Micromechanics of isolated sickle cell hemoglobin fibers: bending moduli and persistence lengths

Principles and Biomedical Applications of Self-Assembled Peptides: Potential Treatment of Type 2 Diabetes Mellitus

Type 2 diabetes mellitus (T2DM) is the most prevalent metabolic disorder worldwide. There have been tremendous efforts to find a safe and prolonged effective therapy for its treatment. Peptide hormones, from certain organisms in the human body, as the pharmaceutical agents, have shown outstanding profiles of efficacy and safety in plasma glucose regulation. Their therapeutic promises have undergone intensive investigations via examining their physicochemical and pharmacokinetic properties. Their major drawback is their short half-life in vivo. To address this challenge, researchers have recently started to apply the state-of-the-art molecular self-assembly on peptide hormones to form nanofibrillar structures, as a smart nanotherapeutic drug delivery technique, to tremendously enhance their prolonged bioactivity in vivo. This revolutionary therapeutic approach would significantly improve patient compliance. First, this review provides a comprehensive summary on the pathophysiology of T2DM, various efforts to treat this chronic disorder, and the limitations and drawbacks of these treatment approaches. Next, this review lays out detailed insights on various aspects of peptide self-assembly: adverse effects, potential applications in nanobiotechnology, thermodynamics and kinetics of the process, as well as the molecular structures of the self-assembled configurations. Furthermore, this review elucidates the recent efforts on applying reversible human-derived peptide self-assembly to generate highly organized smart nanostructured drug formulations known as nanofibrils to regulate and prolong the bioactivity of the human gut hormone peptides in vivo to treat T2DM. Finally, this review highlights the future research directions to advance the knowledge on the state-of-the-art peptide self-assembly process to apply the revolutionary smart nanotherapeutics for treatment of chronic disorders such as T2DM with highly improved patient compliance.

Confined filaments in soft vesicles - the case of sickle red blood cells

Abnormal shapes of red blood cells (RBC) have been associated with various diseases. Diverse RBC shapes have also been intriguing for membrane biophysics. Here we focus on sickle shaped RBC which form due to abnormal growth of semi-rigid hemoglobin (HbS) fibers confined in RBC. Using the area difference elasticity (ADE) model for RBC and worm-like chain model for the confined HbS fibers, we explore shape deformations at equilibrium using Monte-Carlo simulations. We show that while a single HbS fiber is not rigid enough to produce sickle like deformation, a fiber bundle can do so. We also consider multiple disjoint filaments and find that confinement can generate multipolar RBC shapes and can even promote helical filament conformations which have not been discussed before. We show that the same model, when applied to microtubules confined in phospholipid vesicles, predicts vesicle tubulation. In addition we reproduce the tube collapse transition and tennis racket type vesicle shapes, as reported in experiments. We conclude that with a decrease in the surface area to volume ratio, and membrane rigidity, the vesicles prefer tubulation over sickling. The highlight of this work is several important non-axisymmetric RBC and vesicle shapes, which have never been explored in simulations.

Quantitative prediction of erythrocyte sickling for the development of advanced sickle cell therapies

Sickle cell disease is induced by a mutation that converts normal adult hemoglobin to sickle hemoglobin (HbS) and engenders intracellular polymerization of deoxy-HbS and erythrocyte sickling. Development of anti-sickling therapies requires quantitative understanding of HbS polymerization kinetics under organ-specific conditions, which are difficult to assess with existing experimental techniques. Thus, we developed a kinetic model based on the classical nucleation theory to examine the effectiveness of potential anti-sickling drug candidates. We validated this model by comparing its predictability against prior in vivo and in vitro experimental results. We used the model to quantify the efficacy of sickling inhibitors and obtain results consistent with recent screening assays. Global sensitivity analysis on the kinetic parameters in the model revealed that the solubility, nucleation rate prefactor, and oxygen affinity are quantities that dictate HbS polymerization. This finding provides quantitative guidelines for the discovery of intracellular processes to be targeted by sickling inhibitors.

Rapid and inefficient kinetics of sickle hemoglobin fiber growth

In sickle cell disease, the aberrant assembly of hemoglobin fibers induces changes in red blood cell morphology and stiffness, which leads to downstream symptoms of the disease. Therefore, understanding of this assembly process will be important for the treatment of sickle cell disease. By performing the highest spatiotemporal resolution measurements (55 nm at 1 Hz) of single sickle hemoglobin fiber assembly to date and combining them with a model that accounts for the multistranded structure of the fibers, we show that the rates of sickle hemoglobin addition and loss have been underestimated in the literature by at least an order of magnitude. These results reveal that the sickle hemoglobin self-assembly process is very rapid and inefficient (4% efficient versus 96% efficient based on previous analyses), where net growth is the small difference between over a million addition-loss events occurring every second.

Automated tracing of helical assemblies from electron cryo-micrographs

Structure determination of helical specimens commonly requires datasets from thousands of micrographs often obtained by automated cryo-EM data acquisition. Interactive tracing of helical assemblies from such a number of micrographs is labor-intense and time-consuming. Here, we introduce an automated tracing tool MicHelixTrace that precisely locates helix traces from micrographs of rigid as well as very flexible helical assemblies with small numbers of false positives. The computer program is fast and has low computational requirements. In addition to helix coordinates required for a subsequent helical reconstruction work-flow, we determine the persistence length of the polymer ensemble. This information provides a useful measure to characterize mechanical properties of helical assemblies and to evaluate the potential for high-resolution structure determination.

Bending energy penalty enhances the adhesive strength of functional amyloid curli to surfaces

The functional amyloid curli fiber, a major proteinaceous component of biofilm extracellular matrices, plays an important role in biofilm formation and enterobacteriaceae adhesion. Curli nanofibers exhibit exceptional underwater adhesion to various surfaces, have high rigidity and strong tensile mechanical properties, and thus hold great promise in biomaterials. The mechanisms of how curli fibers strongly attach to surfaces and detach under force remain elusive. To investigate curli fiber adhesion to surfaces, we developed a coarse-grained curli fiber model, in which the protein subunit CsgA (curli specific gene A) self-assembles into the fiber. The coarse-grained model yields physiologically relevant and tunable bending rigidity and persistence length. The force-induced desorption of a single curli fiber is examined using coarse-grained modeling and theoretical analysis. We find that the bending energy penalty arising from high persistence length enhances the resistance of the curli fiber against desorption and thus strengthens the adhesion of the curli fiber to surfaces. The CsgA-surface adhesion energy and the curli fiber bending rigidity both play crucial roles in the resistance of curli fiber against desorption from surfaces. To enable the desorption process, the applied peeling force must overcome both the interfacial adhesion energy and the energy barrier for bending the curli fiber at the peeling front. We show that the energy barrier to desorption increases with the interfacial adhesion energy, however, the bending induced failure of a single curli fiber limits the work of adhesion if the proportion of the CsgA-surface adhesion energy to the CsgA-CsgA cohesive energy becomes large. These results illustrate that the optimal adhesion performance of nanofibers is dictated by the interplay between bending, surface energy and cohesive energy. Our model provides timely insight into enterobacteriaceae adhesion mechanisms as well as future designs of engineered curli fiber based adhesives.

Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers

Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.

Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations

Polymerization of sickle hemoglobin (HbS) is the primary pathogenic event of sickle cell disease. For insight into the nature of the HbS polymer fiber formation, we develop a particle model-resembling a coarse-grained molecular model-constructed to match the intermolecular contacts between HbS molecules. We demonstrate that the particle model predicts the formation of HbS polymer fibers by attachment of monomers to rough fiber ends and the growth rate increases linearly with HbS concentration. We show that the characteristic 14-molecule fiber cross section is preserved during growth. We also correlate the asymmetry of the contact sites on the HbS molecular surface with the structure of the polymer fiber composed of seven helically twisted double strands. Finally, we show that the same asymmetry mediates the mechanical and structural properties of the HbS polymer fiber.

Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods

The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.

Development and characterization of a eukaryotic expression system for human type II procollagen

Background

Triple helical collagens are the most abundant structural protein in vertebrates and are widely used as biomaterials for a variety of applications including drug delivery and cellular and tissue engineering. In these applications, the mechanics of this hierarchically structured protein play a key role, as does its chemical composition. To facilitate investigation into how gene mutations of collagen lead to disease as well as the rational development of tunable mechanical and chemical properties of this full-length protein, production of recombinant expressed protein is required.

Results

Here, we present a human type II procollagen expression system that produces full-length procollagen utilizing a previously characterized human fibrosarcoma cell line for production. The system exploits a non-covalently linked fluorescence readout for gene expression to facilitate screening of cell lines. Biochemical and biophysical characterization of the secreted, purified protein are used to demonstrate the proper formation and function of the protein. Assays to demonstrate fidelity include proteolytic digestion, mass spectrometric sequence and posttranslational composition analysis, circular dichroism spectroscopy, single-molecule stretching with optical tweezers, atomic-force microscopy imaging of fibril assembly, and transmission electron microscopy imaging of self-assembled fibrils.

Conclusions

Using a mammalian expression system, we produced full-length recombinant human type II procollagen. The integrity of the collagen preparation was verified by various structural and degradation assays. This system provides a platform from which to explore new directions in collagen manipulation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12896-015-0228-7) contains supplementary material, which is available to authorized users.

Mechanics of single peptide hydrogelator fibrils

The rigidity of peptide fibers is essential for their chemical and biological functions, despite that it remains largely unexplored. Here, we present the first direct measurement of the mechanics of individual fibers in peptide hydrogels by AFM imaging and statistical analysis and find that the intermolecular interactions play a considerable role.

Role of sequence and structural polymorphism on the mechanical properties of amyloid fibrils

Amyloid fibrils playing a critical role in disease expression, have recently been found to exhibit the excellent mechanical properties such as elastic modulus in the order of 10 GPa, which is comparable to that of other mechanical proteins such as microtubule, actin filament, and spider silk. These remarkable mechanical properties of amyloid fibrils are correlated with their functional role in disease expression. This suggests the importance in understanding how these excellent mechanical properties are originated through self-assembly process that may depend on the amino acid sequence. However, the sequence-structure-property relationship of amyloid fibrils has not been fully understood yet. In this work, we characterize the mechanical properties of human islet amyloid polypeptide (hIAPP) fibrils with respect to their molecular structures as well as their amino acid sequence by using all-atom explicit water molecular dynamics (MD) simulation. The simulation result suggests that the remarkable bending rigidity of amyloid fibrils can be achieved through a specific self-aggregation pattern such as antiparallel stacking of β strands (peptide chain). Moreover, we have shown that a single point mutation of hIAPP chain constituting a hIAPP fibril significantly affects the thermodynamic stability of hIAPP fibril formed by parallel stacking of peptide chain, and that a single point mutation results in a significant change in the bending rigidity of hIAPP fibrils formed by antiparallel stacking of β strands. This clearly elucidates the role of amino acid sequence on not only the equilibrium conformations of amyloid fibrils but also their mechanical properties. Our study sheds light on sequence-structure-property relationships of amyloid fibrils, which suggests that the mechanical properties of amyloid fibrils are encoded in their sequence-dependent molecular architecture.

The self-assembly, aggregation and phase transitions of food protein systems in one, two and three dimensions

The aggregation of proteins is of fundamental relevance in a number of daily phenomena, as important and diverse as blood coagulation, medical diseases, or cooking an egg in the kitchen. Colloidal food systems, in particular, are examples that have great significance for protein aggregation, not only for their importance and implications, which touches on everyday life, but also because they allow the limits of the colloidal science analogy to be tested in a much broader window of conditions, such as pH, ionic strength, concentration and temperature. Thus, studying the aggregation and self-assembly of proteins in foods challenges our understanding of these complex systems from both the molecular and statistical physics perspectives. Last but not least, food offers a unique playground to study the aggregation of proteins in three, two and one dimensions, that is to say, in the bulk, at air/water and oil/water interfaces and in protein fibrillation phenomena. In this review we will tackle this very ambitious task in order to discuss the current understanding of protein aggregation in the framework of foods, which is possibly one of the broadest contexts, yet is of tremendous daily relevance.

Length distribution of stiff, self-assembled polymers at thermal equilibrium

We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.

Nanomechanical properties of single amyloid fibrils

Amyloid fibrils are traditionally associated with neurodegenerative diseases like Alzheimer's disease, Parkinson's disease or Creutzfeldt-Jakob disease. However, the ability to form amyloid fibrils appears to be a more generic property of proteins. While disease-related, or pathological, amyloid fibrils are relevant for understanding the pathology and course of the disease, functional amyloids are involved, for example, in the exceptionally strong adhesive properties of natural adhesives. Amyloid fibrils are thus becoming increasingly interesting as versatile nanobiomaterials for applications in biotechnology. In the last decade a number of studies have reported on the intriguing mechanical characteristics of amyloid fibrils. In most of these studies atomic force microscopy (AFM) and atomic force spectroscopy play a central role. AFM techniques make it possible to probe, at nanometer length scales, and with exquisite control over the applied forces, biological samples in different environmental conditions. In this review we describe the different AFM techniques used for probing mechanical properties of single amyloid fibrils on the nanoscale. An overview is given of the existing mechanical studies on amyloid. We discuss the difficulties encountered with respect to the small fibril sizes and polymorphic behavior of amyloid fibrils. In particular, the different conformational packing of monomers within the fibrils leads to a heterogeneity in mechanical properties. We conclude with a brief outlook on how our knowledge of these mechanical properties of the amyloid fibrils can be exploited in the construction of nanomaterials from amyloid fibrils.

Modeling sickle hemoglobin fibers as one chain of coarse-grained particles

Sickle cell disease (SCD) is caused by a single point mutation in the beta-chain hemoglobin gene, resulting in the presence of abnormal hemoglobin S (HbS) in the patients' red blood cells (RBCs). In the deoxygenated state, the defective hemoglobin tetramers polymerize forming stiff fibers which distort the cell and contribute to changes in its biomechanical properties. Because the HbS fibers are essential in the formation of the sickle RBC, their material properties draw significant research interests. Here, a solvent-free coarse-grain molecular dynamics (CGMD) model is introduced to simulate single HbS fibers as a chain of particles. First, we show that the proposed model is able to efficiently simulate the mechanical behavior of single HbS fibers. Then, the zippering process between two HbS fibers is studied and the effect of depletion forces is investigated. Simulation results illustrate that depletion forces play a role comparable to direct fiber-fiber interaction via Van der Waals forces. This proposed model can greatly facilitate studies on HbS polymerization, fiber bundle and gel formation as well as interaction between HbS fiber bundles and the RBC membrane.

Predicting the morphology of sickle red blood cells using coarse-grained models of intracellular aligned hemoglobin polymers

Sickle red blood cells (SS-RBCs) exhibit heterogeneous cell morphologies (sickle, holly leaf, granular, etc.) in the deoxygenated state due to the polymerization of the sickle hemoglobin. Experimental evidence points to a close relationship between SS-RBC morphology and intracellular aligned hemoglobin polymers. Here, we develop a coarse-grained (CG) stochastic model to represent the growth of the intracellular aligned hemoglobin polymer domain. The CG model is calibrated based on the mechanical properties (Young's modulus, bending rigidity) of the sickle hemoglobin fibers reported in experiments. The process of the cell membrane transition is simulated for physiologic aligned hemoglobin polymer configurations and mean corpuscular hemoglobin concentration. Typical SS-RBC morphologies observed in experiments can be obtained from the current model as a result of the intracellular aligned hemoglobin polymer development without introducing any further ad hoc assumptions. It is found that the final shape of SS-RBCs is primarily determined by the angular width of the aligned hemoglobin polymer domain, but it also depends, to a lesser degree, on the polymer growth rate and the cell membrane rigidity. Cell morphologies are quantified by structural shape factors, which agree well with experimental results from medical images.

The mechanics of FtsZ fibers

Inhibition of the Fts family of proteins causes the growth of long filamentous cells, indicating that they play some role in cell division. FtsZ polymerizes into protofilaments and assembles into the Z-ring at the future site of the septum of cell division. We analyze the rigidity of GTP-bound FtsZ protofilaments by using cryoelectron microscopy to sample their bending fluctuations. We find that the FtsZ-GTP filament rigidity is κ=4.7±1.0×10(-27) Nm(2), with a corresponding thermal persistence length of l(p)=1.15±0.25μm, much higher than previous estimates. In conjunction with other model studies, our new higher estimate for FtsZ rigidity suggests that contraction of the Z-ring may generate sufficient force to facilitate cell division. The good agreement between the measured mode amplitudes and that predicted by equipartition of energy supports our use of a simple mechanical model for FtsZ fibers. The study also provides evidence that the fibers have no intrinsic global or local curvatures, such as might be caused by partial hydrolysis of the GTP.

The growth of sickle hemoglobin polymers

The measurement of polymer growth is an essential element in characterization of assembly. We have developed a precise method of measuring the growth of sickle hemoglobin polymers by observing the time required for polymers to traverse a photolytically produced channel between a region in which polymers are created and a detection region. The presence of the polymer is functionally detected by observing its ability to create new polymers through the well-established process of heterogeneous nucleation. Using this method, we have determined the rate constants for monomer addition to and release from polymer ends, as well as their temperature dependences. At 25°C we find k(+) = 84 ± 2 mM⁻¹ s⁻¹ and k(-) = 790 ± 80 molecules/s from each end. These numbers are in accord with differential interference contrast measurements, and their ratio gives a solubility measured on individual fibers. The single-fiber solubility agrees with that measured in sedimentation experiments. The concentration dependence of the monomer addition rate is consistent with monomer addition, but not oligomer addition, to growing polymers. The concentration dependence suggests the presence of an activation enthalpy barrier, and the rate of monomer addition is not diffusion-limited. Analysis of the temperature dependence of the monomer addition rate reveals an apparent activation energy of 9.1 ± 0.6 kcal/mol.

Mechanical stress affects glucagon fibrillation kinetics and fibril structure

Mechanical stress can strongly influence the capability of a protein to aggregate and the kinetics of aggregation, but there is little insight into the underlying mechanism. Here we study the effect of different mechanical stress conditions on the fibrillation of the peptide hormone glucagon, which forms different fibrils depending on temperature, pH, ionic strength, and concentration. A combination of spectroscopic and microscopic data shows that fibrillar polymorphism can also be induced by mechanical stress. We observed two classes of fibrils: a low-stress and a high-stress class, which differ in their kinetic profiles, secondary structure as well as morphology and that are able to self-propagate in a template-dependent fashion. The bending rigidity of the low-stress fibrils is sensitive to the degree of mechanical perturbation. We propose a fibrillation model, where interfaces play a fundamental role in the switch between the two fibrillar classes. Our work also raises the cautionary note that mechanical perturbation is a potential source of variability in the study of fibrillation mechanisms and fibril structures.

Nanomechanics of functional and pathological amyloid materials

Amyloid or amyloid-like fibrils represent a general class of nanomaterials that can be formed from many different peptides and proteins. Although these structures have an important role in neurodegenerative disorders, amyloid materials have also been exploited for functional purposes by organisms ranging from bacteria to mammals. Here we review the functional and pathological roles of amyloid materials and discuss how they can be linked back to their nanoscale origins in the structure and nanomechanics of these materials. We focus on insights both from experiments and simulations, and discuss how comparisons between functional protein filaments and structures that are assembled abnormally can shed light on the fundamental material selection criteria that lead to evolutionary bias in multiscale material design in nature.

The microrheology of sickle hemoglobin gels

Sickle cell disease is a rheological disease, yet no quantitative rheological data exist on microscopic samples at physiological concentrations. We have developed a novel method for measuring the microrheology of sickle hemoglobin gels, based on magnetically driven compression of 5- to 8-microm-thick emulsions containing hemoglobin droplets approximately 80 microm in diameter. Using our method, by observing the expansion of the droplet area as the emulsion is compressed, we were able to resolve changes in thickness of a few nanometers with temporal resolution of milliseconds. Gels were formed at various initial concentrations and temperatures and with different internal domain structure. All behaved as Hookean springs with Young's modulus from 300 to 1500 kPa for gels with polymerized hemoglobin concentration from 6 g/dl to 12 g/dl. For uniform, multidomain gels, Young's modulus mainly depended on the terminal concentration of the gel rather than the conditions of formation. A simple model reproduced the quadratic dependence of the Young's modulus on the concentration of polymerized hemoglobin. Partially desaturated samples also displayed quadratic concentration dependence but with a smaller proportionality coefficient, as did samples that were desaturated in steps; such samples were significantly less rigid than gels formed all at once. The magnitude of the Young's modulus provides quantitative support for the dominant models of sickle pathophysiology.

Sickle cell biomechanics

As the predominant cell type in blood, red blood cells (RBCs) and their biomechanical properties largely determine the rheological and hemodynamic behavior of blood in normal and disease states. In sickle cell disease (SCD), mechanically fragile, poorly deformable RBCs contribute to impaired blood flow and other pathophysiological aspects of the disease. The major underlying cause of this altered blood rheology and hemodynamics is hemoglobin S (HbS) polymerization and RBC sickling under deoxygenated conditions. This review discusses the characterization of the biomechanical properties of sickle RBCs and sickle blood as well as their implications toward a better understanding of the pathophysiology of the disease.

Detection of populations of amyloid-like protofibrils with different physical properties

We used tapping mode atomic force microscopy to study the morphology of the amyloid protofibrils formed at fixed conditions (low pH with high ionic strength) by self-assembly of the N-terminal domain of the hydrogenase maturation factor HypF. Although all protofibrils in the sample share a beaded structure and similar values of height and width, an accurate analysis of contour length and end-to-end distance and the comparison of experimental data with theoretical predictions based on the worm-like chain model show that two different populations of protofibrils are present. These populations are characterized by different physical properties, such as persistence length, bending rigidity and Young's modulus. Fluorescence quenching measurements on earlier globular intermediates provide an independent evidence of the existence of different populations. The finding that differences in mechanical properties exist even within the same sample of protofibrils indicates the presence of different subpopulations of prefibrillar aggregates with potentially diverse tendencies to react with undesired molecular targets. This study describes a strategy to discriminate between such different subpopulations that are otherwise difficult to identify with conventional analyses.

Roles of titin in the structure and elasticity of the sarcomere

The giant protein titin is thought to play major roles in the assembly and function of muscle sarcomeres. Structural details, such as widths of Z- and M-lines and periodicities in the thick filaments, correlate with the substructure in the respective regions of the titin molecule. Sarcomere rest length, its operating range of lengths, and passive elastic properties are also directly controlled by the properties of titin. Here we review some recent titin data and discuss its implications for sarcomere architecture and elasticity.

Fiber depolymerization: fracture, fragments, vanishing times, and stochastics in sickle hemoglobin

The well-characterized rates, mechanisms, and stochastics of nucleation-dependent polymerization of deoxyhemoglobin S (HbS) are important in governing whether or not vaso-occlusive sickle cell crises will occur. The less well studied kinetics of depolymerization may also be important, for example in achieving full dissolution of polymers in the lungs, in resolution of crises and/or in minimizing gelation-induced cellular damage. We examine depolymerization by microscopic observations on depolymerizing HbS fibers, by Monte Carlo simulations and by analytical characterization of the mechanisms. We show that fibers fracture. Experimental scatter of rates is consistent with stochastic features of the analytical model and Monte Carlo results. We derive a model for the distribution of vanishing times and also show the distribution of fracture-dependent fiber fragment lengths and its time dependence. We describe differences between depolymerization of single fibers and bundles and propose models for bundle dissolution. Our basic model can be extended to dissolution of gels containing many fibers and is also applicable to other reversible linear polymers that dissolve by random fracture and end-depolymerization. Under the model, conditions in which residual HbS polymers exist and facilitate repolymerization and thus pathology can be defined; whereas for normal polymers requiring cyclic polymerization and depolymerization for function, conditions for rapid cycling due to residual aggregates can be identified.

Possibilities for 'smart' materials exploiting the self-assembly of polypeptides into fibrils

Programmed assembly and self-assembly of soft materials offers significant promise for the generation of new types of materials with useful properties. Through evolutionary processes occurring over billions of years, nature has produced numerous optimised building blocks for the controlled assembly of a wide range of complex architectures. Our challenge now is to imitate these naturally occurring processes for technological applications, either using biological molecules such as DNA and proteins, or macromolecular mimics that retain many of the important features of biological molecules while introducing new functionalities. We focus on a single example of biomolecular self-assembly-the self-assembly of polypeptides, including polypeptide mimics, into quasi-one-dimensional fibres-to provide a flavour of the utility of soft biological materials for construction purposes.

Role of intermolecular forces in defining material properties of protein nanofibrils

Protein molecules have the ability to form a rich variety of natural and artificial structures and materials. We show that amyloid fibrils, ordered supramolecular nanostructures that are self-assembled from a wide range of polypeptide molecules, have rigidities varying over four orders of magnitude, and constitute a class of high-performance biomaterials. We elucidate the molecular origin of fibril material properties and show that the major contribution to their rigidity stems from a generic interbackbone hydrogen-bonding network that is modulated by variable side-chain interactions.

Deforming biological membranes: how the cytoskeleton affects a polymerizing fiber

We give a theoretical treatment of the force exerted by a fluctuating membrane on a polymer rod tip, taking into account the effects of an underlying biological cytoskeleton by way of a simple harmonic dependence on displacement. We also consider theoretically and experimentally the dynamics of a growing fiber tip under the influence of such a fluctuation-induced membrane force, including the effects of an underlying cytoskeletal network. We compare our model with new experimental data for the growth of hemoglobin fibers within red blood cells, revealing a good agreement. We are also able to estimate the force and membrane/cytoskeletal displacement required to stall growth of, or buckle, a growing fiber. We discuss the significance of our results in a biological context, including how the properties of the membrane and cytoskeleton relate to the thermodynamics of rod polymerization.

Characterization of the nanoscale properties of individual amyloid fibrils

We report the detailed mechanical characterization of individual amyloid fibrils by atomic force microscopy and spectroscopy. These self-assembling materials, formed here from the protein insulin, were shown to have a strength of 0.6 +/- 0.4 GPa, comparable to that of steel (0.6-1.8 GPa), and a mechanical stiffness, as measured by Young's modulus, of 3.3 +/- 0.4 GPa, comparable to that of silk (1-10 GPa). The values of these parameters reveal that the fibrils possess properties that make these structures highly attractive for future technological applications. In addition, analysis of the solution-state growth kinetics indicated a breakage rate constant of 1.7 +/- 1.3 x 10(-8) s(-1), which reveals that a fibril 10 mum in length breaks spontaneously on average every 47 min, suggesting that internal fracturing is likely to be of fundamental importance in the proliferation of amyloid fibrils and therefore for understanding the progression of their associated pathogenic disorders.

Spatial persistence of angular correlations in amyloid fibrils

Using atomic force microscopy height maps, we resolve and quantify torsional fluctuations in one-dimensional amyloid fibril aggregates self-assembled from three different representative polypeptide systems. Furthermore, we show that angular correlation in these nanoscale structures is maintained over several microns, corresponding to many thousands of molecules along the fibril axis. We model disorder in the fibril in respect of both thermal fluctuations and structural defects, and determine quantitative values for the defect density, as well as the energy scales involved in the fundamental interactions stabilizing these generic structures.

Anisotropy in Sickle Hemoglobin Fibers from Variations in Bending and Twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.

Competing Pathways Determine Fibril Morphology in the Self-assembly of β2-Microglobulin into Amyloid

Despite its importance in biological phenomena, a comprehensive understanding of the mechanism of amyloid formation remains elusive. Here, we use atomic force microscopy to map the formation of beta2-microglobulin amyloid fibrils with distinct morphologies and persistence lengths, when protein concentration, pH and ionic strength are varied. Using the resulting state-diagrams, we demonstrate the existence of two distinct competitive pathways of assembly, which define an energy landscape that rationalises the sensitivity of fibril morphology on the solution conditions. Importantly, we show that semi-flexible (worm-like) fibrils, which form rapidly during assembly, are kinetically trapped species, formed via a non-nucleated pathway that is explicitly distinct from that leading to the formation of the relatively rigid long-straight fibrils classically associated with amyloid. These semi-flexible fibrils also share an antibody epitope common to other protein oligomers that are known to be toxic species linked to human disease. The results demonstrate the heterogeneity of amyloid assembly, and have important implications for our understanding of the importance of oligomeric states in amyloid disease, the origins of prion strains, and the development of therapeutic strategies.

Measuring forces between protein fibers by microscopy

We propose a general scheme for measuring the attraction between mechanically frustrated semiflexible fibers by measuring their thermal fluctuations and shape. We apply this analysis to a system of sickle hemoglobin (HbS) fibers that laterally attract one another. These fibers appear to "zip" together before reaching mechanical equilibrium due to the existence of cross-links into a dilute fiber network. We are also able to estimate the rigidities of the fibers. These rigidities are found to be consistent with sickle hemoglobin "single" fibers 20 nm in diameter, despite recent experiments indicating that fiber bundling sometimes occurs. Our estimate of the magnitude of the interfiber attraction for HbS fibers is in the range 8 +/- 7 kBT/microm, or 4 +/- 3 k(B)T/microm if the fibers are assumed, a priori to be single fibers (such an assumption is fully consistent with the data). This value is sufficient to bind the fibers, overcoming entropic effects, although extremely chemically weak. Our results are compared to models for the interfiber attraction that include depletion and van der Waals forces. This technique should also facilitate a similar analysis of other filamentous protein assembles in the future, including beta-amyloid, actin, and tubulin.

The force generated by biological membranes on a polymer rod and its response: Statics and dynamics

We propose a theory for the force exerted by a fluctuating membrane on a polymer rod tip. Using statistical mechanical methods, the expression for the generated force is written in terms of the distance of the rod tip from the membrane "frame." We apply the theory in calculating the stall force and membrane displacement required to cease the growth of a growing fiber induced by membrane fluctuations, as well as the membrane force and membrane displacement required for rod/fiber buckling. We also consider the dynamics of a growing fiber tip under the influence of a fluctuation-induced membrane force. We discuss the importance of our results in various biological contexts. Finally, we present a method to simultaneously extract both the rigidity of the semiflexible rod and the force applied by, e.g., the membrane from the measurements of the bending fluctuations of the rod. Such a measurement of the force would give information about the thermodynamics of the rod polymerization that involves the usual Brownian ratchet mechanism.

Kinks, rings, and rackets in filamentous structures

Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and "tennis racket" shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important determinant of the morphology than any molecular details. Our mesoscopic continuum theory is capable of quantifying observations of these structures and is suggestive of their occurrence in other filamentous assemblies as well.

Sickle hemoglobin fibers: mechanisms of depolymerization

We examined the depolymerization of hemoglobin (Hb) S fibers in the presence of CO by using photolysis of COHbS to create and isolate individual fibers, then removing photolysis to induce depolymerization. Depolymerization occurs at two sites, fiber ends and fiber sides, with different kinetics and by different mechanisms. At low partial pressure of CO (pCO), end-depolymerization is dominant, proceeding at approximately 1 microm s(-1), whereas at high pCO fibers vanish very rapidly, in much less than one second, by side-depolymerization. Each kind of depolymerization could occur by a ligand-independent path, in which deoxyHb depolymerizes and then is prevented from returning to the polymer by liganding with CO, or by a ligand-dependent path in which CO binds to the polymer inducing dissociation of the newly liganded molecules from it. We find that ligand-independent depolymerization is the dominant path for end-depolymerization and ligand-dependent depolymerization dominates, at least at high pCO, for side-depolymerization. On the basis of our kinetic results and electron micrographs of depolymerizing fibers, we propose a model for side-depolymerization in which a hole is nucleated by cooperative loss of a few molecules from fiber sides, followed by rapid depolymerization from the newly created fiber ends abutting the hole. Potential significance of these results for the pathophysiology of sickle cell disease is discussed.