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For proton transfer reactions, the tunneling contributions to the rates are often much larger than thermally activated rates at temperatures of interest. A number of separable tunneling corrections have been proposed that capture the dependence of tunneling rates on barrier height and imaginary frequency size. However, the effects of reaction pathway curvature and barrier anharmonicity are more difficult to quantify. The nonseparable semiclassical transition state theory (TST) of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)] accounts for curvature and barrier anharmonicity, but it requires prohibitively expensive cubic and quartic derivatives of the potential energy surface at the transition state. This paper shows how the reaction path Hamiltonian can be used to approximate the cubic and quartic derivatives used in nonseparable semiclassical transition state theory. This enables tunneling corrections that include curvature and barrier anharmonicity effects with just three frequency calculations as required by a conventional harmonic transition state theory calculation. The tunneling correction developed here is nonseparable, but can be expressed as a thermal average to enable efficient Monte Carlo calculations. For the proton exchange reaction NH2 + CH4==NH3 + CH3, the nonseparable rates are very accurate at temperatures from 300 K up to about 1000 K where the TST rate itself begins to diverge from the experimental results.

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.

We model the hybridization kinetics of surface attached DNA oligomers with solubilized targets. Using both master equation and rate equation formalisms, we show that, for surface coverages at which the surface immobilized molecules interact, barriers to penetration create a distribution of target molecule concentrations within the adsorbed layer. By approximately enumerating probe and target conformations, we estimate the probability of overlap between complementary probe and target regions as a function of probe density and chain length. In agreement with experiments, we find that as probe molecules interact more strongly, fewer nucleation sites become accessible and binding rates are diminished relative to those in solution. Nucleation sites near the grafted end of the probes are least accessible; thus targets which preferentially bind to this region show more drastic rate reductions than those that bind near the free end of the probe. The implications of these results for DNA-based biosensors are discussed.

We study the dynamics of polymers in a random disordered medium of fixed obstacles using kinetic Monte Carlo methods. The polymers can have monomers which have attractive (A-type), repulsive (R-type) or neutral (H-type) interactions with the fixed obstacles that comprise the disordered medium. Several classes of homopolymers and heteropolymers with diverse sequences have been studied. Our most noteworthy result is that, above a threshold temperature, polymer bearing monomers that are attracted to the disordered medium translocate faster through the medium than those bearing neutral or repulsive monomers. We discuss how a delicate balance between energetic and entropic factors leads to this counterintuitive outcome. By examining heteropolymers with different sequences, we also find that the dependence of mobility on average composition is stronger than that on higher order correlations characterizing the sequence distribution. Connections between our results and experiments with synthetic and biological systems are noted.

T lymphocytes (T cells) play an important role in orchestrating an adaptive immune response in complex organisms. Recent experiments have shown that when T cells recognize antigen presenting cells, a complex and large-scale reorganization of intercellular membrane proteins and cell shape occurs. The resulting motif is implicated in information transfer between T cells and antigen presenting cells, and has been labeled the immunological synapse. Numerical solutions of a mathematical model that incorporates binding kinetics, protein mobility, and down regulation, and membrane mechanics has proven successful in describing some of these observations. In this paper, we analyze the equations that describe this model, and this sheds light on the origins of pattern formation in the immunological synapse. In particular, the thermodynamic considerations and dynamic instabilities that lead to pattern formation in and out of equilibrium are elucidated.

We study the microphase segregation of molten randomly grafted copolymers (RGCs) using a Landau field theory. Under one wave number approximation, we find three equilibrium ordered microphases: lamellar phase (LAM), hexagonal cylinder phase (HEX), and bcc sphere phase (BCC). The stability of these phases strongly depends on the architectural parameters describing the RGC chains (e.g., the backbone length, the branch length, and the number of branches). Our calculation reveals that RGCs with high average composition of backbone monomers or with low branching density tend to form LAM microstructures. For a small average composition of backbone monomers, HEX and BCC microphases appear in turn with increasing branching density. Independent of the architectural parameters and composition, the disorder to order transition for molten RGCs is always from the disordered phase to the LAM microphase. The physical reasons underlying this behavior and experimentally testable predictions are discussed.

We study microphase ordering of molten randomly grafted copolymers (RGCs) by using a mean field theory and the replica method to calculate the quenched average. Our results illustrate that in the weak segregation limit (WSI), the optimal wave vector q* of the lamellar phase formed by molten RGCs, has a temperature dependence different from either linear random copolymers (LRCs) or diblock copolymers (DCPs): when close, but below the microphase separation transition (MST) temperature, q* increases sharply with decreasing temperature; then q* gradually acquires an asymptotic value determined by the length of the branch and the average distance between branch points on the backbone. Our results are compared with recent experiments, and the effects of chain architecture on the microphase separation characteristics of RGCs are delineated. Our results suggest a new method for controlling the microphase spacing by exploiting quenched disorder.

We use a Landau theory to study the instability of the homogeneous state of a mixture of linear random copolymers and diblock copolymers. Interesting features of the calculated structure factors for different components of the mixture are found, which can be directly compared with scattering experiments with selectively deuterated samples. We also investigate the least stable concentration fluctuations and find four different types of segregation modes at the spinodal depending upon the characteristics of the mixture (e.g., average compositions, statistical correlation lengths and volume fractions). The different segregation modes are also indicative of the kinetic pathways leading to the formation of ordered microstructures. Experiments probing these pathways are suggested.

We derive a Landau free energy functional for polymeric mixtures containing components with different sequence statistics. We then apply this general field theory to two mixtures that belong to the Ising universality class: mixtures of two different linear random copolymers, and ternary systems of linear random copolymers and two homopolymers. We discuss the instability conditions for the homogeneous state of these mixtures, and calculate the structure factors for different components in the homogeneous state. The structure factors show interesting features which can directly be compared with scattering experiments carried out with selectively deuterated samples. We also work out the eigenmodes representing the least stable concentration fluctuations for these mixtures. The nature of these concentration fluctuations provides information regarding the ordered phases and the kinetic pathways that lead to them. We find various demixing modes for different characteristics of the two mixtures (e.g., average compositions, statistical correlation lengths, and volume fractions).

I use a Landau theory to study the behavior of A–B heteropolymers with disordered sequences immersed in a binary solvent mixture. Segments of type A are preferentially solvated in one type of solvent, and those of type B prefer the other type of solvent. At high temperatures, the behavior is qualitatively the same as that in a single solvent. As the temperature approaches the critical temperature for solvent demixing, however, the chain conformational statistics change dramatically. A phase transition occurs driven by the long-range solvent density fluctuations. The transition is one where on scales larger than a preferred length the chain is collapsed and microphase ordered. On shorter scales it is disordered and exhibits self-avoiding walk statistics. In many circumstances this domain size acquires a limiting value and the system cannot order on shorter length scales by reducing temperature. The ordering disappears when the critical point is approached too closely. Predictions are made for scattering profiles that may be observed in neutron-scattering experiments.

We investigate the potential uses for random heteropolymers (RHPs) as adhesion promoters between a homopolymer melt and a solid surface. We consider homopolymers of monomer (segment) type A which are naturally repelled from a solid surface. To this system we add RHPs with both A and B (attractive to the surface) type monomers to promote adhesion between the two incompatible substrates. We employ Monte Carlo simulations to investigate the effects of variations in the sequence statistics of the RHPs, amount of promoter added, and strength of the segment–segment and segment–surface interaction parameters. Clearly, the parameter space in such a system is quite large, but we are able to describe, in a qualitative manner, the optimal parameters for adhesion promotion. The optimal set of parameters yield interfacial conformational statistics for the RHPs which have a relatively high adsorbed fraction and also long loops extending away from the surface that promote entanglements with the bulk homopolymer melt. In addition, we present qualitative evidence that the concentration of RHP segments per surface site plays an important role in determining the mechanism of failure (cohesive versus adhesive) at such an interface. Our results also provide the necessary input for future simulations in which the system may be strained to the limit of fracture.

Random heteropolymers (RHPs) with uncorrelated sequence fluctuations on the segmental scale can undergo a transition wherein, below a certain temperature, the thermodynamics is determined by a few dominant conformations. We study this “freezing” transition for RHPs with correlated sequence fluctuations. Specifically, we apply our theory to the case where the correlations decay with a single correlation length; a pragmatically realizable example is provided by random block copolymers. Our results show that the temperature at which freezing occurs grows with the block length of such polymers. Freezing also occurs on the scale of the correlation length, thus making experimental observation of this phenomenon (a consequence of frustration coupled with quenched disorder) more accessible. The results are rationalized on physical grounds.

We study the adsorption of random heteropolymers (RHPs) on disordered multifunctional surfaces. Recent replica calculations suggest that when the statistics describing the sequence distribution and the surface site distributions are related in a special way, a first-order adsorption transition occurs in such systems. This phenomenon of recognition between RHPs and disordered surfaces due to statistical pattern matching is studied via Monte Carlo simulations and a simple nonreplica theory. The theory serves to elucidate the simulation results, and suggests that the origin of the first-order adsorption transition is the suppression of loop fluctuations due to competing interactions and the quenched disorder (i.e., frustration).

In many applications, it is desirable to control interfacial properties by employing adsorbed polymer layers. In this work, we study the adsorption of random heteropolymers and find a rich surface phase diagram that suggest ways in which the properties of the adsorbed layers can be controlled rather precisely by manipulating the physical conditions. Specifically, we present a comprehensive field‐theoretic analysis of the surface phase diagram of a solution of random heteropolymers interacting with a chemically homogeneous solid surface, and find many surface transitions that may be exploited in applications. The different types of polymer segments interact with the solid surface in arbitrarily different ways. Our analysis, wherein a replica method is employed to average over the quenched sequence fluctuations, allows us to obtain the surface free energy functionals that show that our problem partially resembles a semi‐infinite Ising spin system. Thus, akin to the Ising system, the phase diagram exhibits e...

Monte Carlo simulation based on Widom’s test particle method is used to study the behavior of dilute ionic solutes in a quenched disordered medium with ionized obstacles. The structure of the medium is assumed to correspond to that of an ionic fluid equilibrated at certain prequenching temperature Tq and permittivity eq different from the corresponding values at the conditions of observation. The correlations among solute ions display qualitative differences from those observed in annealed systems. The ions of equal sign are attracted to domains of the disordered material characterized by charge opposite to that of the ions. The attraction of ions of the same sign to the same domains results in an apparent attractive contribution to the disorder‐averaged interionic potential. At distances sufficiently exceeding the screening length pertaining to the ionized obstacles at the prequenching conditions, the disorder‐induced term prevails over the direct Coulombic repulsion and a net attraction is observed. A similar mechanism leads to a long‐ranged repulsion between oppositely charged ions. These findings are in agreement with earlier calculations of the disorder‐averaged ion–ion potentials based on the asymptotic Debye–Huckel description of the disordered medium. The simulations are also used to estimate the effects of the medium on thermodynamic properties of the embedded ionic solute. The energies and activity coefficients are found to decrease with the product of the prequenching temperature and permittivity, a phenomenon explained in terms of the increase of the potential fluctuations in the disordered medium with growing eqTq. In spite of its global electroneutrality, the quenched medium displays a strong selectivity with respect to the valency of the solute, the tendency towards absorption increasing with the charge of the ions. The selectivity rapidly increases with increasing value of the characteristic product of the prequenching temperature and the permittivity eqTq.Monte Carlo simulation based on Widom’s test particle method is used to study the behavior of dilute ionic solutes in a quenched disordered medium with ionized obstacles. The structure of the medium is assumed to correspond to that of an ionic fluid equilibrated at certain prequenching temperature Tq and permittivity eq different from the corresponding values at the conditions of observation. The correlations among solute ions display qualitative differences from those observed in annealed systems. The ions of equal sign are attracted to domains of the disordered material characterized by charge opposite to that of the ions. The attraction of ions of the same sign to the same domains results in an apparent attractive contribution to the disorder‐averaged interionic potential. At distances sufficiently exceeding the screening length pertaining to the ionized obstacles at the prequenching conditions, the disorder‐induced term prevails over the direct Coulombic repulsion and a net attraction is observed. A s...

We develop a model for the adsorption of random heteropolymers onto solid surfaces from solutions that have a finite concentration of polymer. Previous studies that properly average over the quenched sequence distribution have been concerned with isolated chains near surfaces. Our self‐consistent‐field theory predicts a transition from situations where the surface segment density is enhanced compared with bulk solution concentration to one wherein the surface segment density is depleted. For a specific chemical identity of the random heteropolymer segments and the surface, this adsorption–depletion transition occurs above a threshold value of the strength of the sequence fluctuations. This intriguing finding can be tested directly via neutron scattering experiments (in the reflection mode), and offers opportunities for manipulating interfacial properties. The variation of the excess surface density of segments with polymer concentration in solution near the adsorption–depletion transition is also elucidated.

In this paper, we consider the behavior of random heteropolymers in a quenched disordered medium. We develop a field theory and obtain a mean‐field solution that allows for replica symmetry breaking. The presence of an external disorder leads to the formation of compact states; a homopolymeric effect. We compute the phase diagram for two classes of problems. First, we consider the situation wherein the bare heteropolymer prefers like segments to segregate, and second, we examine cases where the bare heteropolymer prefers unlike segments to mix. For the first class of systems, we find a phase diagram characterized by a replica symmetry broken phase that exists below a particular temperature. This temperature grows with the strength of the external disorder. In the second class of situations, the phase diagram is much richer. Here we find two replica symmetry broken phases with different patterns separated by a reentrant phase. The reentrant phase and one of the two replica symmetry broken phases are induced by interactions with the external disorder. The dependence of the location of the phase boundaries on the strength of the external disorder are elucidated. We discuss our results from a physical standpoint, and note the testable experimental consequences of our findings.

Understanding the interfacial organization of heteropolymers near solid surfaces is an issue of fundamental interest that is relevant for many technological and biological applications. In this paper we address several questions pertaining to the surface‐induced ordering and the adsorption–desorption phase behavior of a dilute solution of two‐letter random heteropolymers interacting with a solid surface. Our analysis is based on a statistical field theoretic formulation of the propagator for the problem of interest. We employ the replica trick to alleviate analytical difficulties which arise when considering averaging over the sequence distribution of the A and the B units. In order to highlight the effects of the surface, we consider the situation wherein the intersegment interactions are of the excluded volume type while the segment–surface interactions of the A and B segments are arbitrarily different. Within the replica symmetric solution, we show that proper coarse‐graining of the interaction potentials leads to exact analytical expressions for the self‐consistent propagator of the heteropolymer at theta conditions and for the case where excluded volume interactions prevail. One of our interesting findings is that heteropolymers undergo an adsorption–desorption transition in the vicinity of a surface that interacts with the different types of segments in arbitrarily different ways. This is consistent with our previous numerical findings for much more restricted circumstances.We explicitly analyze the influence of the fluctuations in the sequence distribution on the conformational organization of the adsorbed chains and obtain the scaling behavior of properties of interest in the vicinity of the adsorption–desorption threshold with respect to the disorder strength and other polymer interaction parameters. Specifically, invoking the Ehrenfest theorem we find that the adsorption–desorption transition at theta conditions is a second‐order phase transition while in the case where excluded volume interaction prevails the transition becomes first order. We also obtain exact analytical expressions for the adsorption–desorption threshold. The threshold exhibits quite an unusual dependence on the strength of the disorder. Finally, we compute the point of onset of repulsive forces between plates that confine a random copolymer solution as a function of chain sequence distribution. We suggest specific experiments employing the surface force apparatus that could directly test our predictions.

Motivated by practical issues that pertain to polymer adhesion, we consider the equilibrium behavior of a dilute solution of ideal A–B random block copolymers confined between two solid surfaces. We develop a general theory for the situation wherein the A–A, B–B, and A–B intersegment interactions are different, and furthermore, the A and B segments interact differently with the solid surfaces. Random block copolymers constitute a class of materials wherein a quenched disorder (the sequence distribution) is carried by the fluid whose statistical properties are of interest. In our theory, we perform quenched disorder averages using the replica trick. The nonlocal terms in our action functional are decoupled by introducing a set of random fields. The resulting equations for the propagator are analyzed within the framework of eigenfunction expansions. Since we consider long chains in confined geometries, we invoke the ground state approximation. We also carry out the functional integrals over the random field...

The relaxation dynamics of a polymer chain strongly adsorbed to a solid surface are simulated via a kinetic Ising model that includes chain connectivity constraints (steric hindrance, rotational strain, and configurational entropy). The two polymer architectures examined consist of one or two chemisorbing functional groups per segment. In both architectures, the chemisorbed polymer chain is trapped in nonequilibrium conformational states at low temperatures, but relaxes to equilibrium at higher temperatures with stretched exponential (KWW) relaxation kinetics. The average relaxation time for the two pendant group architecture has a strongly non‐Arrhenius temperature dependence that obeys the Vogel–Fulcher law. In contrast, average relaxation times for the one pendant group architecture cannot be described by the Vogel–Fulcher law.

Polymer–metal interfaces are of increasing technological importance in a variety of applications. These interfaces are characterized by specific interactions between functional groups of the organic polymer and the metallic substrate. In order to study the structure of these interfaces at the molecular level, the energetics of the segment–surface interactions must be well characterized. We have used density functional theory to investigate the interactions of poly(methyl methacrylate) (PMMA) oligomers with aluminum surfaces. The aluminum surface is represented by the simple jellium model. The energetics of the interactions between the organic molecules and the aluminum surface are calculated as a function of the orientation with respect to the surface of the organic molecule and various internal degrees of freedom. The computed energy hypersurfaces exhibit a rich structure characterized by several energy minima and barriers. Implications of such an energy hypersurface for the architecture of long chain molecules at the interface are discussed. The energy hypersurfaces also show that the rotational conformational statistics of PMMA interacting with an aluminum surface should be quite different from that of bulk PMMA. The reported energy hypersurfaces have been used to construct an empirical force‐field for future molecular simulations of long chains subject to the proper potentials.Polymer–metal interfaces are of increasing technological importance in a variety of applications. These interfaces are characterized by specific interactions between functional groups of the organic polymer and the metallic substrate. In order to study the structure of these interfaces at the molecular level, the energetics of the segment–surface interactions must be well characterized. We have used density functional theory to investigate the interactions of poly(methyl methacrylate) (PMMA) oligomers with aluminum surfaces. The aluminum surface is represented by the simple jellium model. The energetics of the interactions between the organic molecules and the aluminum surface are calculated as a function of the orientation with respect to the surface of the organic molecule and various internal degrees of freedom. The computed energy hypersurfaces exhibit a rich structure characterized by several energy minima and barriers. Implications of such an energy hypersurface for the architecture of long chain mo...

In many types of cells, binding of molecules to their receptors enables cascades of intracellular chemical reactions to take place (signaling). However, a low level of signaling also occurs in most unstimulated cells. Such basal signaling in resting cells can have many functions, one of which is that it is thought to be required for fast cellular responses to external stimuli. A mechanistic understanding of why this is true and which features of cellular signaling networks make basal signaling necessary for fast responses is unknown. We address this issue by obtaining the time required for activation of common types of cell signaling modules with and without basal signaling. Our results show that the absence of basal signaling does not have any dramatic effects on the response time for signaling modules that exhibit a graded response to increasing stimulus levels. In sharp contrast, signaling modules that exhibit sharp dose-response curves which discriminate sensitively between stimuli to which the cell needs to respond and low-grade inputs (or stochastic noise) require basal signaling for fast cellular responses. In such cases, we find that an optimal level of basal signaling balances the requirements for fast cellular responses while minimizing spurious activation without appropriate stimulation.

Positive feedback regulation is ubiquitous in cell signaling networks, often leading to binary outcomes in response to graded stimuli. However, the role of such feedbacks in clustering, and in spatial spreading of activated molecules, has come to be appreciated only recently. We focus on the latter, using a simple model developed in the context of Ras activation with competing negative and positive feedback mechanisms. We find that positive feedback, in the presence of slow diffusion, results in clustering of activated molecules on the plasma membrane, and rapid spatial spreading as the front of the cluster propagates with a constant velocity (dependent on the feedback strength). The advancing fronts of the clusters of the activated species are rough, with scaling consistent with the Kardar-Parisi-Zhang (KPZ) equation in one dimension. Our minimal model is general enough to describe signal transduction in a wide variety of biological networks where activity in the membrane-proximal region is subject to feedback regulation., 37 pages, 8 figures. Journal of Chemical Physics (in press)