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Many industrial scale water treatment processes depend on ultrafiltration polymer membranes fabricated through highly nonequilibrium methods. Facile control over these nonequilibrium processes has remained elusive, constraining manufacturing facilities and experimentalists alike to rely on trial and error to construct a suitable membrane. Nonsolvent-induce phase separation (NIPS) is a common fabrication technique whereby the immersion of a polymer solution into a nonsolvent bath induces phase separation that ultimately forms the membrane matrix and pores. Although NIPS yields a favorable asymmetric structure, the broad pore size distribution at the surface leaves much to be desired. Addressing this issue, much effort has been devoted to coupling the self-assembling nature of block copolymers with NIPS (SNIPS) to produce next-generation integral-asymmetric membranes with an isoporous surface. The work of this thesis aims to provide insights into both NIPS and SNIPS that serve as guidance for future fabrication efforts. We accomplish this by leveraging dynamical field-theoretic simulations to model membrane morphology formation via NIPS and SNIPS. In a collaboration with experimentalists, we demonstrate that the influence of solvent and nonsolvent variation on morphology and kinetics during NIPS can be tied to changes in the size of the two-phase region. To model SNIPS, we developed a novel workflow using equilibrium self-consistent field theory (SCFT) to approximate an isoporous surface that is stitched onto a film prior to employing dynamical SCFT (DSCFT). Based on results obtained by varying several formulation parameters, we present guidelines for membrane preparation such that the resulting morphology retains an isoporous surface and forms a connection between the surface and substructure throughout the NIPS process.We conclude our work by addressing the question of \textit{which} block copolymer membrane morphologies are ideal for water filtration. To this end, we develop a multiscale workflow that allows us to determine the diffusivity of solute throughout a given block copolymer morphology. Solvated morphologies generated using SCFT are input into a kinetic Monte Carlo scheme that simulates the diffusion of solute through the pores. Our workflow serves as a tool for screening a wide array of structures to aid in the inverse design of desirable membrane morphologies.

Loop-extrusion and phase-separation have been proposed as mechanisms that shape chromosome large-scale spatial organization. It is unclear, however, how they perform relative to each other in explaining chromatin architecture data and whether they compete or co-exist at the single-molecule level. Here, we compare models of polymer physics based on loop-extrusion and phase-separation, as well as models where both mechanisms act simultaneously in a single molecule, against multiplexed FISH data available in human loci in IMR90 and HCT116 cells. We find that the different models recapitulate bulk Hi-C and average microscopy data. Single-molecule chromatin conformations are also well captured, especially by phase-separation based models that better reflect the experimentally reported segregation in globules of the considered genomic loci and their cell-to-cell structural variability. Such a variability is consistent with two main concurrent causes: single-cell epigenetic heterogeneity and an intrinsic thermodynamic conformational degeneracy of folding. Overall, the model combining loop-extrusion and polymer phase-separation provides a very good description of the data, particularly higher-order contacts, showing that the two mechanisms can co-exist in shaping chromatin architecture in single cells.

Phytoglycogen (PG) is a natural polysaccharide produced in the form of compact, 44 nm diameter nanoparticles (NPs) in the kernels of sweet corn. Its highly branched, dendritic structure and soft, compressible nature leads to interesting and useful properties that make the particles ideal as unique additives in personal care, nutrition, and biomedical formulations. To enhance the practical use of PG NPs towards these applications, it is often desirable to modify their properties. In this thesis, we consider the effects of three chemical modifications of PG NPs: acid hydrolysis, the covalent attachment of positively charged glycidyltrimethylammonium chloride (GTAC) chemical groups and the covalent attachment of negatively charged, hydrophobic octenyl succinic anhydride (OSA) chains to the particle surface. We have performed rheology measurements to investigate the effects of these chemical modifications on the flow properties and interactions between PG NPs in water as a function of the effective volume fraction of the particles, focusing on steady shear rheology measurements of the zero-shear viscosity and oscillatory measurements of the storage 𝐺′ and loss 𝐺" moduli. The rheology of acid hydrolyzed PG NPs was consistent with softer particles relative to native PG NPs, as indicated by a smaller fragility index 𝑚 value and enhanced interpenetration between the particles that led to highly dissipative viscoelastic behaviour with an experimentally accessible 𝛼-relaxation time. Dispersions of GTAC-modified PG NPs were significantly more viscous than those of native PG NPs, showing a much steeper increase in viscosity with increasing concentration 𝐶, and exhibited a more pronounced solid-like viscoelastic response. GTAC-modified PG dispersions were sensitive to the addition of salts and showed a significant reduction in viscosity with added NaCl. The behaviour of OSA-modified PG NPs was dependent on the degree of substitution (DS) of OSA: for low DS values, the rheology of OSA-modified PG NPs was dominated by electrostatic interactions. For higher DS values, hydrophobic interactions were more significant, and we observed evidence for clustering of the particles when NaCl was added to the dispersions. These results highlight the high degree of tunability of PG NPs and suggest promising new applications for the particles. Natural Sciences and Engineering Research Council of Canada

Molecular fluctuations directly reflect the underlying energy landscape. Variance analysis examines protein dynamics in several biochemistry-driven approaches, yet measurement of probe-independent fluctuations in proteins exposed to mechanical forces remains only accessible through steered molecular dynamics simulations. Using single molecule magnetic tweezers, here we conduct variance analysis to show that individual unfolding and refolding transitions occurring in dynamic equilibrium in a single protein under force are hallmarked by a change in the protein's end-to-end fluctuations, revealing a change in protein stiffness. By unfolding and refolding three structurally distinct proteins under a wide range of constant forces, we demonstrate that the associated change in protein compliance to reach force-induced thermodynamically stable states scales with the protein's contour length increment, in agreement with the sequence-independent freely jointed chain model of polymer physics. Our findings will help elucidate the conformational dynamics of proteins exposed to mechanical force at high resolution which are of central importance in mechanosensing and mechanotransduction.

The design of new types of macromolecular architecture is one of the main directions in the development of modern polymer physics. As applied to electronics, electroconductive π-conjugated molecules occupy a special place. In this review, the distinctive features of the electronic properties of organic semiconductors when compared with their solid-state analogs are considered. Special attention is paid to the role of electron–electron and electron–phonon interactions in the formation of self-localized excited states, i.e., solitons and polaritons. The constructive and destructive interference effects in molecular structures containing branching nodes and ring groups are discussed. The size of a branched molecule should herewith be small to conserve quantum coherence. Self-localization effects in such molecules are insignificant and transport is determined by electrons and holes injected from contacts. Two approaches to the description of quantum interference in branched molecules are proposed, notably, based on molecular orbitals and in the scope of the pattern of localized atomic orbitals. These approaches make it possible to formulate design rules for molecular structures, in which interference is observed. The latest results on the design of quantum-interference molecular transistors with ultralow energy consumption are presented. Nonconjugated tree-branched polymers, so-called dendrimers, which can be efficient for designing systems of the collection and transformation of electromagnetic radiation are briefly considered.

The combination of modelling and experimental advances can provide deep insights for understanding chromatin 3D organization and ultimately its underlying mechanisms. In particular, models of polymer physics can help comprehend the complexity of genomic contact maps, as those emerging from technologies such as Hi-C, GAM or SPRITE. Here we discuss a method to reconstruct 3D structures from Genome Architecture Mapping (GAM) data, based on PRISMR, a computational approach introduced to find the minimal polymer model best describing Hi-C input data from only polymer physics. After recapitulating the PRISMR procedure, we describe how we extended it for treating GAM data. We successfully test the method on a 6 Mb region around the Sox9 gene and, at a lower resolution, on the whole chromosome 7 in mouse embryonic stem cells. The PRISMR derived 3D structures from GAM co-segregation data are finally validated against independent Hi-C contact maps. The method results to be versatile and robust, hinting that it can be similarly applied to different experimental data, such as SPRITE or microscopy distance data.

The development of novel experimental technologies able to map genome-wide chromatin contacts, as Hi-C, GAM or SPRITE, allowed to derive detailed information about the spatial structure of chromosomes in the cell nucleus. They revealed that the genome has a complex spatial organisation, which is highly connected with its activity. In the last years, such an abundance of experimental data prompted the development of quantitative models based on Polymer Physics to describe the chromatin architecture, clarifying many aspects about the molecular mechanisms underlying genome folding. Efficient algorithms are thus fundamental to perform massive numerical simulations for testing the accuracy of these models and provide a good description for small genomic regions or for whole chromosomes. Here, we consider the performances of Molecular Dynamics (MD) implementation of commonly used polymer physics models. Such models can be combined with Machine Learning approaches informed with experimental data to produce more accurate descriptions of real genomic regions. However, the execution times increase as a power-law with the size of the input data, which ultimately reflects the complexity of the investigated system. The best strategy is therefore a convenient trade-off between the accuracy in the description and the availability of computational resources. The combination of innovative experimental data and polymer physics theories allow to reconstruct the 3D genome structure. This is achieved by the use of machine learning approaches and massive parallel computing. Efficient algorithms and computational resources are then fundamental to produce models of increasingly high accuracy.

Macromolecules in an entangled environment are constrained to wriggle predominantly along a confining tube, giving rise to the so-called reptation or tube-like motion. While the principles of polymer physics were well developed to understand its conformational dynamics, the quantitative characterization of the tube diameter and resulting reptation remains an open question. Here, using highly confined parallel plate geometry nanoslits down to sub-30 nm, we directly observe reptation in a one-dimensional (1D) confined nanoenvironment. We provide a quantitative analysis scheme, by introducing the segmental tangential vector and its associated correlation function, to characterize the strand reptation and connect it to the confinement degree. Our analysis shows that the amplitude of the transverse fluctuations (the virtual 2D "tube") exhibits the typical scaling of fluctuating interfaces, contact lines, or charge density waves, with a roughness exponent, which depends on the slit height. Our results are shown to lead to less rough DNA profiles in shallower nanoslits. We anticipate our analysis to be a starting point for a more detailed understanding of the relationship between polymer physics and other nonequilibrium physical systems.

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures., 14 pages, 5 figures

Novel technologies are revealing that chromosomes have a complex three-dimensional organization within the cell nucleus that serves functional purposes. Models from polymer physics have been developed to quantitively understand the molecular principles controlling their structure and folding mechanisms. Here, by using massive molecular-dynamics simulations we show that classical scaling laws combined with finite-size effects of a simple polymer model can effectively explain the scaling behavior that chromatin exhibits at the topologically associating domains level, as revealed by experimental observations. Model results are then validated against recently published high-resolution in situ Hi-C data.

Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.

The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the ‘registration’ of aligned protein chains using intermolecularly interacting ‘sticky’ patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein–chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

The native state structures of globular proteins are stable and well-packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry of the building blocks of protein structures, alpha-helices and strands assembled into beta-sheets, with no adjustable parameters, no amino acid sequence information, and no chemistry. There is an almost perfect fit between the dictates of mathematics and physics and the rules of quantum chemistry. Our theory establishes an energy landscape that channels protein evolution by providing sequence-independent platforms for elaborating sequence-dependent functional diversity. Our work highlights the vital role of discreteness in life and has implications for the creation of artificial life and on the nature of life elsewhere in the cosmos., 32 pages, 6 figures, 2 tables; Added key sentence about the important role of amino acid side chains in providing steric constraints

The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a square lattice. Here, we consider the effect of nearest-neighbor attractive interactions on the growing self-avoiding walk, and examine the effect that self-attraction has both on the statistics of trapping as well as on chain statistics through the transition between expanded and collapsed walks at the theta point. We find the trapping length increases exponentially with the nearest-neighbor contact energy, but that there is a local minimum in trapping length for weakly self-attractive walks. While it has been controversial whether growing self-avoiding walks have the same asymptotic behavior as traditional self-avoiding walks, we find that the theta point is not at the same location for growing self-avoiding walks, and that the persistence length converges much more rapidly to a smaller value., 9 pages, 8 figures + 2 in appendix

In concentrated electrolytes with asymmetric or irregular ions, such as ionic liquids and solvent-in-salt electrolytes, ion association is more complicated than simple ion-pairing. Large branched aggregates can form at significant concentrations at even moderate salt concentrations. When the extent of ion association reaches a certain threshold, a percolating ionic gel network can form spontaneously. Gelation is a phenomenon that is well known in polymer physics, but it is practically unstudied in concentrated electrolytes. However, despite this fact, the ion-pairing description is often applied to these systems for the sake of simplicity. In this work, drawing strongly from established theories in polymer physics, we develop a simple thermodynamic model of reversible ionic aggregation and gelation in concentrated electrolytes accounting for the competition between ion solvation and ion association. Our model describes, with the use of several phenomenological parameters, the populations of ionic clusters of different sizes as a function of salt concentration; it captures the onset of ionic gelation and also the post-gel partitioning of ions into the gel. We discuss the applicability of our model, as well as the implications of its predictions on thermodynamic, transport, and rheological properties.

New theoretical and experimental work suggests that 10-nm chromatin fiber is folded into tree-like domains in single cells., With the textbook view of chromatin folding based on the 30-nm fiber being challenged, it has been proposed that interphase DNA has an irregular 10-nm nucleosome polymer structure whose folding philosophy is unknown. Nevertheless, experimental advances suggest that this irregular packing is associated with many nontrivial physical properties that are puzzling from a polymer physics point of view. Here, we show that the reconciliation of these exotic properties necessitates modularizing three-dimensional genome into tree data structures on top of, and in striking contrast to, the linear topology of DNA double helix. These functional modules need to be connected and isolated by an open backbone that results in porous and heterogeneous packing in a quasi–self-similar manner, as revealed by our electron and optical imaging. Our multiscale theoretical and experimental results suggest the existence of higher-order universal folding principles for a disordered chromatin fiber to avoid entanglement and fulfill its biological functions.

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon. This process is driven by the formation of chromosome loops. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over ~50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE., How chromosomes, which are polymers with nearly billion base pairs, are packaged in the restricted nuclear volume is not well understood. Here, the authors combine polymer physics, nonequilibrium fluctuation theorem, and simulations to quantitatively predict the force-dependent velocity and step-size distribution of condensin, which facilitates the folding of chromosomes by loop extrusion.

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality as the numerical evaluation of Marko's and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests, that our analytical expressions for the finite-chain length corrections are of similar quality. As an application of our results we discuss the possibility of inferring the changing number of nicks in a double-stranded DNA molecule in single-molecule stretching experiments from the accompanying changes in the effective chain length., Comment: 21 pages, 12 figures, submitted for publication

Chromatin loop extrusion is a popular model for the formation of CTCF loops and topological domains. Recent HiC data have revealed a strong bias in favour of a particular arrangement of the CTCF binding motifs that stabilize loops, and extrusion is the only model to date which can explain this. However, the model requires a motor to generate the loops, and although cohesin is a strong candidate for the extruding factor, a suitable motor protein (or a motor activity in cohesin itself) has yet to be found. Here we explore a new hypothesis: that there is no motor, and thermal motion within the nucleus drives extrusion. Using theoretical modelling and computer simulations we ask whether such diffusive extrusion could feasibly generate loops. Our simulations uncover an interesting ratchet effect (where an osmotic pressure promotes loop growth), and suggest, by comparison to recent in vitro and in vivo measurements, that diffusive extrusion can in principle generate loops of the size observed in the data. Extra View on : C. A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi, P. R. Cook, and D. Marenduzzo "Non-equilibrium chromosome looping via molecular slip-links", Physical Review Letters 119, 138101 (2017), Comment: 7 pages, 3 figures

Microscopy and sequencing-based technologies are providing increasing insights into chromatin architecture. Nevertheless, a full comprehension of chromosome folding and its link with vital cell functions is far from accomplished at the molecular level. Recent theoretical and computational approaches are providing important support to experiments to dissect the three-dimensional structure of chromosomes and its organizational mechanisms. Here, we review, in particular, the String&Binders polymer model of chromatin that describes the textbook scenario where contacts between distal DNA sites are established by cognate binders. It has been shown to recapitulate key features of chromosome folding and to be able at predicting how phenotypes causing structural variants rewire the interactions between genes and regulators.

The constant development of sophisticated technologies is allowing to dissect three-dimensional chromatin structure at high resolution level. The tremendous amount of quantitative experimental data available today requires a conceptual framework able to make sense of them. In this perspective, polymer physics offers a key tool to interpret chromatin architecture data and to unveil the basic mechanisms shaping its structure. In the very last years, several polymer models have been proposed and have allowed to capture complex features emerging from the data. The major peculiarity distinguishing the different models is represented by the more or less complicated physical mechanism used to explain chromatin folding. Here, we review very popular models which have been recently developed and which represent brilliant examples from this interdisciplinary research field. In order to highlight the wide range of practical applications they have, we discuss the cases of the murine Pitx1 and the human EPHA4 loci, showing that polymer physics allows to effectively study chromatin structure in different cell lines and to predict the impact of pathogenic structural variants on the genome three-dimensional architecture. This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods Theoretical and Physical Chemistry > Statistical Mechanics.

Polymeric materials are ubiquitous in our daily lives, and they play a significant role in many technological applications. The general predictive framework for the behavior of soft polymeric materials can be divided into two vastly different approaches. Highly coarse-grained models capture polymers as flexible random walks, resulting in general predictions of physical behavior but lack chemical specificity. Detailed atomistic models contain molecular detail but are frequently computationally intractable for exhaustive materials discovery. In this perspective, we discuss theoretical models that successfully bridge these disparate approaches. We identify intermediate-scale physical models that are amenable to theoretical analyses while containing sufficient granular detail to capture a range of molecular-level processes. We then provide several problems in materials engineering and biological physics where multiscale physics is essential in their behavior.

An article in Physical Review Letters reports a formalism enabling the use of a D-Wave quantum annealer to sample the equilibrium ensemble of dense polymer mixtures.

Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and replicate DNA. A common aspect of these machines is that their functions are driven out of equilibrium. It is a challenge to provide a general framework for understanding the functions of biological machines, such as molecular motors, molecular chaperones, and helicases. Using these machines as prototypical examples, we describe a few general theoretical methods providing insights into their functions. Although the theories rely on coarse-graining of these complex systems they have proven useful in not only accounting for many in vitro experiments but also addressing questions such as how the trade-off between precision, energetic costs and optimal performances are balanced. However, many complexities associated with biological machines will require one to go beyond current theoretical methods. Simple point mutations in the enzyme could drastically alter functions, making the motors bi-directional or result in unexpected diseases or dramatically restrict the capacity of molecular chaperones to help proteins fold. These examples are reminders that while the search for principles of generality in biology is intellectually stimulating, one also ought to keep in mind that molecular details must be accounted for to develop a deeper understanding of processes driven by biological machines. Going beyond generic descriptions of in vitro behavior to making genuine understanding of in vivo functions will likely remain a major challenge for some time to come. The combination of careful experiments and the use of physical principles will be useful in elucidating the rules governing the workings of biological machines.

This chapter describes chromatin dynamics using stochastic modeling and polymer physics. It summarizes briefly modeling and analysis approaches that goes beyond classical Brownian motion and reviews how the cell imposes biological constraints on molecular motion. The chapter shows how single-particle trajectory data can be used to recover the chromatin organization and the ensemble of interactions it experiences. Trajectories of an individual particle inside a fluid, on the chromatin or a membrane, are usually described and analyzed in the physical literature using the Smoluchowski’s limit of the Langevin equation. To extract biophysical parameters from Single-Particle Trajectory of a chromatin locus, a physical model for the locus motion is needed. The dynamics of the locus reflects the local chromatin organization and the ensemble of interactions it experiences. The relation between chromatin structure/organization can be described using the dynamics of a tagged monomer when the chromatin is described as a static fractal globule.

We study the hydrodynamic transport of knotted ring polymers through modulated channels, establishing that the transport velocity is strongly dependent on the ring topology for Peclet numbers smaller than unity. As soon as convection dominates, transport properties become insensitive to the presence and type of knots. We identify two distinct modes of transport, corresponding to the motion being led by the knotted or unknotted portions of the ring, most surprisingly without impact on separation efficiency. The modes can be selected by the channel geometry, and this could be harnessed to design nanofluidic devices for the continuous topological sorting of entangled biopolymers.

A key assumption of polymer physics is that the random chain polymers extend in flow. Recent experimental evidence has shown that polymer chains compress in Couette flow in a manner counter to expectation. Here, scaling arguments and experimental evidence from the literature are used to determine the relationship between the viscosity, η, and chain radius of gyration, RG. The viscosity-radius of gyration relationship is found to be $${\boldsymbol{\eta }}{\boldsymbol{ \sim }}{{\boldsymbol{R}}}_{{\boldsymbol{G}}}^{{\boldsymbol{m}}{\boldsymbol{(}}\dot{{\boldsymbol{\gamma }}}{\boldsymbol{)}}}$$ η ~ R G m ( γ ˙ ) where m($$\dot{{\boldsymbol{\gamma }}}$$ γ ˙ ) is the power law exponent of the viscosity-temperature relationship that depends on the specific polymer-solvent system and the shear rate, $$\dot{{\boldsymbol{\gamma }}}$$ γ ˙ . The viscosity is shown to be a power law function of the radius, and to decrease with decreasing radius under conditions where the chains are ideal random walks in concentrated solution. Furthermore, this relationship is consistent with both the widely observed viscosity-temperature and viscosity-shear rate behavior observed in polymer rheology. The assumption of extension is not consistent with these observations as it would require that the chains increase in size with increasing temperature. Shear thinning is thus a result of a decreasing radius with increasing shear rate as $${{\boldsymbol{R}}}_{{\boldsymbol{G}}} \sim {\dot{{\boldsymbol{\gamma }}}}^{-{\boldsymbol{n}}{\boldsymbol{/}}{\boldsymbol{m}}{\boldsymbol{(}}\dot{{\boldsymbol{\gamma }}}{\boldsymbol{)}}}$$ R G ~ γ ˙ − n / m ( γ ˙ ) where n is the power law exponent. Furthermore, the thermal expansion coefficients determine the variation in the power law exponents that are measured for different polymer systems. Typical values of n enable the measured reduction in coils size behavior to be fitted. Furthermore, the notion that polymer chains extend to reduce the viscosity implies that an increasing chain size results in a reduced viscosity is addressed. This assumption would require that the viscosity increases with reducing coil radius which is simply unphysical.

I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that strong localization confines quantum transport along paths which are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent $\zeta$ characterizing the transverse fluctuations of these paths and find that its value $\zeta=2/3$ is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder, and more spin-glass-like behavior at strong disorder., Comment: 6 + 5 (supplemental material) pages, 4 + 6 figures. Corresponds to the published version

Summary Conventional EOR polymers are acrylamide-based copolymers. Their viscosity in aqueous solution depends on various physicochemical parameters such as: monomer composition, concentration, average molecular weight, polydispersity, salinity level and ionic composition, temperature… Moreover, solutions are non-Newtonian, they exhibit a Low shear Newtonian plateau viscosity at low shear rate followed by a shear thinning region at higher shear rate. In the absence of predictive model, for any new polymer grade or lot, any new or slightly varying field conditions, it is necessary to perform a whole set of viscosity measurements at varying concentrations which is tedious, time consuming and not valuable. Flow curves (Viscosity vs. Shear rate) were measured on a great number of polymers solutions in various physicochemical conditions (variation of the polymer microstructure, monomer composition, molecular weight, brine salinity and temperature). The flow curves in both dilute, semidilute non-entangled and semidilute entangled regimes were modelled by only two adjustable parameters: the intrinsic viscosity [η] and the relaxation time in the diluted regime λd. The low shear plateau viscosity η0 (more specifically, the specific viscosity ηspe) and the shear thinning index n obey mastercurves which are solely function of the overlap parameter C[η]. The relaxation time λ depends on C[η] and the relaxation time in the diluted regime λd. All these results are consistent with predictions for a neutral polymer in good solvent. By using these mastercurves, intrinsic viscosity of any polymer/brine system can be easily obtained at various temperatures from a single measurement in the semi-dilute regime in which viscosity is higher than water, and classic rheometers are very sensitive. The whole flow curve (η=f(γ)) can be predicted at any concentration, temperature and molecular weight. For any unknown polymer/brine system, the determination of λd enables to determine the viscosimetric average molecular weight M of the polymer. Finally, by using the additive property of the intrinsic viscosity of binary solutions, a method is proposed to evaluate molecular weight of field samples. Polymer physics is today considered as well described and well known. However, the beauty and the usefulness of this physics have been partly ignored by the EOR community up to now. This study gives a methodology to predict the viscosifying behavior and the molecular weight of any acrylamide based copolymer/brine system. By attributing molecular weight rather than a viscosity value, on-site and lab QA/QC will be greatly improved.

The main focus of this thesis lies on confining and/or pulling on two important biopolymers, i.e. cellulose nanofibrils (CNF) and amyloid fibrils. The results of these studies have implications for understanding in vivo biopolymer systems, improving the engineering of novel green materials, and furthering concepts in polymer physics. The first chapter introduces the reader to the motivations behind this work, as well as provides background information on CNF and amyloid fibrils and on the major polymer physics theories needed to devise experiments and simulations. In the second chapter, an experiment to study CNF under weak rectangular confinement is displayed. CNF were adsorbed into slits, previously obtained by thermal scanning probe nanolithography. Atomic force microscopy (AFM) coupled with single-molecule statistics allowed me to observe the alignment and self-folding of CNF under confinement. Simulations confirmed that the slits were not simply selecting a preexisting fibril population, but that the CNF were folding upon themselves as a result of the confinement. In addition, a kink preferential bending direction and an inverse correlation between kink angle and number of kinks, i.e. the fewer kinks the higher the angle, were noted. The combination of these observations provides further evidence that the kinks are a result of mechanical breaking. In the third chapter, an experiment to study subtle interplay between concurrent pulling and confinement of amyloid fibrils is explained. This was achieved by pulling the fibrils into a microcapillary device. AFM allowed a detailed single molecule statistics of the system. These results indicated that the extension of the fibrils was force- or confinement dominated at short and large length scales, respectively. This was in contrast to the order of the system, which was confinement-dominated at all length scales. Simulations both confirmed this result and brought to light the existence of other regimes. Therefore displaying the potential to tailor the system through the fine-tuning of the contribution of either effect. This data may in addition help understand in vivo amyloid phenomena in blood vessels, as well as other physiological occurrences involving the stretching and confining of semi-flexible biopolymers. The fourth chapter focuses on a technique to deposit gradients of amyloid fibrils from the liquid-liquid interface while under simultaneous compression, thus imposing macroscopic confinement. Orientation was induced perpendicularly to the compression, from isotropic to nematic. Reproducible transitions, from a monolayer to a bilayer and from a bilayer to a multilayer, were observed. This method brings forth an approach to overcome the engineering challenge associated with manipulating sticky amyloid fibrils. It further shows great potential for investigating amyloid aggregation at interfaces, which is of great relevance for understanding the propagation of certain amyloid fibril-related diseases. In conclusion, confinement successfully produced alignment, independently of the polymer and of the length scale. The effects of confinement can be modulated by adding a pulling force to the system. These experiments may not only be valid for CNF and amyloids, but show great potential for investigating divers biopolymers.

Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton, an ensemble of 'extra-chromatin' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell, their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue, in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-versus-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales, we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems, namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.

The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grun (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. The KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to be used in micromechanical constitutive models.

Intrinsically disordered proteins (IDPs) are often modeled using ideas from polymer physics that suggest they smoothly explore all corners of configuration space. Experimental verification of this random, dynamic behavior is difficult as random fluctuations of IDPs cannot be synchronized across an ensemble. Single molecule fluorescence (or Förster) resonance energy transfer (smFRET) is one of the few approaches that are sensitive to transient populations of sub-states within molecular ensembles. In some implementations, smFRET has sufficient time resolution to resolve transitions in IDP behaviors. Here we present experimental issues to consider when applying smFRET to study IDP configuration. We illustrate the power of applying smFRET to IDPs by discussing two cases in the literature of protein systems for which smFRET has successfully reported phosphorylation-induced modification (but not elimination) of the disordered properties that have been connected to impacts on the related biological function. The examples we discuss, PAGE4 and a disordered segment of the GluN2B subunit of the NMDA receptor, illustrate the great potential of smFRET to inform how IDP function can be regulated by controlling the detailed ensemble of disordered states within biological networks.

Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers ( ~ 5 ? n m ) govern the mechanics of the entire network ( ~ 10 ? µ m ). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples. We model crosslinked biopolymer networks with Brownian dynamics beam finite elements.Decoupling chemical and mechanical resolution, we boost computational efficiency.Our approach allows for network simulations reaching the scale of eukaryotic cells.We account for polar and chiral polymers and filament-linker reaction kinetics.We simulate the evolution, rheology, and effects of chirality of large networks.