Relating interactions between neurofilaments to the structure of axonal neurofilament distributions through polymer brush models

Neurofilaments (NFs) have been proposed to interact with one another through mutual steric exclusion of their unstructured C-terminal "sidearm" domains, producing order in axonal NF distributions and conferring mechanical strength to the axon. Here we apply theory developed for polymer brushes to examine the relationship between the brush properties of the sidearms and NF organization in axons. We first measure NF-NF radial distribution functions and occupancy probability distributions for adult mice. Interpreting the probability distributions using information theory, we show that the NF distributions may be represented by a single pair potential of mean force. Then, to explore the relationship between model parameters and NF architecture, we conduct two-dimensional Monte Carlo simulations of NF cross-sectional distributions. We impose purely repulsive interaction potentials in which the sidearms are represented as neutral and polyelectrolyte chains. By treating the NFs as telechelic polymer brushes, we also incorporate cross-bridging interactions. Both repulsive potentials are capable of reproducing NF cross-sectional densities and their pair correlations. We find that NF structure is sensitive to changes in brush thickness mediated by chain charge, consistent with the experimental observation that sidearm phosphorylation regulates interfilament spacing. The presence of attractive cross-bridging interactions contributes only modestly to structure for moderate degrees of cross-bridging and leads to NF aggregation for extensive cross-bridging.     

Entropic interaction chromatography: separating proteins on the basis of size using end-grafted polymer brushes

Partitioning of a macromolecule into the interfacial volume occupied by a grafted polymer brush decreases the configurational entropy (DeltaSbrush(c)) of the terminally attached linear polymer chains due to a loss of free volume. Self-consistent field theory (SCF) calculations are used to show that DeltaSbrush(c) is a strong function of both the size (MWp) of the partitioning macromolecule and the depth of penetration into the brush volume. We further demonstrate that the strong dependence of DeltaSbrush(c) on MWp provides a novel and powerful platform, which we call entropic interaction chromatography (EIC), for efficiently separating mixtures of proteins on the basis of size. Two EIC columns, differing primarily in polymer grafting density, were prepared by growing a brush of poly(methoxyethyl acrylamide) chains on the surface of a wide-pore (1,000-A pores, 64-microm diameter rigid beads) resin (Toyopearl AF-650M) bearing surface aldehyde groups. Semipreparative 0.1-L columns packed with either EIC resin provide reduced-plate heights of 2 or less for efficient separation of globular protein mixtures over at least three molecular-weight decades. Protein partitioning within these wide-pore EIC columns is shown to be effectively modeled as a thermodynamically controlled process, allowing partition coefficients (K(P)) and elution chromatograms to be accurately predicted using a column model that combines SCF calculation of K(P) values with an equilibrium-dispersion type model of solute transport through the column. This model is used to explore the dependence of column separation efficiency on brush properties, predicting that optimal separation of proteins over a broad MWp range is achieved at low to moderate grafting densities and intermediate chain lengths.     

Osmotic properties of poly(ethylene glycols): quantitative features of brush and bulk scaling laws

From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander-de Gennes theory of polymer brushes successfully fits the intermembrane distance versus applied osmotic stress data of Kenworthy et al. for poly(ethylene glycol)-grafted multilamellar liposomes. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent monomer density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semidilute regime of bulk polymer solutions). The condition that attached polymers behave as semidilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of semidilute polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander-de Gennes brush scaling laws to the Kenworthy et al. data yield effective monomer lengths of 3.3-3.6 A, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal mole fraction of poly(ethylene glycol)-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.     

AFM force measurements on microtubule-associated proteins: the projection domain exerts a long-range repulsive force

Microtubule-associated proteins (MAPs) are thought to control spacing between microtubules. We propose that the projection domain is largely unstructured and exerts a long-range repulsive force that is predominantly entropic in origin, providing a physical mechanism for maintaining spacing. To test this hypothesis, we developed an experimental system where MAPs are electrostatically end-attached to a flat surface, such that the projection domains extend away from the surface. Atomic force microscopy force measurements on this system show that projection domains exert a long-range (>100 nm) repulsive force. This force depends on the ionic strength of the solution in a way that is consistent with a polyelectrolyte polymer brush.     

Configurational entropy modulates the mechanical stability of protein GB1

Configurational entropy plays important roles in defining the thermodynamic stability as well as the folding/unfolding kinetics of proteins. Here we combine single-molecule atomic force microscopy and protein engineering techniques to directly examine the role of configurational entropy in the mechanical unfolding kinetics and mechanical stability of proteins. We used a small protein, GB1, as a model system and constructed four mutants that elongate loop 2 of GB1 by 2, 5, 24 and 46 flexible residues, respectively. These loop elongation mutants fold properly as determined by far-UV circular dichroism spectroscopy, suggesting that loop 2 is well tolerant of loop insertions without affecting GB1′s native structure. Our single-molecule atomic force microscopy results reveal that loop elongation decreases the mechanical stability of GB1 and accelerates the mechanical unfolding kinetics. These results can be explained by the loss of configurational entropy upon closing an unstructured flexible loop using classical polymer theory, highlighting the important role of loop regions in the mechanical unfolding of proteins. This study not only demonstrates a general approach to investigating the structural deformation of the loop regions in mechanical unfolding transition state, but also provides the foundation to use configurational entropy as an effective means to modulate the mechanical stability of proteins, which is of critical importance towards engineering artificial elastomeric proteins with tailored nanomechanical properties.     

Role of ionic strength on the relationship of biopolymer conformation,DLVO contributions,and steric interactions to bioadhesion of Pseudomonas putida KT2442

Biopolymers produced extracellularly by Pseudomonas putida KT2442 were examined via atomic force microscopy (AFM) and single molecule force spectroscopy. Surface biopolymers were probed in solutions with added salt concentrations ranging from that of pure water to 1 M KCl. By studying the physicochemical properties of the polymers over this range of salt concentrations, we observed a transition in the steric and electrostatic properties and in the conformation of the biopolymers that were each directly related to bioadhesion. In low salt solutions, the electrophoretic mobility of the bacterium was negative, and large theoretical energy barriers to adhesion were predicted from soft-particle DLVO theory calculations. The brush layer in low salt solution was extended due to electrostatic repulsion, and therefore, steric repulsion was also high (polymers extended 440 nm from surface in pure water). The extended polymer brush layer was "soft", characterized by the slope of the compliance region of the AFM approach curves (-0.014 nN/nm). These properties resulted in low adhesion between biopolymers and the silicon nitride AFM tip. As the salt concentration increased to > or =0.01 M, a transition was observed toward a more rigid and compressed polymer brush layer, and the adhesion forces increased. In 1 M KCl, the polymer brush extended 120 nm from the surface and the rigidity of the outer cell surface was greater (slope of the compliance region = -0.114 nN/nm). A compressed and more rigid polymer layer, as well as a less negative electrophoretic mobility for the bacterium, resulted in higher adhesion forces between the biopolymers and the AFM tip. Scaling theories for polyelectrolyte brushes were also used to explain the behavior of the biopolymer brush layer as a function of salt concentration.     

Nuclear Pore Complex Protein Sequences Determine Overall Copolymer Brush Structure and Function

The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature. We perform coarse-grained simulations of both individual nucleoporins and grafted rings of nups mimicking the in vivo geometry of the NPC and supplement this with polymer brush modeling. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature. Furthermore, this block structure at the individual protein level is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability.     

Nuclear Pore Complex Protein Sequences Determine Overall Copolymer Brush Structure and Function

The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature. We perform coarse-grained simulations of both individual nucleoporins and grafted rings of nups mimicking the in vivo geometry of the NPC and supplement this with polymer brush modeling. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature. Furthermore, this block structure at the individual protein level is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability.     

Prediction of unfolded segments in a protein sequence based on amino acid composition

MOTIVATION: Partially and wholly unstructured proteins have now been identified in all kingdoms of life--more commonly in eukaryotic organisms. This intrinsic disorder is related to certain critical functions. Apart from their fundamental interest, unstructured regions in proteins may prevent crystallization. Therefore, the prediction of disordered regions is an important aspect for the understanding of protein function, but may also help to devise genetic constructs. RESULTS: In this paper we present a computational tool for the detection of unstructured regions in proteins based on two properties of unfolded fragments: (1) disordered regions have a biased composition and (2) they usually contain either small or no hydrophobic clusters. In order to quantify these two facts we first calculate the amino acid distributions in structured and unstructured regions. Using this distribution, we calculate for a given sequence fragment the probability to be part of either a structured or an unstructured region. For each amino acid, the distance to the nearest hydrophobic cluster is also computed. Using these three values along a protein sequence allows us to predict unstructured regions, with very simple rules. This method requires only the primary sequence, and no multiple alignment, which makes it an adequate method for orphan proteins. AVAILABILITY: http://genomics.eu.org/     

Probing a Structural Model of the Nuclear Pore Complex Channel through Molecular Dynamics

The central pore of a nuclear pore complex (NPC) is filled with unstructured proteins that contain many FG-repeats separated by hydrophilic regions. An example of such protein is nsp1. By simulating an array of nsp1 segments, we identified, in an earlier study, a spontaneously formed brushlike structure that promises to explain selective transport in the NPC channel. Here we report four (350,000 atom, 200 ns) simulations probing this structure via its interaction with transport receptor NTF2 as well as with an inert protein. NTF2 dimers are observed to gradually enter the brush, but the inert protein is not. Both NTF2 and the inert protein are found to bind to FG-repeats, but binding periods lasted more briefly for the inert protein. A simulation also investigated the behavior of a brush made of mutant nsp1 that is known to be less effective in NPC-selective transport, finding that this brush does not attract NTF2.     

Bim, Bad and Bmf: intrinsically unstructured BH3-only proteins that undergo a localized conformational change upon binding to prosurvival Bcl-2 targets

All BH3-only proteins, key initiators of programmed cell death, interact tightly with multiple binding partners and have sequences of low complexity, properties that are the hallmark of intrinsically unstructured proteins (IUPs). We show, using spectroscopic methods, that the BH3-only proteins Bim, Bad and Bmf are unstructured in the absence of binding partners. Detailed sequence analyses are consistent with this observation and suggest that most BH3-only proteins are unstructured. When Bim binds and inactivates prosurvival proteins, most residues remain disordered, only the BH3 element becomes structured, and the short alpha-helical molecular recognition element can be considered to behave as a 'bead on a string'. Coupled folding and binding is typical of many IUPs that have important signaling roles, such as BH3-only proteins, as the inherent structural plasticity favors interaction with multiple targets. This understanding offers promise for the development of BH3 mimetics, as multiple modes of binding are tolerated.     

Natively unfolded proteins: a point where biology waits for physics

The experimental material accumulated in the literature on the conformational behavior of intrinsically unstructured (natively unfolded) proteins was analyzed. Results of this analysis showed that these proteins do not possess uniform structural properties, as expected for members of a single thermodynamic entity. Rather, these proteins may be divided into two structurally different groups: intrinsic coils, and premolten globules. Proteins from the first group have hydrodynamic dimensions typical of random coils in poor solvent and do not possess any (or almost any) ordered secondary structure. Proteins from the second group are essentially more compact, exhibiting some amount of residual secondary structure, although they are still less dense than native or molten globule proteins. An important feature of the intrinsically unstructured proteins is that they undergo disorder-order transition during or prior to their biological function. In this respect, the Protein Quartet model, with function arising from four specific conformations (ordered forms, molten globules, premolten globules, and random coils) and transitions between any two of the states, is discussed.     

Model Inspired by Nuclear Pore Complex Suggests Possible Roles for Nuclear Transport Receptors in Determining Its Structure

Nuclear transport receptors (NTRs) mediate nucleocytoplasmic transport via their affinity for unstructured proteins (polymers) in the nuclear pore complex (NPC). Here, we have modeled the effect of NTRs on polymeric structure in the nanopore confinement of the NPC central conduit. The model explicitly takes into account inter- and intramolecular interactions, as well as the finite size of the NTRs (∼20% of the NPC channel diameter). It reproduces various proposed scenarios for the channel structure, ranging from a central polymer condensate (selective phase) to brushlike polymer arrangements localized at the channel wall (virtual gate, reduction of dimensionality), with the transport receptors lining the polymer surface. In addition, it predicts a new structure in which NTRs become an integral part of the transport barrier by forming a cross-linked network with the unstructured proteins stretching across the pore. The model provides specific and distinctive predictions for the equilibrium spatial distributions of NTRs for these different scenarios that can be experimentally verified by, e.g., superresolution fluorescence microscopy. Moreover, it suggests mechanisms by which globular macromolecules (colloidal particles) can cause polymer-coated nanopores to switch between open and closed configurations, a possible explanation of the biological function of the NPC, and suggests potential technological applications for filtration and single-molecule sensing.     

Control of nanobiointerfaces generated from well-defined biomimetic polymer brushes for protein and cell manipulations

To better understand protein/material and cell/material interactions at the submolecular level, well-defined polymer brushes consisting of poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC) on silicon wafers were prepared by atom transfer radical polymerization (ATRP). Silicon wafers were treated with 3-(2-bromoisobutyryl)propyl dimethylchlorosilane (BDCS) to form a monolayer that acts as initiators for ATRP. Silicon-supported BDCS monolayers were soaked in a methanol/water mixture solution containing Cu(I)Br, bipyridine, and a sacrificial initiator. After MPC was added to the solution, ATRP was carried out for 18 h. The molecular weight and thickness of the PMPC brush layer on the silicon surface increased with an increase in the polymerization time. The dense polymer brushes were obtained by the "grafting from" system. By selective decomposition of the BDCS monolayer by UV light-irradiation, the PMPC brush region and the sizes were well controlled, resulting in fabricating micropatterns of the PMPC brushes. When the thickness of the PMPC brush layer was greater than 5.5 +/- 1.0 nm (3 h polymerization), serum protein adsorption and fibroblast adhesion were effectively reduced, i.e., proteins and cells could recognize such thin polymer brushes on the surface. In addition, the density of the adherent cells on the patterned PMPC brush surface could be controlled by changing the size of the pattern.     

Erratum to: How the projection domains of NF-L and α-internexin determine the conformations of NF-M and NF-H in neurofilaments

Making use of a numerical self-consistent field method and polymer brush concepts, we model the solvated corona of neurofilaments (NF) composed of projection domains (unstructured tails) of constituent proteins. Projections are modeled with amino acid resolution. We focus on the importance of the two shortest ones (α-internexin and NF-L) in regulating the conformations of the two longer ones (NF-M and NF-H) in an isolated NF. We take the wild-type NF with no α-internexin as the reference, for which the phosphorylation-induced translocation of M- and H-tails has been examined previously. We demonstrate that a subbrush of L-tails creates an electrostatic potential profile with an approximately parabolic shape. An experimentally relevant (2:1) ratio of L- to α-projections reduces the charge density of the L subbrush and shifts the translocation transition of the H-tails to slightly higher degrees of phosphorylation. Replacing all L-tails by α-projections destroys the substructure of the NF corona and this alters the NF response to the phosphorylation of long tails.     

How do immobilised cell-adhesive Arg–Gly–Asp-containing peptides behave at the PAA brush surface?

Bio-engineered surfaces that aim to induce normal cell behaviour in vitro need to ‘mimic’ the extracellular matrix in a way that allows cell adhesion. In this computational work, several model cell-binding peptides with a minimal cell-adhesive Arg–Gly–Asp sequence are investigated in the bulk as well as immobilised on a soft surface. For this reason, a combination of density functional theory and all-atom MD simulations is applied. The major goal of the modelling is to characterise the accessibility of the cell-recognition motif on the functionalised soft polymer surface. As a reference system, the behaviour of three peptide sequences is preliminarily studied in explicit water simulations. From the analysis of the MD trajectories, the solvent accessible surface area, the distribution of water molecules around peptide groups, the secondary structure and the thermodynamics of hydration are evaluated. Furthermore, each peptide is immobilised on the surface of a homopolymer poly(acrylic acid) brush. During MD simulations, all three peptides approach closely toward PAA brush, and their surface accessibility is characterised. Although the peptides are adsorbed onto the brush, they are not hidden by the polymer strands, with RGD unit accessible on the surface and available for guided cell adhesion.     

Correction

Nuclear transport receptors (NTRs) mediate nucleocytoplasmic transport via their affinity for unstructured proteins (polymers) in the nuclear pore complex (NPC). Here, we have modeled the effect of NTRs on polymeric structure in the nanopore confinement of the NPC central conduit. The model explicitly takes into account inter- and intramolecular interactions, as well as the finite size of the NTRs (∼20% of the NPC channel diameter). It reproduces various proposed scenarios for the channel structure, ranging from a central polymer condensate (selective phase) to brushlike polymer arrangements localized at the channel wall (virtual gate, reduction of dimensionality), with the transport receptors lining the polymer surface. In addition, it predicts a new structure in which NTRs become an integral part of the transport barrier by forming a cross-linked network with the unstructured proteins stretching across the pore. The model provides specific and distinctive predictions for the equilibrium spatial distributions of NTRs for these different scenarios that can be experimentally verified by, e.g., superresolution fluorescence microscopy. Moreover, it suggests mechanisms by which globular macromolecules (colloidal particles) can cause polymer-coated nanopores to switch between open and closed configurations, a possible explanation of the biological function of the NPC, and suggests potential technological applications for filtration and single-molecule sensing.     

Crowding-induced membrane remodeling: Interplay of membrane tension,polymer density,architecture

The plasma membrane hosts a wide range of biomolecules, mainly proteins and carbohydrates, that mediate cellular interactions with its environment. The crowding of such biomolecules regulates cellular morphologies and cellular trafficking. Recent discoveries have shown that the structure and density of cell surface polymers and hence the signaling machinery change with the state of the cell, especially in cancer progression. The alterations in membrane-attached glycocalyx and glycosylation of proteins and lipids are common features of cancer cells. The overexpression of glycocalyx polymers, such as mucin and hyaluronan, strongly correlates with cancer metastasis. Here, we present a mesoscale biophysics-based model that accounts for the shape regulation of membranes by crowding of membrane-attached biopolymer-glycocalyx and actin networks. Our computational model is based on the dynamically triangulated Monte Carlo model for membranes and coarse-grained representations of polymer chains. The model allows us to investigate the crowding-induced shape transformations in cell membranes in a tension- and graft polymer density-dependent manner. Our results show that the number of membrane protrusions and their shape depend on membrane tension, with higher membrane tension inducing more tubular protrusions than the vesicular shapes formed at low tension at high surface coverage of polymers. The shape transformations occur above the threshold density predicted by the polymer brush theory, but this threshold also depends on the membrane tension. Increasing the size of the polymer, either by changing the length or by adding side chains, is shown to increase the crowding-induced curvature. The effect of crowding is more prominent for flexible polymers than for semiflexible rigid polymers. We also present an extension of the model that incorporates properties of the actin-like filament networks and demonstrate how tubular structures can be generated by biopolymer crowding on the cytosolic side of cell membranes.     

The growth-suppressive function of the polycomb group protein polyhomeotic is mediated by polymerization of its sterile alpha motif (SAM) domain

Polyhomeotic (Ph), a member of the Polycomb Group (PcG), is a gene silencer critical for proper development. We present a previously unrecognized way of controlling Ph function through modulation of its sterile alpha motif (SAM) polymerization leading to the identification of a novel target for tuning the activities of proteins. SAM domain containing proteins have been shown to require SAM polymerization for proper function. However, the role of the Ph SAM polymer in PcG-mediated gene silencing was uncertain. Here, we first show that Ph SAM polymerization is indeed required for its gene silencing function. Interestingly, the unstructured linker sequence N-terminal to Ph SAM can shorten the length of polymers compared with when Ph SAM is individually isolated. Substituting the native linker with a random, unstructured sequence (RLink) can still limit polymerization, but not as well as the native linker. Consequently, the increased polymeric Ph RLink exhibits better gene silencing ability. In the Drosophila wing disc, Ph RLink expression suppresses growth compared with no effect for wild-type Ph, and opposite to the overgrowth phenotype observed for polymer-deficient Ph mutants. These data provide the first demonstration that the inherent activity of a protein containing a polymeric SAM can be enhanced by increasing SAM polymerization. Because the SAM linker had not been previously considered important for the function of SAM-containing proteins, our finding opens numerous opportunities to manipulate linker sequences of hundreds of polymeric SAM proteins to regulate a diverse array of intracellular functions.     

Three intrinsically unstructured mussel adhesive proteins,mfp‐1, mfp‐2, and mfp‐3: Analysis by circular dichroism

Mussel foot proteins (mfps) mediate fouling by the byssal holdfast and have been extensively investigated as models for versatile polymer‐mediated underwater adhesion and coatings. However, insights into the structural properties of mfps have lagged far behind the nanomechanical advances, owing in part to the inability of these proteins to crystallize as well as their limited solubility. Here, solution secondary structures of mfp‐1, mfp‐2, and mfp‐3, localized in the mussel byssal cuticle, adhesive plaque, and plaque–substratum interface, respectively, were investigated using circular dichroism. All three have significant extended coil solution structure, but two, mfp‐1 and mfp‐2, appear to have punctuated regions of structure separated by unstructured domains. Apart from its punctuated distribution, the structure in mfp‐1 resembles other structural proteins such as collagen and plant cell‐wall proteins with prominent polyproline II helical structure. As in collagen, PP II structure of mfp‐1 is incrementally disrupted by increasing the temperature and by raising pH. However, no recognizable change in mfp‐1's PP II structure was evident with the addition with Ca²⁺ and Fe³⁺. In contrast, mfp‐2 exhibits Ca²⁺‐ and disulfide‐stabilized epidermal growth factor‐like domains separated by unstructured sequence. Mfp‐2 showed calcium‐binding ability. Bound calcium in mfp‐2 was not removed by chelation at pH 5.5, but it was released upon reduction of disulfide bonds. Mfp‐3, in contrast, appears to consist largely of unstructured extended coils.