Search

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities—over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model’s parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Intrinsically disordered proteins play important roles throughout biology, yet our understanding of the relationship between their sequences, structural properties, and functions remains incomplete. The dynamic nature of these proteins, however, makes them difficult to characterize structurally. Many disordered proteins can attain both compact and expanded conformations, and the level of expansion may be regulated and important for function. Experimentally, the level of compaction and shape is often determined either by small-angle x-ray scattering experiments or pulsed-field-gradient NMR diffusion measurements, which provide ensemble-averaged estimates of the radius of gyration and hydrodynamic radius, respectively. Often, these experiments are interpreted using molecular simulations or are used to validate them. We here provide, to our knowledge, a new and efficient method to calculate the hydrodynamic radius of a disordered protein chain from a model of its structural ensemble. In particular, starting from basic concepts in polymer physics, we derive a relationship between the radius of gyration of a structure and its hydrodynamic ratio, which in turn can be used, for example, to compare a simulated ensemble of conformations to NMR diffusion measurements. The relationship may also be valuable when using NMR diffusion measurements to restrain molecular simulations.

Force-spectroscopy has been an essential tool for understanding how proteins fold and unfold, and their involvement in regulating cell responses to mechanical stimuli. Hence, it is of significance to establish an accurate free energy model of proteins under force capable of describing the mechanisms of protein folding. Even though numerous models have been proposed, the role of polymer physics and the changes in entropy involved in protein elasticity are still controversial. We have developed a model to construct the free energy of elastic proteins under force based on protein folding and polymer physics. The model is constructed by combining Morse and Gaussian potentials describing the enthalpic interactions in the folded state, and the freely jointed-chain (FJC) energy model accounting for the entropic changes during unfolding and stretching. The free parameters of each component are dependent on the protein and thus regulate its mechanical properties [J. Valle-Orero et al, BBRC 460 (2015)]. Here we aim to prove the accuracy of the model by reproducing force-spectroscopy data of a model protein, protein L (B1 domain from Peptostreptococcus magnus). We experimentally fit the force dependent extension of unfolded domains with the FJC using a contour length of 16.3 nm and a Kuhn length of 1.1 nm. The Morse depth of 2 kBT was established by measuring the probability that a domain folds at a given force. A Gaussian barrier of 10.5 kBT was chosen by comparing the experimental unfolding kinetics to those obtained using Brownian dynamics on our energy model. The excellent agreement of our model with experimental data validates and reinforces the theoretical foundations of our physics model. Furthermore, we demonstrate that changes in entropy during extending or collapsing a protein results in departure from simple Bell-like models.

Sic1 is a cyclin-dependent kinase inhibitor which must be phosphorylated on at least six sites (termed Cdc4 phosphodegrons, CPDs) to allow its recognition by the WD40 binding domain of Cdc4. The highly-cooperative switch-like dependence on the number of phosphorylated sites on Sic1 cannot be accounted for by traditional thermodynamic models of cooperativity. Further experimental attention is necessary to determine the physicochemical/mechanistic basis of its highly cooperative binding.We used single molecule fluorescence techniques to study the dimensions and dynamics of Sic1's N-terminal targeting region (residues 1-90, henceforth Sic1), phosphorylated Sic1 (pSic1), and the pSic1-WD40 dynamic complex. Using time-resolved fluorescence anisotropy, we find local segment specific rotational correlation times which are complexly modulated by chain compactness and electrostatics (charge screening and phosphorylation).Previous single molecule Fӧrster Resonance Energy Transfer (smFRET) measurements [1] observed end-to-end reconfiguration on timescales larger than ∼1ms; resulting in FRET histograms with multiple conformational sub-ensembles. These sub-ensembles and their dynamics are further explored by trapping single Sic1, pSic1 and WD40 in nanometer sized surface-tethered lipid vesicles and modulating their electrostatics and compactness. In a refinement to the conventional approaches for inferring dimensions from smFRET experiments, we use distance distributions from Monte Carlo simulations which extensively sample coarse-grained protein conformations. The application of polymer physics theory/simulation towards smFRET data interpretation, and towards IDP binding, contributes to the growing toolkit for understanding the diverse behaviours of IDPs.[1] Liu B. et al., J. Phys. Chem. B. 2014 118(15):4088-97.

Sic1 is a cyclin-dependent kinase inhibitor which must be phosphorylated on at least six sites (termed Cdc4 phosphodegrons, CPDs) to allow its recognition by the WD40 binding domain of Cdc4. The highly-cooperative switch-like dependence on the number of phosphorylated sites on Sic1 cannot be accounted for by traditional thermodynamic models of cooperativity. Further experimental attention is necessary to determine the physicochemical/mechanistic basis of its highly cooperative binding.We used single molecule fluorescence techniques to study the dimensions and dynamics of Sic1's N-terminal targeting region (residues 1-90, henceforth Sic1), phosphorylated Sic1 (pSic1), and the pSic1-WD40 dynamic complex.Previous single molecule Fӧrster Resonance Energy Transfer (smFRET) measurements [Liu, 2014] observed end-to-end reconfiguration on timescales larger than ∼1ms; resulting in FRET histograms with multiple conformational sub-ensembles. Sic1, pSic1, and the pSic1-WD40 complex are examined using smFRET to study the dynamics and dimensions of the various sub-ensembles. In a refinement to the conventional approaches for inferring dimensions from smFRET experiments, we use distance distributions from Monte Carlo simulations which extensively sample coarse-grained protein conformations. The application of polymer physics theory/simulation towards smFRET data interpretation, and towards IDP binding, contributes to the growing toolkit for understanding the diverse behaviours of IDPs.

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.

Single DNA Molecule Swollen and Trapped in NanoslitDirect visualization of individual DNA molecules confined within a nano/microfluidic geometry has provided a new route for the study of polymer physics. Molecular confinement has been utilized to evaluate theoretical predictions developed over several decades. Particularly, nanoslit confined DNA molecules are an interesting topic to show the conformational transition from 3D to 2D depending on nanoslit heights. Although several experiments have recently reported the dependence of DNA conformation on nanoslit confinement, a controversy still remains because the results have not been consistent with one another nor with theoretical predictions. Here we present nanoslit confined DNA conformations at various low ionic strength conditions down to 0.18 mM, which increase the repulsion between DNA−DNA and DNA−nanoslit. Moreover, we derived a new theoretical explanation for most measurements of single DNA molecule size under strong nanoslit confinement. Our findings demonstrates that very low ionic strength conditions not only increase the DNA persistence length dramatically, but also cause DNA molecules to swell to the extent that the effective diameter of DNA becomes larger than the nanoslit height (h < w), which can be considered as electrostatic trapping to confine molecules to geometry smaller than the physical boundaries. Consequently, by accounting for these effects, our results and theory provide a reasonable solution for a current controversy regarding the dependence of the DNA conformation on slit height (h), persistence length (p), and effective diameter (w).1. Lee J, Kim S, Jeong H, Jung GY, Chang R, Chen YL, Jo, K (2014) Nanoslit Confined DNA at Low Ionic Strengths. ACS Macro Letters 3(9): 926-930

Thereisanoldjokeaboutalazydoctorwho, instead of looking at each patientindividually, requested informationabout average body temperature of allpatients in the hospital. The joke pre-tends to be funny because an ensembleview of patients is absurd. But in someother cases, including in the life sci-ences, an ensemble view is not onlynot absurd, but the right instrument,and Liu and Hyeon (1) in this issueof the Biophysical Journal offer anice example: not only do they lookat ensembles, they compare twodifferent ones—ensemble of proteinsand ensemble of RNAs. Their findingsare remarkably thought-provoking.Their main technical tool is thestudyofcontactprobability—theprob-ability that two monomers of a specificpolymer chain, separated by a contourdistance of s monomers, are found incontact in three dimensions (Fig. 1).In polymer physics, a similarlydefined quantity P(s) is widely usedto distinguish between differentphases of a polymer chain. In partic-ular, for various fractal conformations,P(s)decaysas apower lawPðsÞ s

An accurate description of unfolded states under folding conditions is important for quantitative studies of protein stability, protein folding kinetics, and an understanding of how features of the unfolded state may have contributed to the convergent evolution toward foldable sequences. Here, we present results from multi-pronged biophysical investigations that uncover a comprehensive description of conformational ensembles accessed by unfolded states of proteins under folding conditions. We combined results from experiments based on time-resolved Forster resonance energy transfer, using multiple non-perturbing, amino-acid-sized dye pairs, and time-resolved small angle X-ray scattering, with novel molecular simulations and polymer physics theories. Previous work showed that aqueous milieus are poor solvents for polypeptide backbones. This should drive chain collapse and globule formation. Our current results, obtained for the N-terminal domain of the ribosomal protein L9, show that under folding conditions, native and non-native intra-chain interactions lead to transient globule formation, while large conformational fluctuations brought about by favorable sidechain-solvent interactions lead to an unfolded ensemble that behaves statistically like a flexible polymer would in a theta-solvent. Therefore, the unfolded state under folding conditions may be described as an ensemble with fluctuating elements of native and non-native non-random elements of structure that are averaged over to yield random coil-like statistics of chains in theta solvents. This behavior derives from the sequence-encoded interplay between backbone- and sidechain-mediated intra-chain and chain-solvent interactions. Our results have broad implications for interactions of unfolded proteins in crowded milieus, for folding-unfolding transitions, and for tilting the balance toward heterogeneous ensembles as is the case with intrinsically disordered proteins.

Nuclear Pore Complex (NPC) is a biological “nano-machine” that controls the macromolecular transport between the cell nucleus and the cytoplasm. It is a remarkable device that combines selectivity with robustness and speed. Unlike many other biological nano-channels, it functions without direct input of metabolic energy and without transitions of the gate from a 'closed' to an 'open' state during transport. The key aspect of transport is the interaction of the cargo-carrying transport factors with the unfolded, natively unstructured proteins that partially occlude the channel of the NPC and its nuclear and cytoplasmic exits.Mechanistic understanding of the transport through the Nuclear Pore Complex, and in particular its selectivity, is still lacking. Conformational transitions of the unfolded proteins of the NPC, induced by the transport factors, have been hypothesized to underlie the transport mechanism and its selectivity. These conformational changes are hard to access in vivo; they have been investigated in vitro, generating apparently contradictory results.We have investigated the biophysical underpinning of these conformational changes, using computational modeling based on the ideas the ideas of the polymer physics. We show that the differences in the experimentally observed behaviors can be explained by rather general physical factors, such as the attraction strength between the transport factors and the unfolded chains, protein density and the transport factor size. We also show how these general behaviors can be modulated by molecule-specific details, such as the aminoacid sequence and the relative arrangement in space of the charged and hydrophobic residues. Finally, we extend the model into a realistic NPC geometry. These results provide new insights into the fundamental principles of transport through the NPC and the control of the behavior of natively unfolded proteins in general.

For intrinsically disordered proteins (IDPs) containing a high density of charged residues, a Gaussian chain is an inadequate description of the protein's shape. One such IDP is Sic1, a highly positively charged IDP in the budding yeast Saccharomyces Cerevisiae which prevents the cell cycle from entering the S-phase from the G1-phase. Sic1's binding affinity for Cdc4 is highly phosphorylation state dependent, although the corresponding physical basis is not fully understood. NMR data supports the presence of a dynamic complex of Sic1:Cdc4 and a poly-electrostatic model has been proposed by Forman-Kay and coworkers.We studied the Sic1 N-terminal targeting region (1-90) to better understand the role of intrachain electrostatics, and to compare with the structural ensembles calculated from NMR and SAXS data. Sic1 is characterized using time-resolved fluorescence anisotropy (TRFA), which is sensitive to rotational and conformational dynamics. Sic1 exists in a dynamic ensemble of conformations and ensemble-averaged experiments have limitations in identifying and characterizing static and/or dynamic inhomogeneity in the motional dynamics. Therefore, we also performed burst spectroscopy and single-molecule TRFA on freely diffusing Sic1. Shape and flexibility were probed by varying the degree of intrachain repulsion screening through adjusting salt concentrations and described within a polymer physics framework, the polyelectrolyte model. To investigate the relative contributions of “global rotation” and “conformational flexibility”, Sic1 was labelled at three different sites. Sic1 is found to be well modelled as a prolate ellipsoid with internal flexibility.The single-molecule derived TRFA distribution data may be valuable as a constraint incorporated in future conformational ensemble calculations, complementary to SAXS and NMR data. Additionally, these measurements raise questions about the accuracy of highly charged IDP's radii of gyration when calculated from sm-FRET derived end-to-end distances, which often assume a Gaussian chain model for the end-to-end distance probability distribution.

We investigate experimentally the effect of ionic strength on λ DNA molecule in glass/PDMS nanoslit by using fluorescence microscope. The radius of gyration Rg was measured as a function of slit height (250 ∼ 1049 nm), and ionic strength (0.183 ∼ 1.75 mM) as a result, we observed the Rg values increases as channel heights and ionic strengths decrease. Furthermore, based on Odijk's and de Gennes polymer physics theory, we interpret our experimental findings as a function of channel heights and ionic strengths. We also study the effect of EDTA concentration, radius of gyration of λ DNA change drastically in response to the varying EDTA concentration at low ionic strength condition. Our results are useful for understanding the manipulation of biomolecules in nanofluidic devices.

Light has been used to observe cells since Leeuwenhoek's times; however, we use the forces caused by light described by Maxwell's surface tensor to feel for the cellular cytoskeleton. The cytoskeleton a compound of highly dynamic polymers and active nano-elements inside biological cells is responsible for a cell's stability and organization. It mechanically senses a cell's environment and generates cellular forces sufficiently strong to push rigid AFM-cantilevers out of the way. The active cytoskeleton is described by a new type of polymer physics since nano-sized molecular motors and active polymerization overcome the inherently slow, often glass-like brownian polymer dynamics. The optical stretcher exploits the nonlinear, thus amplified response of a cell's mechanical strength to small changes between different cytoskeletal proteomic compositions as a high precision cell marker that uniquely characterizes different cell types. Consequentially, the optical stretcher detects tumors and their stages with accuracy unparalleled by molecular biology. As implied by developmental biology the compartmentalization of cells and the epithelial-mesenchymal transition that allows cells to overcome compartmental boundaries strongly depend on cell stiffness and adhesiveness. Consequentially, biomechanical changes are key when metastatic cells become able to leave the boundaries of the primary tumor.

Histone tails are highly flexible N terminal protrusions of histone proteins which help to fold DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolites with high degree of conformational disorder, allowing them to function as bio-molecular “switches”, regulating various genetic regulatory processes. Because of being intrinsically disordered, the structural and dynamical aspects of histone tails are still poorly understood. In this work we have carried out 3 microsecond all atom replica exchange molecular dynamics (REMD) simulations of four histone tails, H4, H3, H2B and H2A, to probe for their intrinsic conformational preferences. Our subsequent energy landscape analysis demonstrated that some tails are not fully disordered, but contain residual secondary structure elements. In particular, H4 formed beta hairpins, H3 and H2B adopted alpha helical elements while H2A was fully disordered. We also carried out polymer physics based analysis of the histone tails' conformational ensembles. We found an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by the way mobile counterions associate with the protein chains at various temperatures.

Intricate interplay of temperature and pressure on protein folding leads to interesting phase diagram. In addition, kinetics of pressure induced folding exhibit complex behavior. Here, we propose a simple mesoscopic model, a combination of landscape theory and microscopic details based on polymer physics to investigate this interesting phenomenon. The model is applied to experimental data to understand physical principles of pressure induced denaturation.

We use statistical mechanics and simple ideas from polymer physics to develop a quantitative model of proteins whose activity is controlled by flexibly tethered ligands and receptors. We predict how the properties of tethers influence the function of these proteins and demonstrate how their tether length dependence can be exploited to construct proteins whose integration of multiple signals can be tuned. One case study to which we apply these ideas is that of the Wiskott-Aldrich Syndrome Proteins as activators of actin polymerization. More generally, tethered ligands competing with those free in solution are common phenomena in biology, making this an important specific example of a widespread biological idea.

The entropic confinement and manipulation of DNA in fabricated nanostructures has facilitated both the study of DNA-protein interactions and the polymer physics of DNA conformations in different solvent conditions and geometries. Moreover, it holds great promise as a powerful tool for rapid genomic sequencing. Ethanol precipitation is a common tool in molecular biology used to purify and concentrate DNA, typically in 70% (or greater) ethanol solutions. Even at lower ethanol concentrations, however, DNA has been shown to undergo a transformation from its physiological B-form to A-form, a shorter yet slightly less twisted molecular conformation. To examine this transition, we isolated individual YOYO-1 labeled λ-DNA molecules in 100nm×100nm nanochannels in 0, 20, 40 and 60% ethanol solutions. We observed a dramatic shortening in the mean measured lengths with increasing ethanol and a broadening of the distribution of measured lengths at the intermediate ethanol concentrations. These observed lengths are less than that of fully A-form λ-DNA, suggesting that other mechanisms are involved in shortening the observed molecules. First, the possible effect of ethanol dislodging of the intercolated fluorophores and subsequent shortening the observed molecule is discussed. Second, the substantial variations in intensity in our observed molecules at the higher ethanol concentrations are (i) suggestive of the higher order DNA conformations such as loops and toroids that have been observed in DNA dried on mica surfaces and (ii) in accord with the observation that the effective persistence length of DNA is reduced in ethanol solutions.

We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity. Deriving the partitioning equilibrium equations and solving them numerically allows us to introduce the concept of "polymers-pushing-polymers" for the action of non-penetrating polymers on the partitioning of the penetrating polymers. Polymer partitioning into a pore even within a very simple model of a binary polymer mixture is shown to depend in a complicated way on the composition of the polymer mixture and/or the pore-penetration penalty. This can lead to enhanced as well as diminished partitioning, due to two separate energy scales that we analyse in detail., 10 pages, 6 figures

In nanochannels with dimensions smaller than the DNA radius of gyration, DNA will extend along the channel. We investigate long DNA confined in nanochannels using fluorescence microscopy and intercalated dyes. Studies of the dynamics and statics of the DNA extension or position in such nanoscale confinements as a function of e.g. DNA contour length, degree and shape of confinement as well as ionic strength have yielded new insights in the physical properties of DNA with relevance for applications in genomics as well as fundamental understanding of DNA packaging in vivo. Our work extends the field by not only studying the location of the emitting dyes along a confined DNA molecule but also monitoring the polarization of the emitted light. We use intercalating dyes (YOYO-1) whose emission is polarized perpendicular to the DNA extension axis, and by measuring the emission polarized parallel and perpendicular to the extension axis of the stretched DNA, information on the local spatial distribution of the DNA backbone can be obtained. The results obtained are analogous to linear dichroism (LD) but on a single-molecule level, and obtained in a highly parallel fashion. We will discuss results in shallow (60 nm) and deep (180 nm) channels and describe an example of how the technique can be used to investigate non-uniform stretching of DNA on the single molecule level. Comparing polarizations in two directions for DNA confined in channels of effective diameters of 85 nm and 170 nm reveals a striking difference. Whereas the DNA in the larger channels shows an isotropic polarization of the emitted light, the light is to a large extent polarized perpendicular to the elongation of the DNA in the smaller channels. The ratio of the polarization parallel and perpendicular to the elongation direction, I|| / I⊥, is a measure of the relative local orientation of the DNA backbone. We believe that this technique will have a large impact on the studies of changes in DNA conformation induced by protein binding or during DNA compactation as well as in fundamental polymer physics studies of DNA in confined environments, for example in bacterial spores and viruses.

The plasma membrane is commonly considered the boundary of the living cell, although peripheral polysaccharides and glycoproteins often self-organize into an additional coating layer on the cell surface. Chondrocytes and oocytes, for example, build strongly hydrated coats that are rich in the polysaccharide hyaluronan, and that can reach several micrometers in thickness. These pericellular coats play a crucial role in the general protection of the cell, and act as a mediator in the communication with its environment. The highly hydrated nature of these coats, and the complex structure and dynamics of the living cell make them difficult to probe in their native environment or to determine the coat's structure with high resolution methods. Therefore, to understand structure/function inter-relationships of these coats it is vital to move from living cells to simplified model systems.We have recently developed a new method to create in vitro model systems of the pericellular coat that is based on the end-grafting of hyaluronan to a supported lipid bilayer1. The model systems are well-controlled and capture characteristic properties of the pericellular coat, including its dimensions and hydration. With these models, the dynamics of coat reorganization and relevant physico-chemical properties can be investigated in a quantitative manner, and related to polymer physics theory.Here, we present data on the characterization of the properties inherent to films of end-grafted hyaluronan, including its permeability to solutes, its response to hyaluronan-binding proteins and its mechanical properties. Ultimately, we expect to gain novel information about the relationship between the pericellular coat's composition, supramolecular structure and biological function.(1) Richter, R.P. Hock, K.K. Burkhartsmeyer, J. Boehm, H. Bingen, P. Wang, G. Steinmetz, N.F. Evans, D.J. Spatz, J.P. JACS 2007, 127, 5306-5307.

We show that the folding rates (k_F) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free energy barriers separating the folded and the unfolded states is Gaussian, which follows from central limit theorem arguments and polymer physics concepts, we show that k_F ~ k_0 exp(-alpha N^0.5). Remarkably, the theory fits the experimental rates spanning over seven orders of magnitude with k_0 ~ 1.0 (microsec)^{-1}. An immediate consequence of our finding is that the speed limit of RNA folding is about one microsecond just as it is in the folding of globular proteins., 3 pages, 1 figure, 1 Table

The dynamics of chromatin folding has an important role in regulating gene expression in higher eukaryotes. Detailed studies of several model loci, such as beta-globin, have shown that the formation of loops mediated by the interaction between specific regulatory elements that are located hundreds of kilobases away is crucial in gene control. This observation gives rise to an important question: how can a set of widely spaced elements communicate in order to regulate a specific target gene.Recently a computational model has been proposed by Mukhopadhyay et al to explain the formation of long-range chromatin loops. This model is based on attractive nucleosome-nucleosome interaction, allowing the monomers of a chromatin polymer to stick to each other temporarily when in the vicinity of each other. This model shows the enhanced long range contact behavior consistent with shown in recent studies and predicts suppression of pseudoknot formation in chromatin folding. However, it remains to be understood why the chromatin polymer model behaves this way. To answer this question, we propose to look at the structure of the temporarily collapsed configurations of a polymer in certain ranges of lengths and attraction strengths. In particular, our aim is to calculate the crossover scale between the collapsed polymer at longer distance and the folded branched polymer at shorter distance. Such theoretical predictions from a polymer model combined with simulations of polymer conformations (both lattice polymer models and bead-spring models), would tell us whether, in the realistic model, there are certain parameter combinations that has to be fine-tuned to get the suppression of pseudoknots. We hope this study leads to a better understanding of the role of non-specific interactions of the polymer physics of chromatin.

Nanofluidic channels have become an important tool to investigate single DNA molecules both from a fundamental polymer physics perspective as well as in e.g. optical mapping techniques. However, less effort has been made to study DNA-protein complexes. A main reason is that the extreme surface-to-volume ratio in the nanochannels causes most proteins to stick to the channel walls. We have recently overcome this problem by coating the channels with a lipid bilayer, thereby eliminating sticking.

Many proteins associated with neurodegenerative diseases are intrinsically disordered, i.e. they lack a stable, folded structure under physiological conditions. It is currently believed that the aggregation of these proteins plays a causative role in neurodegenerative disease pathogenesis. Therefore, understanding how and why these proteins aggregate is crucial to understanding and possibly suppressing disease.Proteins are polymers and protein aggregation is akin to phase separation. We employ techniques and theories borrowed from polymer physics to help understand the driving forces and mechanisms of protein aggregation. Our system of interest is polyglutamine, as expansions of polyglutamine are thought to be causally linked to the development of at least nine different neurodegenerative diseases. In this work, we measure the saturation concentrations of aqueous polyglutamine solutions containing 30 and 40 glutamines and either 2 or 4 lysines. We use classical polymer physics theory to construct the entire (soluble-insoluble) phase diagram from the measured saturation concentrations. The low-concentration arm of the phase diagram provides a thermodynamic basis for assessing aggregation propensity. For a given chain length of polyglutamine, we find that aggregation propensity increases with fewer lysines, and, for a fixed number of lysines, the aggregation propensity increases with increasing chain length. Although the phase diagrams are thermodynamic in nature, they still provide insights regarding the kinetic mechanisms of phase separation. For the concentrations used in most in vitro experiments, the phase diagrams predict that intrinsically disordered monomers first form disordered, higher-order oligomers or clusters which then undergo a nucleated structural conversion into an ordered, insoluble form. These predictions are supported by detailed atomic force microscopy studies. This work highlights the prominence of intrinsic disorder even in multimolecular complexes and its role in facilitating conformational conversion to ordered supramolecular aggregates.

Nanofluidic channels have become a versatile tool to manipulate single DNA molecules. They allow investigation of confined single DNA molecules from a fundamental polymer physics perspective as well as for example in DNA barcoding techniques.Circular DNA is of interest since it is found in many biologically relevant contexts, such as bacterial plasmids, viruses and eukaryotic mitochondrial DNA. Furthermore, the circular topology forces two strands in close proximity to each other in nanochannel, which changes the polymer physics compared to linear DNA. Circular DNA is difficult to study with traditional single molecule techniques because such techniques generally require the attachment of handles to the, but is readily accessed using nanofluidics.Circular DNA has less entropy and higher conformational free energy than in its unfolded configuration. Therefore, as a double-strand break occurs and circular DNA opens up, it unfolds to its linear configuration inside the nanochannel. This study compares the static properties of confined linear and circular DNA as well as investigates the dynamics of the transition from circular to linear DNA as a double-strand break occurs.We observe that the difference in extension between the circular and linear configurations depends on the degree of confinement, which we confirm with theoretical predictions. Our data for unfolding of the circular DNA to the linear configuration suggests that hydrodynamic friction between the DNA and the solvent is the main rate-determining factor but that DNA-DNA contacts are also important. Finally, by staining the DNA inhomogeneously, we can follow the local dynamics of the DNA as the folding occurs and conclude, for example, how the two different strands move relative to each other during the unfolding process. We are thus able to study the dynamics of confined DNA with unprecedented resolution and obtain completely new information about confined polymers.