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Single-molecule force-extension experiments have allowed quantitative measurements of the mechanical responses of biomolecules to applied forces explaining their roles in key biological functions. Electrophoretic stretching of charged polymers such as DNA in uniform electric fields is one such example, currently, used for sequencing purposes. Field-extension statistics of charged polymers differ from laser optical tweezer setups due to a non-uniform tension along the backbone of the chain, the effects of which remain poorly understood. In this paper, we modify an existing analytically tractable mean-field (MF) approach to account for the heterogeneity in tension for electric fields. Naively using this model for stretching of charged polymers such as DNA under electric fields results in local overstretching of the chain and gives inaccurate field-extension statistics. We improve this approach and account for the inhomogeneity in the tension by subdividing the chain into smaller segments while imposing the inextensibility of the chain. We find that the subdivided MF model shows better agreement with the simulations for the force-extension plots. We also show that using an isotropic mean-field model overestimates the longitudinal fluctuations both for tension forces as well as for fields. We correct the quantitative predictions for the fluctuations in the mean extension by numerically differentiating the field-extension plots. We also find that the subdivided MF model can accurately predict the statistics of experimentally relevant quantities, such as transverse fluctuations, due to the analytical tractability of the model. These field-extension predictions may be further used to introduce confinement effects in the subdivided MF model and develop a comprehensive understanding of sequencing technologies.

We compute the free energy of confinement ${\cal{F}}$ for a wormlike chain (WLC), with persistence length $l_p$, that is confined to the surface of a cylinder of radius $R$ under an external tension $f$ using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of $l_p$, the Odijk deflection length ($l_d=(R^2l_p)^{1/3}$), and the Pincus length ($l_f = {k_BT}/{f}$, with $k_BT$ being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at $f=0$, with ${\cal{F}}\sim Ll_p^{-1/3}R^{-2/3}$. For moderate values of $f$, the Odijk scaling is discernible only when ${l_p}\gg R$ for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes., Comment: 17 pages, 4 figures

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. As has been understood for centuries, slender rods can only be compressed so far until they buckle, adopting an intrinsically bent state that may be unable to bear a compressive load. In the low-temperature limit and for a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression, and we determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates the transition. We find the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble that the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show the theory is highly sensitive to fluctuations in length, and that the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.

Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper, we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight on the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than two promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosin-like motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape., Comment: 10 figures

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single molecule experimental techniques and give insight into biologically relevant processes {\em{in vivo}}. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit, and leverage the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance., Comment: This resubmission corrects some incorrect statistics in the simulations in an earlier version, includes numerous new figures and text to clarify the paper, and removed some aspects of inference of transverse statistics from longitudinal observations. The mathematics and analysis in the paper is identical to the first version, but quantitative aspects of the paper have changed

Patent data represent a significant source of information on innovation and the evolution of technology through networks of citations, co-invention and co-assignment of new patents. A major obstacle to extracting useful information from this data is the problem of name disambiguation: linking alternate spellings of individuals or institutions to a single identifier to uniquely determine the parties involved in the creation of a technology. In this paper, we describe a new algorithm that uses high-resolution geolocation to disambiguate both inventor and assignees on more than 3.6 million patents found in the European Patent Office (EPO), under the Patent Cooperation treaty (PCT), and in the US Patent and Trademark Office (USPTO). We show that our algorithm has both high precision and recall in comparison to a manual disambiguation of EPO assignee names in Boston and Paris, and show it performs well for a benchmark of USPTO inventor names that can be linked to a high-resolution address (but poorly for inventors that never provided a high quality address). The most significant benefit of this work is the high quality assignee disambiguation with worldwide coverage coupled with an inventor disambiguation that is competitive with other state of the art approaches. To our knowledge this is the broadest and most accurate simultaneous disambiguation and cross-linking of the inventor and assignee names for a significant fraction of patents in these three major patent collections., Comment: 25 pages, 3 figures

International trade has been increasingly organized in the form of global value chains (GVCs) where different stages of production are located in different countries. This recent phenomenon has substantial consequences for both trade policy design at the national or regional level and business decision making at the firm level. In this paper, we provide a new method for comparing GVCs across countries and over time. First, we use the World Input-Output Database (WIOD) to construct both the upstream and downstream global value networks, where the nodes are individual sectors in different countries and the links are the value-added contribution relationships. Second, we introduce a network-based measure of node similarity to compare the GVCs between any pair of countries for each sector and each year available in the WIOD. Our network-based similarity is a better measure for node comparison than the existing ones because it takes into account all the direct and indirect relationships between country-sector pairs, is applicable to both directed and weighted networks with self-loops, and takes into account externally defined node attributes. As a result, our measure of similarity reveals the most intensive interactions among the GVCs across countries and over time. From 1995 to 2011, the average similarity between sectors and countries have clear increasing trends, which are temporarily interrupted by the recent economic crisis. This measure of the similarity of GVCs provides quantitative answers to important questions about dependency, sustainability, risk, and competition in the global production system., Comment: 30 pages, 14 figures

In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic.

We present a new network model accounting for multidimensional assortativity. Each node is characterized by a number of features and the probability of a link between two nodes depends on common features. We do not fix a priori the total number of possible features. The bipartite network of the nodes and the features evolves according to a stochastic dynamics that depends on three parameters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. Our model also takes into account a mechanism of triadic closure. We provide theoretical results and statistical estimators for the parameters of the model. We validate our approach by means of simulations and an empirical analysis of a network of scientific collaborations., Comment: 32 pages, 8 figures, 4 tables, submitted. Exposition of the work improved. Title upadated to : Modeling Networks with a Growing Feature-Structure

Although species longevity is subject to a diverse range of selective forces, the mortality curves of a wide variety of organisms are rather similar. We argue that aging and its universal characteristics may have evolved by means of a gradual increase in the systemic interdependence between a large collection of biochemical or mechanical components. Modeling the organism as a dependency network which we create using a constructive evolutionary process, we age it by allowing nodes to be broken or repaired according to a probabilistic algorithm that accounts for random failures/repairs and dependencies. Our simulations show that the network slowly accumulates damage and then catastrophically collapses. We use our simulations to fit experimental data for the time dependent mortality rates of a variety of multicellular organisms and even complex machines such as automobiles. Our study suggests that aging is an emergent finite-size effect in networks with dynamical dependencies and that the qualitative and quantitative features of aging are not sensitively dependent on the details of system structure., Comment: 11 pages, 10 figures, Preprint

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (Pfold = 0.5). Using results for the forced-unfolding of a RNA hairpin, an exactly soluble model and an analytic theory, we show that Pfold is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles., Comment: 6 pages, 4 figures, Phys. Rev. Lett. (in press)

We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline., Comment: 4 pages, 3 figures, 1 table

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense., Comment: 48 pages, 9 figures

Single molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench, using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, $\tau_F$, depends asymmetrically on $\delta f_S = f_S - f_m$ and $\delta f_Q = f_m - f_Q$ where $f_S$ ($f_Q$) is the stretch (quench) force, and $f_m$ is the transition mid-force of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, $R(t)$, occurs in three stages: a rapid initial decrease in the extension is followed by a plateau, and finally an abrupt reduction in $R(t)$ that occurs as the native state is approached. The duration of the plateau increases as $\lambda =\tau_Q/\tau_F$ decreases (where $\tau_Q$ is the time in which the force is reduced from $f_S$ to $f_Q$). Variations in the mechanisms of force quench relaxation as $\lambda$ is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in $R(t)$. The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding., Comment: 31 pages 11 figures

We develop an analytical method for studying the properties of a non-interacting Wormlike Chain (WLC) in confined geometries. The mean field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as $f^{-1}$ at large forces, in contrast to the unconfined chain that approaches the contour length as $f^{-1/2}$. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the MF approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids., Comment: 29 pages, 8 figures

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated using single molecule force clamp experiments by attaching semiflexible polymers to the ends of hairpins have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free energy profile $F^o_{eq}(z_m)$, where $z_m$ is the molecular extension of the hairpin. Accurate measurements of $F^o_{eq}(z_m)$ requires stiff polymers with small $L/l_p$, where $L$ is the contour length of the handle, and $l_p$ is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made using flexible handles. Nevertheless, we show that the equilibrium free energy profile $F^o_{eq}(z_m)$ at an external tension $f_m$, the force ($f$) at which the folded and unfolded states are equally populated, in conjunction with Kramers' theory, can provide accurate estimates of the force-dependent hopping rates in the absence of handles at arbitrary values of $f$. Our theoretical framework shows that $z_m$ is a good reaction coordinate for nucleic acid hairpins under tension., Comment: 26 pages, 9 figures

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $\tau_c\sim \tau_0 N^2$ (where $\tau_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $\tau_c\sim N^{\alpha_\tau}$, where $1.5<{\alpha_\tau}\le 2$ in the range $7

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $\sim f$ for small $f$, and $\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for $\la Z\ra$ as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments., Comment: 24 pages, 7 figures