Emergence of selectivity and specificity in a coarse-grained model of the nuclear pore complex with sequence-agnostic FG-Nups.

The role of hydrophobicity of phenylalanine-glycine nucleoporins (FG-Nups) in determining the transport of receptor-bound cargo across the nuclear pore complex (NPC) is investigated using Langevin dynamics simulations. A coarse-grained, minimal model of the NPC, comprising a cylindrical pore and hydrophobic-hydrophilic random copolymers for FG-Nups was employed. Karyopherin-bound receptor-cargo complexes (Kaps) were modeled as rigid, coarse-grained spheres without (inert) and with (patchy) FG-binding hydrophobic domains. With a sequence-agnostic description of FG-Nups and the absence of any anisotropies associated with either NPC or cargo, the model described tracer transport only as a function of FG-Nup hydrophobicity, f. The simulations showed the emergence of two important features of cargo transport, namely, NPC selectivity and specificity. NPC selectivity to patchy tracers emerged due to hydrophobic Kap-FG interactions and despite the sequence-agnostic description of FG-Nups. Furthermore, NPC selectivity was observed only in a specific range of FG-hydrophobic fraction, 0.05 ≤ f ≤ 0.20, resulting in specificity of NPC transport with respect to f. Significantly, this range corresponded to the number fraction of FG-repeats observed in both S. cerevisiae and H. sapiens NPCs. This established the central role of the FG-hydrophobic fraction in determining NPC transport, and provided a biophysical basis for conservation of the FG-Nup hydrophobic fraction across evolutionarily distant NPCs. Specificity in NPC transport emerged from the formation of a hydrogel-like network inside the pore with a characteristic mesh size dependent on f. This network rejected cargo for f > 0.2 based on size exclusion, which resulted in enhanced translocation probability for 0.05 ≤ f ≤ 0.20. Extended brush configurations outside the pore resulted in entropic repulsion and exclusion of inert cargo in this range. Thus, our minimal NPC model exhibited a hybrid cargo translocation mechanism, with aspects of both virtual gate and selective-phase models, in this range of FG-hydrophobic fraction.

Thermodynamics predicts a stable microdroplet phase in polymer-gel mixtures undergoing elastic phase separation.

We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopolymers undergoing liquid-liquid phase separation.

A Lamin-Associated Chromatin Model for Chromosome Organization.

We propose a simple model for chromatin organization based on the interaction of the chromatin fibers with lamin proteins along the nuclear membrane. Lamin proteins are known to be a major factor that influences chromatin organization and hence gene expression in the cells. We provide a quantitative understanding of lamin-associated chromatin organization in a crowded macromolecular environment by systematically varying the heteropolymer segment distribution and the strength of the lamin-chromatin attractive interaction. Our minimal polymer model reproduces the formation of lamin-associated-domains and provides an in silico tool for quantifying domain length distributions for different distributions of heteropolymer segments. We show that a Gaussian distribution of heteropolymer segments, coupled with strong lamin-chromatin interactions, can qualitatively reproduce observed length distributions of lamin-associated-domains. Further, lamin-mediated interaction can enhance the formation of chromosome territories as well as the organization of chromatin into tightly packed heterochromatin and the loosely packed gene-rich euchromatin regions.

A two-step biopolymer nucleation model shows a nonequilibrium critical point.

Biopolymer self-assembly pathways are complicated by the ability of their monomeric subunits to adopt different conformational states. This means nucleation often involves a two-step mechanism where the monomers first condense to form a metastable intermediate, which then converts to a stable polymer by conformational rearrangement of constituent monomers. Nucleation intermediates play a causative role in amyloid diseases such as Alzheimer's and Parkinson's. While existing mathematical models neglect the conversion dynamics, experiments show that conversion events frequently occur on comparable timescales to the condensation of intermediates and growth of mature polymers and thus cannot be ignored. We present a model that explicitly accounts for simultaneous assembly and conversion. To describe conversion, we propose an experimentally motivated initiation-propagation mechanism in which the stable phase arises locally within the intermediate and then spreads by nearest-neighbor interactions, in a manner analogous to one-dimensional Glauber dynamics. Our analysis shows that the competing timescales of assembly and conversion result in a nonequilibrium critical point, separating a regime where intermediates are kinetically unstable from one where conformationally mixed intermediates accumulate. This strongly affects the accumulation rate of the stable biopolymer phase. Our model is uniquely able to explain experimental phenomena such as the formation of mixed intermediates and abrupt changes in the scaling exponent γ, which relates the total monomer concentration to the accumulation rate of the stable phase. This provides a first step toward a general model of two-step biopolymer nucleation, which can quantitatively predict the concentration and composition of biologically crucial intermediates.

Ribbon curling via stress relaxation in thin polymer films.

The procedure of curling a ribbon by running it over a sharp blade is commonly used when wrapping presents. Despite its ubiquity, a quantitative explanation of this everyday phenomenon is still lacking. We address this using experiment and theory, examining the dependence of ribbon curvature on blade curvature, the longitudinal load imposed on the ribbon, and the speed of pulling. Experiments in which a ribbon is drawn steadily over a blade under a fixed load show that the ribbon curvature is generated over a restricted range of loads, the curvature/load relationship can be nonmonotonic, and faster pulling (under a constant imposed load) results in less tightly curled ribbons. We develop a theoretical model that captures these features, building on the concept that the ribbon under the imposed deformation undergoes differential plastic stretching across its thickness, resulting in a permanently curved shape. The model identifies factors that optimize curling and clarifies the physical mechanisms underlying the ribbon's nonlinear response to an apparently simple deformation.

Dynamic Morphologies and Stability of Droplet Interface Bilayers.

We develop a theoretical framework for understanding dynamic morphologies and stability of droplet interface bilayers (DIBs), accounting for lipid kinetics in the monolayers and bilayer, and droplet evaporation due to imbalance between osmotic and Laplace pressures. Our theory quantitatively describes distinct pathways observed in experiments when DIBs become unstable. We find that when the timescale for lipid desorption is slow compared to droplet evaporation, the lipid bilayer will grow and the droplets approach a hemispherical shape. In contrast, when lipid desorption is fast, the bilayer area will shrink and the droplets eventually detach. Our model also suggests there is a critical size below which DIBs can become unstable, which may explain experimental difficulties in miniaturizing the DIB platform.

Generating a Metal-responsive Transcriptional Regulator to Test What Confers Metal Sensing in Cells.

FrmR from Salmonella enterica serovar typhimurium (a CsoR/RcnR-like transcriptional de-repressor) is shown to repress the frmRA operator-promoter, and repression is alleviated by formaldehyde but not manganese, iron, cobalt, nickel, copper, or Zn(II) within cells. In contrast, repression by a mutant FrmRE64H (which gains an RcnR metal ligand) is alleviated by cobalt and Zn(II). Unexpectedly, FrmR was found to already bind Co(II), Zn(II), and Cu(I), and moreover metals, as well as formaldehyde, trigger an allosteric response that weakens DNA affinity. However, the sensory metal sites of the cells' endogenous metal sensors (RcnR, ZntR, Zur, and CueR) are all tighter than FrmR for their cognate metals. Furthermore, the endogenous metal sensors are shown to out-compete FrmR. The metal-sensing FrmRE64H mutant has tighter metal affinities than FrmR by approximately 1 order of magnitude. Gain of cobalt sensing by FrmRE64H remains enigmatic because the cobalt affinity of FrmRE64H is substantially weaker than that of the endogenous cobalt sensor. Cobalt sensing requires glutathione, which may assist cobalt access, conferring a kinetic advantage. For Zn(II), the metal affinity of FrmRE64H approaches the metal affinities of cognate Zn(II) sensors. Counter-intuitively, the allosteric coupling free energy for Zn(II) is smaller in metal-sensing FrmRE64H compared with nonsensing FrmR. By determining the copies of FrmR and FrmRE64H tetramers per cell, then estimating promoter occupancy as a function of intracellular Zn(II) concentration, we show how a modest tightening of Zn(II) affinity, plus weakened DNA affinity of the apoprotein, conspires to make the relative properties of FrmRE64H (compared with ZntR and Zur) sufficient to sense Zn(II) inside cells.

Elasticity Dominated Surface Segregation of Small Molecules in Polymer Mixtures.

We study the phenomenon of migration of the small molecular weight component of a binary polymer mixture to the free surface using mean field and self-consistent field theories. By proposing a free energy functional that incorporates polymer-matrix elasticity explicitly, we compute the migrant volume fraction and show that it decreases significantly as the sample rigidity is increased. A wetting transition, observed for high values of the miscibility parameter can be prevented by increasing the matrix rigidity. Estimated values of the bulk modulus suggest that the effect should be observable experimentally for rubberlike materials. This provides a simple way of controlling surface migration in polymer mixtures and can play an important role in industrial formulations, where surface migration often leads to decreased product functionality.

Theoretical analysis for the optical deformation of emulsion droplets.

We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry. Experimentally, two-dimensional droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. Our model elucidates and quantifies this difference for the first time. We also provide a dimensionless number that indicates the shape transformation (ellipsoidal to dumbbell) at a value ≈ 1.0, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.

Wetting Behavior of a Three-Phase System in Contact with a Surface.

We extend the Cahn-Landau-de Gennes mean field theory of wetting in binary mixtures to understand the wetting thermodynamics of a three phase system (e.g., polymer dispersed liquid crystals or polymer-colloid mixtures) that is in contact with an external surface, which prefers one of the phases. Using a model free-energy, which has three minima in its landscape, we show that as the central minimum becomes more stable compared to the remaining ones, the bulk phase diagram encounters a triple point and then bifurcates and we observe a novel non-monotonic dependence of the surface tension as a function of the stability of the central minimum. We show that this non-monotonicity in surface tension is associated with a complete to partial wetting transition. We obtain the complete wetting phase behavior as a function of phase stability and the surface interaction parameters when the system is close to the bulk triple point. The model free-energy that we use is qualitatively similar to that of a renormalized free energy, which arises in the context of polymer-liquid crystal mixtures. Finally, we study the thermodynamics of wetting for an explicit polymer-liquid crystal mixture and show that its thermodynamics is similar to that of our model free-energy.

Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures.

Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer ( O P ) and oligomer-gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel-oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz-Slyozov-Wagner (LSW) law ℓ ( τ ) ∼ τ 1 / 3 . Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.

Complex dynamics of a sheared nematic fluid.

Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, e.g. 'rheochaos' in solutions of wormlike micelles and 'elastic turbulence' in polymer solutions. Since both phenomena involve anisotropic objects, their contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of spatiotemporal chaos and transient shear banding. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to elastic turbulence phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.

Shear unzipping of DNA.

We study theoretically the mechanical failure of a simple model of double-stranded DNA under an applied shear. Starting from a more microscopic Hamiltonian that describes a sheared DNA, we arrive at a nonlinear generalization of a ladder model of shear unzipping proposed earlier by deGennes [de Gennes, P. G. C. R. Acad. Sci., Ser. IV: Phys., Astrophys. 2001, 1505]. Using this model and a combination of analytical and numerical methods, we study the DNA "unzipping" transition when the shearing force exceeds a critical threshold at zero temperature. We also explore the effects of sequence heterogeneity and finite temperature and discuss possible applications to determine the strength of colloidal nanoparticle assemblies functionalized by DNA.

Orientation-dependent interactions of DNA with an alpha-hemolysin channel.

We present experimental and theoretical results on the voltage-dependent escape dynamics of DNA hairpins of different orientations threaded into an alpha -hemolysin channel. Using a coarse-grained formulation, we map the motion of the polymer in the pore to that of a biased single-particle random walk along the translocation coordinate. By fitting the escape probability distributions obtained from theory to experimental data, we extract the voltage-dependent diffusion constants and bias-induced velocities. Using our two-parameter theory, we obtain excellent agreement with experimentally measured escape time distributions. Further, we find that the ratio of mean escape times for hairpins of different orientations is strongly voltage dependent, with the ratio of 3' - to 5' -threaded DNA decreasing from approximately 1.7 to approximately 1 with increasing assisting voltages V(a) . We also find that our model describes 5' -threaded DNA escape extremely well, while providing inadequate fits for 3' escape. Finally, we find that the escape times for both orientations are equal for high assisting voltages, suggesting that the interactions of DNA with the alpha -hemolysin channel are both orientation and voltage dependent.

Reprogramming, oscillations and transdifferentiation in epigenetic landscapes.

Waddington's epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

Elasticity of smectic liquid crystals with in-plane orientational order and dispiration asymmetry.

The Nelson-Peliti formulation of the elasticity theory of isolated fluid membranes with orientational order emphasizes the interplay between geometry, topology, and thermal fluctuations. Fluid layers of lamellar liquid crystals such as smectic-C, hexatic smectics, and smectic-C^{*} are endowed with in-plane orientational order. We extend the Nelson-Peliti formulation so as to bring these smectics within its ambit. Using the elasticity theory of smectics-C^{*}, we show that positive and negative dispirations (topological defects in Smectic-C^{*} liquid crystals) with strengths of equal magnitude have disparate energies-a result that is amenable to experimental tests.

Equilibrium of fluid membranes endowed with orientational order.

Minimization of the low-temperature elastic free-energy functional of orientationlly ordered membranes involves independent variation of the membrane-shape, while keeping the orientational order on it (its texture) fixed. We propose an operational, coordinate-independent method for implementing such a variation. Using the Nelson-Peliti formulation of elasticity that emphasizes the interplay between geometry, topology, and thermal fluctuations of orientationally ordered membranes, we minimize the elastic free energy to obtain equations governing their equilibrium shape, together with associated free boundary conditions. Our results are essential for understanding and predicting equilibrium shapes as well as textures of membranes and vesicles; particularly under conditions in which shape deformations are large.

Nonlinear elasticity of an alpha-helical polypeptide: Monte Carlo studies.

We report on Monte Carlo studies of the elastic properties of the helix-coil wormlike chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising-like) variable that controls the local chain bending modulus. We characterize the nonlinear elastic properties of these molecules including their response to applied tensile forces and bending torques both individually and in combination. We find a pronounced effect of applied torque on the extensional compliance of the molecule and a similar effect of tension on the bending compliance. Finally we speculate that the strongly nonlinear response of alpha-helical polypeptides to combinations of torque and force plays a role in allosteric transitions in proteins.

Interplay of instabilities in mounded surface growth.

We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a nonequilibrium phase transition between two mounded states, one of which exhibits slope selection and the other does not. The coarsening behavior of the mounds in these two phases is studied in detail. In the absence of noise, the steady-state configuration depends crucially on which of the two instabilities dominates the early time behavior.

Nonlinear elasticity of an alpha -helical polypeptide.

We study a minimal extension of the wormlike chain model to describe polypeptides having alpha-helical secondary structure. In this model the presence or absence of secondary structure enters as a scalar variable that controls the local chain bending modulus. Using this model we compute the extensional compliance of an alpha-helix under tensile stress, the bending compliance of the molecule under externally imposed torques, and the nonlinear interaction of such torques and forces on the molecule. We find that, due to coupling of the "internal" secondary structure variables to the conformational degrees of freedom of the polymer, the molecule has a highly nonlinear response to applied stress and force couples. In particular we demonstrate a sharp lengthening transition under applied force and a buckling transition under applied torque. Finally, we speculate that the inherent bistability of the molecule may underlie protein conformational change in vivo.