Browsing by Author "Dutta, Sandipan"

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Adsorption of highly charged Gaussian polyelectrolytes onto oppositely charged surfaces
(AIP, 2016-03) Dutta, Sandipan
In many biological processes highly charged biopolymers are adsorbed onto oppositely charged surfaces of macroions and membranes. They form strongly correlated structures close to the surface which cannot be explained by the conventional Poisson-Boltzmann theory. In this work strong coupling theory is used to study the adsorption of highly charged Gaussian polyelectrolytes. Two cases of adsorptions are considered, when the Gaussian polyelectrolytes are confined (a) by one charged wall, and (b) between two charged walls. The effects of salt and the geometry of the polymers on their adsorption-depletion transitions in the strong coupling regime are discussed.
Bundle formation in parallel aligned polymers with competing interactions
(IOP, 2016) Dutta, Sandipan
Aggregation of like-charged polymers is widely observed in biological- and soft-matter systems. In many systems, bundles are formed when a short-range attraction of diverse physical origin like charge bridging, hydrogen bonding or hydrophobic interaction, overcomes the longer-range charge repulsion. In this letter, we present a general mechanism of bundle formation in these systems as the breaking of the translational invariance in parallel aligned polymers with competing interactions of this type. We derive a criterion for finite-sized bundle formation as well as for macroscopic phase separation
Classical Representation of a Quantum System at Equilibrium
(Wiley, 2012-01) Dutta, Sandipan
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved
Classical representation of a quantum system at equilibrium: Applications
(APS, 2013-03) Dutta, Sandipan
In the preceding paper, the structure and thermodynamics of a given quantum system was represented by a corresponding classical system having an effective temperature, local chemical potential, and pair potential. Here, that formal correspondence is implemented approximately for applications to two quantum systems. The first is the electron gas (jellium) over a range of temperatures and densities. The second is an investigation of quantum effects on shell structure for charges confined by a harmonic potential.
Classical representation of a quantum system at equilibrium: Theory
(APS, 2013-03) Dutta, Sandipan
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong-coupling theories and molecular dynamics simulation to quantum systems at strong coupling. The correspondence is made at the level of the grand-canonical ensembles for the two systems. An effective temperature, local chemical potential, and pair potential are introduced to define the corresponding classical system. These are determined formally by requiring the equivalence of the grand potentials and their functional derivatives. Practical inversions of these formal definitions are indicated via the integral equations for densities and pair correlation functions of classical liquid theory. Application to the ideal Fermi gas is demonstrated, and the weak-coupling form for the pair potential is given. In a companion paper two applications are described: the thermodynamics and structure of uniform jellium over a range of temperatures and densities and the shell structure of harmonically bound charges.
Colossal Power Extraction from Active Cyclic Brownian Information Engines
(ACS, 2022-07) Dutta, Sandipan
Brownian information engines can extract work from thermal fluctuations by utilizing information. To date, the studies on Brownian information engines consider the system in a thermal bath; however, many processes in nature occur in a nonequilibrium setting, such as the suspensions of self-propelled microorganisms or cellular environments called an active bath. Here, we introduce an archetypal model for a Maxwell-demon type cyclic Brownian information engine operating in a Gaussian correlated active bath capable of extracting more work than its thermal counterpart. We obtain a general integral fluctuation theorem for the active engine that includes additional mutual information gained from the active bath with a unique effective temperature. This effective description modifies the generalized second law and provides a new upper bound for the extracted work. Unlike the passive information engine operating in a thermal bath, the active information engine extracts colossal power that peaks at the finite cycle period. Our study provides fundamental insights into the design and functioning of synthetic and biological submicrometer motors in active baths under measurement and feedback control.
Complexation and coacervation of like-charged polyelectrolytes inspired by mussels
(PNAS, 2016-02) Dutta, Sandipan
It is well known that polyelectrolyte complexes and coacervates can form on mixing oppositely charged polyelectrolytes in aqueous solutions, due to mainly electrostatic attraction between the oppositely charged polymers. Here, we report the first (to the best of our knowledge) complexation and coacervation of two positively charged polyelectrolytes, which provides a new paradigm for engineering strong, self-healing interactions between polyelectrolytes underwater and a new marine mussel-inspired underwater adhesion mechanism. Unlike the conventional complex coacervate, the like-charged coacervate is aggregated by strong short-range cation–π interactions by overcoming repulsive electrostatic interactions. The resultant phase of the like-charged coacervate comprises a thin and fragile polyelectrolyte framework and round and regular pores, implying a strong electrostatic correlation among the polyelectrolyte frameworks. The like-charged coacervate possesses a very low interfacial tension, which enables this highly positively charged coacervate to be applied to capture, carry, or encapsulate anionic biomolecules and particles with a broad range of applications.
Efficiency fluctuations and noise induced refrigerator-to-heater transition in information engines
(Springer Nature, 2020-02) Dutta, Sandipan
Understanding noisy information engines is a fundamental problem of non-equilibrium physics, particularly in biomolecular systems agitated by thermal and active fluctuations in the cell. By the generalized second law of thermodynamics, the efficiency of these engines is bounded by the mutual information passing through their noisy feedback loop. Yet, direct measurement of the interplay between mutual information and energy has so far been elusive. To allow such examination, we explore here the entire phase-space of a noisy colloidal information engine, and study efficiency fluctuations due to the stochasticity of the mutual information and extracted work. We find that the average efficiency is maximal for non-zero noise level, at which the distribution of efficiency switches from bimodal to unimodal, and the stochastic efficiency often exceeds unity. We identify a line of anomalous, noise-driven equilibrium states that defines a refrigerator-to-heater transition, and test the generalized integral fluctuation theorem for continuous engines.
Entangled polymer complexes as Higgs phenomena
(RSC, 2015-08) Dutta, Sandipan
We derive an effective Maxwell–London equation for entangled polymer complexes under topological constraints, borrowing the theoretical framework from topological field theory. We find that the transverse current flux of a test polymer chain, surrounded by entangled chains, decays exponentially from its centerline position with a finite penetration depth, which is analogous to the magnetic-field decay in a superconductor (SC), referred to as the Meissner effect. Just as the mass acquirement of photons in a SC is the origin of the magnetic-field decay, the polymer obtains uncrossable intersections along the chain due to the preservation of the linking number, which restricts the deviation of the transverse polymer current in the normal direction. The underlying physics is as follows: less flexible polymers have stronger current–current correlations, giving rise to a heavier effective mass of the gauge fields and resulting in a shorter decay length. Interestingly, this picture is well incorporated within the most successful phenomenological theory of the, so called, tube model, the microscopic origins of which researchers have long pursued. The correspondence of our equation of motion to the tube model claims that the confining tube potential is a consequence of the topological constraint (linking number). The tube radius is attributed to the decay length. On increasing the effective mass (by strengthening the interaction at an uncrossable intersection or a number of intersections), the tube becomes narrower. Using this argument, the exponential decay of the chain leakage out of the tube is well understood.
Entropy production in active Rouse polymers
(IOP, 2023-03) Dutta, Sandipan
Active polymers are the archetype of nonequilibrium viscoelastic systems that constantly consume energy to produce motion. The activity of many biopolymers is essential to many life processes. The entropy production rate quantifies their non-equilibrium nature through the breaking of the time reversal symmetry. In this work we build an analytical model of active polymers as active Rouse polymers where the beads are active OrnsteinUhlenbeck particles (AOUP) and calculate their entropy production. The interactions between the beads are decoupled through the normal mode analysis and the entropy production can be solved analytically. We obtain the contribution of each Rouse mode in the entropy production and the dependence of the entropy production on the polymer properties like length. We find that the entropy production is zero for a passive Rouse polymer in the presence of thermal bath as well as for an active Rouse polymer in the absence of thermal bath. For an active chain in the presence of a thermal bath the entropy production is non-zero. In this case we find that the local temporal entropy production dominates the non-local entropy production.
Enzyme leaps fuel antichemotaxis
(PNAS, 2018) Dutta, Sandipan
There is mounting evidence that enzyme diffusivity is enhanced when the enzyme is catalytically active. Here, using superresolution microscopy [stimulated emission-depletion fluorescence correlation spectroscopy (STED-FCS)], we show that active enzymes migrate spontaneously in the direction of lower substrate concentration (“antichemotaxis”) by a process analogous to the run-and-tumble foraging strategy of swimming microorganisms and our theory quantifies the mechanism. The two enzymes studied, urease and acetylcholinesterase, display two families of transit times through subdiffraction-sized focus spots, a diffusive mode and a ballistic mode, and the latter transit time is close to the inverse rate of catalytic turnover. This biochemical information-processing algorithm may be useful to design synthetic self-propelled swimmers and nanoparticles relevant to active materials. Executed by molecules lacking the decision-making circuitry of microorganisms, antichemotaxis by this run-and-tumble process offers the biological function to homogenize product concentration, which could be significant in situations when the reactant concentration varies from spot to spot.
Exploring the unfolding pathways of protein families using elastic network model
(Springer Nature, 2024-10) Dutta, Sandipan
We explore how a protein’s native structure determines its unfolding process. We examine how the local structural features, like shear, and the global structural properties, like the number of soft modes, change during unfolding. Simulations are performed using a Gaussian Network Model (GNM) with bond breaking for both thermal and force-induced unfolding scenarios. We find that unfolding starts in areas of high shear in the native structure and progressively spreads to the low shear regions. Interestingly, analysis of single domain protein families (Chymotrypsin inhibitor and Barnase) reveal that proteins with distinct unfolding pathways exhibit divergent behavior of the number of soft modes during unfolding. This suggests that the number of soft modes might be a valuable tool for understanding thermal unfolding pathways. Additionally, we found a strong link between a protein’s overall structural similarity (TM-score) and its unfolding pathways, highlighting the importance of the native structure in determining how a protein unfolds.
Finite Temperature Quantum Effects in Many-Body Systems by Classical Methods
(Elsevier, 2016) Dutta, Sandipan
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas, weak coupling) and illustrated by calculation of pair correlations for the uniform electron gas and shell structure for harmonically confined charges. A wide range of temperatures and densities are addressed in each case. For the electron gas, comparisons are made to recent path integral Monte Carlo simulations showing good agreement. Finally, the relevance for orbital-free density functional theory for conditions of warm, dense matter is discussed briefly.
Finite-temperature quantum effects on confined charges
(APS, 2016-11) Dutta, Sandipan
A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the rather complete classical description of harmonic confinement via liquid-state theory. Here, the effects of quantum mechanics on that representation are described with attention focused on the origin and nature of shell structure. The analysis extends from the classical strong Coulomb coupling conditions of dusty plasmas to the opposite limit of low temperatures and large densities characteristic of “warm, dense matter.”
Green function of correlated genes in a minimal mechanical model of protein evolution
(PNAS, 2018) Dutta, Sandipan
The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis—the interaction among mutations in the gene—is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.
Hydration of ions in two-dimensional water
(APS, 2015-10) Dutta, Sandipan
We present a two-dimensional lattice model of water to study the effects of ion hydration on the properties of water. We map the water molecules as lattice particles consisting of a single oxygen atom at the center of a site and two hydrogen atoms on each side. The internal state of the system, such as the dipole moment at a site, is defined with respect to the location of the hydrogen atoms at the site depending on their role in hydrogen bonds (H bonds) being a donor or an acceptor. We study the influence of the charge and the radius of the ion on the insertion energy and on the H bonds in the first and second hydration layers around the ion and in the bulk. In particular we analyze how the competing interactions of the short-ranged H bonds and the long-ranged electrostatics influence the hydration properties. The role of the ion both as a source of the electrostatic interactions as well as a defect is also discussed. Our model also shows the well-known fact that the polarizability of the water molecules destroys the hydrogen bond network and increases the dipole moment of the molecules near the ion.
Inequivalence of fixed-force and fixed-extension statistical ensembles for a flexible polymer tethered to a planar substrate
(RSC, 2018-07) Dutta, Sandipan
Recent advances in single macromolecule experiments have sparked interest in the ensemble dependence of force–extension relations. The thermodynamic limit may not be attainable for such systems, which leads to inequivalence of the fixed-force and the fixed-extension ensembles. We consider an ideal Gaussian chain described by the Edwards Hamiltonian with one end tethered to a rigid planar substrate. We analytically calculate the force–extension relation in the two ensembles and we show their inequivalence, which is caused by the confinement of the polymer to half space. The inequivalence is quite remarkable for strong compressional forces. We also perform Monte-Carlo simulations of a tethered wormlike chain with contour length 20 times its persistence length, which corresponds to experiments measuring the conformations of DNA tethered to a wall. The simulations confirm the ensemble inequivalence and qualitatively agree with the analytical predictions of the Gaussian model. Our analysis shows that confinement due to tethering causes ensemble inequivalence, irrespective of the polymer model.
Most probable paths for active Ornstein-Uhlenbeck particles
(APS, 2023-05) Dutta, Sandipan
Fluctuations play an important role in the dynamics of stochastic systems. In particular, for small systems, the most probable thermodynamic quantities differ from their averages because of the fluctuations. Using the Onsager Machlup variational formalism we analyze the most probable paths for nonequilibrium systems, in particular, active Ornstein-Uhlenbeck particles, and investigate how the entropy production along these paths differs from the average entropy production. We investigate how much information about their nonequilibrium nature can be obtained from their extremum paths and how these paths depend on the persistence time and their swim velocities. We also look at how the entropy production along the most probable paths varies with the active noise and how it differs from the average entropy production. This study would be useful to design artificial active systems with certain target trajectories.
Quantum potential for diffraction and exchange effects
(Wiley, 2009-04) Dutta, Sandipan
Semiclassical methods of statistical mechanics can incorporate essential quantum effects by using effective quantum potentials. An ideal Fermi gas interacting with an impurity is represented by a classical fluid with effective electron–electron and electron-impurity quantum potentials. The electron-impurity quantum potential is evaluated at weak coupling, leading to a generalization of the Kelbg potential to include both diffraction and degeneracy effects. The electron–electron quantum potential for exchange effects only is the same as that discussed earlier by others
Reaching and violating thermodynamic uncertainty bounds in information engines
(APS, 2020-09) Dutta, Sandipan
Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information engine operating in a nonequilibrium steady state. Close to its maximal efficiency, we find that the engine violates the original TUR. This experimental demonstration of TUR violation agrees with recently proposed softer bounds: The engine satisfies two generalized TUR bounds derived from the detailed fluctuation theorem with feedback control and another bound linking fluctuation and dissipation to mutual information and Renyi divergence. We examine how the interplay of work fluctuation and dissipation shapes the information conversion efficiency of the engine, and find that dissipation is minimal at a finite noise level, where the original TUR is violated.