent-based method that addresses this issue. In contrast to the current paradigm of imputation methods, our method assigns a different reference dataset for each sample in the studied population, and for each region in the genome. This allows the flexibility to account for the diversity within populations, as well as across populations. Furthermore, because our approach treats each region in the genome separately, our method is suitable for the imputation of recently admixed populations. We evaluated our method across a large set of populations and found that our choice of reference data set considerably improves the accuracy of imputation, especially for regions with low LD and for populations without a reference population available as well as for admixed populations such as the Hispanic population. Our method is generic and can potentially be incorporated in any of the available imputation methods as an add-on.

Programming active cohesive granular matter with mechanically induced phase changes.

At the macroscale, controlling robotic swarms typically uses substantial memory, processing power, and coordination unavailable at the microscale, e.g., for colloidal robots, which could be useful for fighting disease, fabricating intelligent textiles, and designing nanocomputers. To develop principles that can leverage physical interactions and thus be used across scales, we take a two-pronged approach: a theoretical abstraction of self-organizing particle systems and an experimental robot system of active cohesive granular matter that intentionally lacks digital electronic computation and communication, using minimal (or no) sensing and control. As predicted by theory, as interparticle attraction increases, the collective transitions from dispersed to a compact phase. When aggregated, the collective can transport non-robot "impurities," thus performing an emergent task driven by the physics underlying the transition. These results reveal a fruitful interplay between algorithm design and active matter robophysics that can result in principles for programming collectives without the need for complex algorithms or capabilities.

Angular super-resolution retrieval in small-angle X-ray scattering.

Small-angle X-ray scattering (SAXS) techniques enable convenient nanoscopic characterization for various systems and conditions. Unlike synchrotron-based setups, lab-based SAXS systems intrinsically suffer from lower X-ray flux and limited angular resolution. Here, we develop a two-step retrieval methodology to enhance the angular resolution for given experimental conditions. Using minute hardware additions, we show that translating the X-ray detector in subpixel steps and modifying the incoming beam shape results in a set of 2D scattering images, which is sufficient for super-resolution SAXS retrieval. The technique is verified experimentally to show superior resolution. Such advantages have a direct impact on the ability to resolve finer nanoscopic structures and can be implemented in most existing SAXS apparatuses both using synchrotron- and laboratory-based sources.

Order and disorder in intermediate filament proteins.

Intermediate filaments (IFs), important components of the cytoskeleton, provide a versatile, tunable network of self-assembled proteins. IF proteins contain three distinct domains: an α-helical structured rod domain, flanked by intrinsically disordered head and tail domains. Recent studies demonstrated the functional importance of the disordered domains, which differ in length and amino-acid sequence among the 70 different human IF genes. Here, we investigate the biophysical properties of the disordered domains, and review recent findings on the interactions between them. Our analysis highlights key components governing IF functional roles in the cytoskeleton, where the intrinsically disordered domains dictate protein-protein interactions, supramolecular assembly, and macro-scale order.