Finite-strain elasticity theory and liquid-liquid phase separation in compressible gels

The theory of finite-strain elasticity is applied to the phenomenon of cavitation observed in polymer gels following liquid-liquid phase separation of the solvent, which opens a fascinating window on the role of finite-strain elasticity theory in soft materials in general. We show that compressibility effects strongly enhance cavitation in simple materials that obey neo-Hookean elasticity. On the other hand, cavitation phenomena in gels of flexible polymers in a binary solvent that phase separates are surprisingly similar to those of incompressible materials. We find that, as a function of the interfacial energy between the two solvent components, there is a sharp transition between cavitation and classical nucleation and growth. Next, biopolymer gels are characterized by strain hardening and even very low levels of strain hardening turn out to suppress cavitation in polymer gels that obey Flory-Huggins theory in the absence of strain hardening. Our results indicate that cavitation is, in essence, not possible for polymer networks that show strain hardening.

Spanning tree model and the assembly kinetics of RNA viruses

Single-stranded RNA (ssRNA) viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules and it is not known whether this also can be understood by free energy minimization. We address this question using a simple mathematical model, the spanning tree model, that was recently proposed for the assembly of small ssRNA viruses. We present a statistical physics analysis of the properties of this model. RNA selection takes place via a kinetic mechanism that operates during the formation of the nucleation complex and that is related to Hopfield kinetic proofreading.

Packaging contests between viral RNA molecules and kinetic selectivity

The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.

Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells

A general phase plot is proposed for discrete particle shells that allows for thermal fluctuations of the shell geometry and of the inter-particle connectivities. The phase plot contains a first-order melting transition, a buckling transition, and a collapse transition and is used to interpret the thermodynamics of microbiological shells.

Invariant theory and orientational phase transitions

The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational symmetry breaking of simple atomic or molecular clusters that are not true phase transitions. In this paper, we address fundamental problems that arise with the Landau theory when it is applied to rotational symmetry breaking transitions of more complex particle clusters that involve order parameters characterized by larger values of the l index of the dominant spherical harmonic that describes the broken symmetry state. The problems are twofold. First, one may encounter a thermodynamic instability of the expected ground state with respect to states with lower symmetry. A second problem concerns the proliferation of quartic invariants that may or may not be physical. We show that the combination of a geometrical method based on the analysis of the space of invariants, developed by Kim to study symmetry breaking of the Higgs potential, with modern visualization tools provides a resolution to these problems. The approach is applied to the outcome of numerical simulations of particle ordering on a spherical surface and to the ordering of protein shells.

Specific inter-domain interactions stabilize a compact HIV-1 Gag conformation

HIV-1 Gag is a large multidomain poly-protein with flexible unstructured linkers connecting its globular subdomains. It is compact when in solution but assumes an extended conformation when assembled within the immature HIV-1 virion. Here, we use molecular dynamics (MD) simulations to quantitatively characterize the intra-domain interactions of HIV-1 Gag. We find that the matrix (MA) domain and the C-terminal subdomain CA_ctd of the CA capsid domain can form a bound state. The bound state, which is held together primarily by interactions between complementary charged and polar residues, stabilizes the compact state of HIV-1 Gag. We calculate the depth of the attractive free energy potential between the MA/ CA_ctd sites and find it to be about three times larger than the dimerization interaction between the CA_ctd domains. Sequence analysis shows high conservation within the newly-found intra-Gag MA/CA_ctd binding site, as well as its spatial proximity to other well known elements of Gag –such as CA_ctd’s SP1 helix region, its inositol hexaphosphate (IP6) binding site and major homology region (MHR), as well as the MA trimerization site. Our results point to a high, but yet undetermined, functional significance of the intra-Gag binding site. Recent biophysical experiments that address the binding specificity of Gag are interpreted in the context of the MA/CA_ctd bound state, suggesting an important role in selective packaging of genomic RNA by Gag.

Gaussian curvature and the budding kinetics of enveloped viruses

The formation of a membrane-enveloped virus starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer develops into a spherical shell (capsid) enveloped by a lipid-rich membrane. In many cases, the budding process stalls prior to the release of the virus. Recently, Brownian dynamics simulations of a coarse-grained model system reproduced protracted pausing and stalling, which suggests that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we propose that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with the neck geometry. A geometrical potential energy barrier develops during the budding that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the capsid. The barrier is generated by a conflict between the positive Gauss curvature of the assembling capsid and the negative Gauss curvature of the neck region. A continuum theory description is proposed and is compared with the Brownian simulations of the budding of enveloped viruses.

Despite intense study, the life-cycle of the HIV-1 virus continues to pose mysteries. One of these is the fact that the assembly of an HIV-1 virus along the plasma membrane (PM) of the host cell—the budding process—stalls prior to release of the virus. Many other important viral pathogens with a surrounding lipid membrane envelope display similar stalling. Combining numerical and analytical methods, we demonstrate that the neck-like shape of the membrane that forms prior to release of the virus creates a barrier that blocks the proteins required for the assembly process from reaching the budding virus. An improved understanding of the physics of the blocking process could enable new strategies to combat enveloped viruses.

Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension. Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

Confining annealed branched polymers inside spherical capsids

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.

Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion

The amphibian sacculus (AS) is an end organ that specializes in the detection of low-frequency auditory and vestibular signals. In this paper, we propose a model for the AS in the form of an array of phase oscillators with long-range coupling, subject to a steady load that suppresses spontaneous oscillations. The array is exposed to significant levels of frequency dispersion and intrinsic noise. We show that such an array can be a sensitive and robust subthreshold detector of low-frequency stimuli, though without significant frequency selectivity. The effects of intrinsic noise and frequency dispersion are contrasted. Intermediate levels of intrinsic noise greatly enhance the sensitivity through stochastic resonance. Frequency dispersion, on the other hand, only degrades detection sensitivity. However, frequency dispersion can play a useful role in terms of the suppression of spontaneous activity. As a model for the AS, the array parameters are such that the system is poised near a saddle-node bifurcation on an invariant circle. However, by a change of array parameters, the same system also can be poised near an emergent Andronov-Hopf bifurcation and thereby function as a frequency-selective detector.

Orientational phase transitions and the assembly of viral capsids

We present a Landau theory for large-l orientational phase transitions and apply it to the assembly of icosahedral viral capsids. The theory predicts two distinct types of ordering transitions. Transitions dominated by the l=6,10,12, and 18 icosahedral spherical harmonics resemble robust first-order phase transitions that are not significantly affected by chirality. The remaining transitions depend essentially on including mixed l states denoted as l=15+16 corresponding to a mixture of l=15 and l=16 spherical harmonics. The l=15+16 transition is either continuous or weakly first-order and it is strongly influenced by chirality, which suppresses spontaneous chiral symmetry breaking. The icosahedral state is in close competition with states that have tetrahedral, D_{5}, and octahedral symmetries. We present a group-theoretic method to analyze the competition between the different symmetries. The theory is applied to a variety of viral shells.

Sequence Dependence of Viral RNA Encapsidation

We develop a Flory mean-field theory for viral RNA (vRNA) molecules that extends the current RNA folding algorithms to include interactions between different sections of the secondary structure. The theory is applied to sequence-selective vRNA encapsidation. The dependence on sequence enters through a single parameter: the largest eigenvalue of the Kramers matrix of the branched polymer obtained by coarse graining the secondary structure. Differences between the work of encapsidation of vRNA molecules and of randomized isomers are found to be in the range of 20 kBT, more than sufficient to provide a strong bias in favor of vRNA encapsidation. The method is applied to a packaging competition experiment where large vRNA molecules compete for encapsidation with two smaller RNA species that together have the same nucleotide sequence as the large molecule. We encounter a substantial, generic free energy bias, that also is of the order of 20 kBT, in favor of encapsidating the single large RNA molecule. The bias is mainly the consequence of the fact that dividing up a large vRNA molecule involves the release of stored elastic energy. This provides an important, nonspecific mechanism for preferential encapsidation of single larger vRNA molecules over multiple smaller mRNA molecules with the same total number of nucleotides. The result is also consistent with recent RNA packaging competition experiments by Comas-Garcia et al.1 Finally, the Flory method leads to the result that when two RNA molecules are copackaged, they are expected to remain segregated inside the capsid.

Impurities in Bose-Einstein Condensates: From Polaron to Soliton

We propose that impurities in a Bose-Einstein condensate which is coupled to a transversely laser-pumped multimode cavity form an experimentally accessible and analytically tractable model system for the study of impurities solvated in correlated liquids and the breakdown of linear-response theory [corrected]. As the strength of the coupling constant between the impurity and the Bose-Einstein condensate is increased, which is possible through Feshbach resonance methods, the impurity passes from a large to a small polaron state, and then to an impurity-soliton state. This last transition marks the breakdown of linear-response theory.

Chromatin hydrodynamics

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory-the two-fluid model-in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model-the Maxwell fluid-for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.

Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation

The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells-the hair cells-are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes-sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.

Low frequency entrainment of oscillatory bursts in hair cells

Sensitivity of mechanical detection by the inner ear is dependent upon a highly nonlinear response to the applied stimulus. Here we show that a system of differential equations that support a subcritical Hopf bifurcation, with a feedback mechanism that tunes an internal control parameter, captures a wide range of experimental results. The proposed model reproduces the regime in which spontaneous hair bundle oscillations are bistable, with sporadic transitions between the oscillatory and the quiescent state. Furthermore, it is shown, both experimentally and theoretically, that the application of a high-amplitude stimulus to the bistable system can temporarily render it quiescent before recovery of the limit cycle oscillations. Finally, we demonstrate that the application of low-amplitude stimuli can entrain bundle motility either by mode-locking to the spontaneous oscillation or by mode-locking the transition between the quiescent and oscillatory states.

Phase slips in oscillatory hair bundles

Hair cells of the inner ear contain an active amplifier that allows them to detect extremely weak signals. As one of the manifestations of an active process, spontaneous oscillations arise in fluid immersed hair bundles of in vitro preparations of selected auditory and vestibular organs. We measure the phase-locking dynamics of oscillatory bundles exposed to low-amplitude sinusoidal signals, a transition that can be described by a saddle-node bifurcation on an invariant circle. The transition is characterized by the occurrence of phase slips, at a rate that is dependent on the amplitude and detuning of the applied drive. The resultant staircase structure in the phase of the oscillation can be described by the stochastic Adler equation, which reproduces the statistics of phase slip production.

Physics of shell assembly: line tension, hole implosion, and closure catastrophe

The self-assembly of perfectly ordered closed shells is a challenging process involved in many biological and nanoscale systems. However, most of the aspects that determine their formation are still unknown. Here we investigate the growth of shells by simulating the assembly of spherical structures made of N identical subunits. Remarkably, we show that the formation and energetics of partially assembled shells are dominated by an effective line-tension that can be described in simple thermodynamic terms. In addition, we unveil two mechanisms that can prevent the correct formation of defect-free structures: "hole implosion," which leads to a premature closure of the shell; and "closure catastrophe," which causes a dramatic production of structural disorder during the later stages of the growth of big shells.

Mode-locking dynamics of hair cells of the inner ear

We explore mode locking of spontaneous oscillations of saccular hair cell bundles to periodic mechanical deflections. A simple dynamic systems framework is presented that captures the main features of the experimentally observed behavior in the form of an Arnold tongue. We propose that the phase-locking transition can proceed via different bifurcations. At low stimulus amplitudes F, the transition to mode locking as a function of the stimulus frequency ω has the character of a saddle-node bifurcation on an invariant circle. At higher stimulus amplitudes, the mode-locking transition has the character of a supercritical Andronov-Hopf bifurcation.

Nonlinear-dynamics theory of up-down transitions in neocortical neural networks

The neurons of the neocortex show ~1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.

Pseudoelasticity and Pseudotwinning in Ordered Shape-Memory Alloys

Shape-memory behavior is a complicated phenomenon which Intimately relates macroscopic strain recovery with martensitic phase transformation. A vital step In the theoretical understanding of this effect is a clear picture of a superficially rather simpler phenomenon: martensitic pseudoelasticity. Within the martensftic phase, a number of ordered alloys exhibit deformation strain recovery which Is reminiscent of rubber elasticity. The deformation Is observed to occur via coherent motion of parallel twin boundaries. In this case, where long range elastic accomodatlon forces play no role, the origin of the restoring force on the twin boundaries is still unclear. In this work, we present a quantitative theory which generalizes previous suggestions in the literature and unifies this phenomenon with elastic mechanical untwinning. Our description is based on the concept of a “pseudotwin” originally proposed by Laves and later elucidated by Cahn. Here, the motion of a twin boundary generates a new metastable crystallographic structure (the pseudo-twin) of locally higher free energy. This notion not only provides a source for a “volume” restoring force but leads to a natural descriptioni of observed stabilization effects. Specific experiments to test our description will be proposed.

Melting of branched RNA molecules

In this Letter we show that the melting thermodynamics of RNA molecules is very sensitive to the branching geometry. We find that, when pairing interactions are described by a Gō model, unbranched RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents while RNA molecules with the branching geometry of a Cayley tree, with coordination number three, have a free energy that shows no thermodynamic singularity within numerical precision. Nevertheless, we provide an analytical proof that the free energy does have a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge but only on the high-temperature side of this singularity.

Soft elasticity of RNA gels and negative Poisson ratio

We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.

Theory of conformational transitions of viral shells

We propose a continuum theory for the conformational transitions of viral shells. Conformational transitions of viral shells, as encountered during viral maturation, are associated with a soft mode instability of the capsid proteins [F. Tama and C. L. Brooks, J. Mol. Biol. 345(2), 299 (2005)]. The continuum theory presented here is an adaptation of the Ginzburg-Landau theory of soft-mode structural phase transitions of solids to viral shells. The theory predicts that the conformational transitions are characterized by a pronounced softening of the shell elasticity in the critical region. We demonstrate that the thermodynamics of the conformational transition can be probed quantitatively by a micromechanical atomic force microscope study. The external force can drive a capsid into a state of phase coexistence characterized by a highly nonlinear force deformation curve.

Evaluation of two different epidural catheters in clinical practice. narrowing down the incidence of paresthesia!

Although epidural anesthesia is considered safe, several complications may occur during puncture and insertion of a catheter. Incidences of paresthesia vary between 0.2 and 56%. A prospective, open, cohort-controlled pilot study was conducted in 188 patients, ASA I-III, age 19-87 years, scheduled for elective surgery and epidural anesthesia. We evaluated a 20 G polyamide (standard) catheter and a 20 G combined polyurethane-polyamide (new) catheter. Spontaneous reactions upon catheter-insertion, paresthesia on questioning, inadvertent dural or intravascular puncture, and reasons for early catheter removal were recorded. The incidence of paresthesia reported spontaneously was 21.3% with the standard catheter and 16.7% with the new catheter. Systematically asking for paresthesia almost doubled the paraesthesia rate. Intravascular cannulation occurred in 5%. No accidental dural punctures occurred. An overall incidence of 13.3% of technical problems led to early catheter removal. The new catheter was at least equivalent to the standard regarding epidural success rate and safety : rate of paresthesia, intravascular and dural cannulation.

Monte Carlo simulations of polyelectrolytes inside viral capsids

Structural features of polyelectrolytes as single-stranded RNA or double-stranded DNA confined inside viral capsids and the thermodynamics of the encapsidation of the polyelectrolyte into the viral capsid have been examined for various polyelectrolyte lengths by using a coarse-grained model solved by Monte Carlo simulations. The capsid was modeled as a spherical shell with embedded charges and the genome as a linear jointed chain of oppositely charged beads, and their sizes corresponded to those of a scaled-down T=3 virus. Counterions were explicitly included, but no salt was added. The encapisdated chain was found to be predominantly located at the inner capsid surface, in a disordered manner for flexible chains and in a spool-like structure for stiff chains. The distribution of the small ions was strongly dependent on the polyelectrolyte-capsid charge ratio. The encapsidation enthalpy was negative and its magnitude decreased with increasing polyelectrolyte length, whereas the encapsidation entropy displayed a maximum when the capsid and polyelectrolyte had equal absolute charge. The encapsidation process remained thermodynamically favorable for genome charges ca. 3.5 times the capsid charge. The chain stiffness had only a relatively weak effect on the thermodynamics of the encapsidation.

Electrostatics and the assembly of an RNA virus

Electrostatic interactions play a central role in the assembly of single-stranded RNA viruses. Under physiological conditions of salinity and acidity, virus capsid assembly requires the presence of genomic material that is oppositely charged to the core proteins. In this paper we apply basic polymer physics and statistical mechanics methods to the self-assembly of a synthetic virus encapsidating generic polyelectrolyte molecules. We find that (i) the mean concentration of the encapsidated polyelectrolyte material depends on the surface charge density, the radius of the capsid, and the linear charge density of the polymer but neither on the salt concentration nor the Kuhn length, and (ii) the total charge of the capsid interior is equal but opposite to that of the empty capsid, a form of charge reversal. Unlike natural viruses, synthetic viruses are predicted not to be under an osmotic swelling pressure. The design condition that self-assembly only produces filled capsids is shown to coincide with the condition that the capsid surface charge exceeds the desorption threshold of polymer surface adsorption. We compare our results with studies on the self-assembly of both synthetic and natural viruses.

Theory of force regulation by nascent adhesion sites

The mechanical coupling of a cell with the extracellular matrix relies on adhesion sites, clusters of membrane-associated proteins that communicate forces generated along the F-Actin filaments of the cytoskeleton to connecting tissue. Nascent adhesion sites have been shown to regulate these forces in response to tissue rigidity. Force-regulation by substrate rigidity of adhesion sites with fixed area is not possible for stationary adhesion sites, according to elasticity theory. A simple model is presented to describe force regulation by dynamical adhesion sites.

Helicoid to spiral ribbon transition

We present a continuum description for the transition between the helicoid and spiral ribbon structures of chiral materials. At a critical value of the ratio between the bending and stretching moduli, the Föppl-von Kármán number, we encounter a continuous buckling transition from a straight helicoid to a spiral ribbon. Two of the three persistence lengths of the ribbon become very short at the transition point, indicating strong thermal shape fluctuations. The transition is discontinuous if the ribbon width is treated as a free thermodynamic variable.

Helicoid to spiral ribbon transition

We present a continuum description for the transition between the helicoid and spiral ribbon structures of chiral materials. At a critical value of the ratio between the bending and stretching moduli, the Föppl-von Kármán number, we encounter a continuous buckling transition from a straight helicoid to a spiral ribbon. Two of the three persistence lengths of the ribbon become very short at the transition point, indicating strong thermal shape fluctuations. The transition is discontinuous if the ribbon width is treated as a free thermodynamic variable.

Physics of RecA-mediated homologous recognition

To accomplish its DNA strand exchange activities, the Escherichia coli protein RecA polymerizes onto DNA to form a stiff helical nucleoprotein filament within which the DNA is extended by 50%. Homology search and recognition occurs between ssDNA within the filament and an external dsDNA molecule. We show that stretching the internal DNA greatly enhances homology recognition by increasing the probability that the homologous regions of a stretched DNA molecule and a parallel, unstretched DNA molecule will be "in register" at some position. We also show that the stretching and stiffness of the filament act together to ensure that initiation of homologous exchange between the substrate DNA molecules at one position precludes initiation of homologous exchange at any other position. This prevents formation of multiple exchange site "topological traps" which would prevent completion of the exchange reaction and resolution of the products.

Icosahedral packing of RNA viral genomes

Many spherelike RNA viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph-theoretical constraints forbid exact realization of icosahedral symmetry. This paper explores the consequences of graph-theoretical constraints on quasi-icosahedral genome structures. A key result is the prediction that the genome organization is a Hamiltonian path or cycle and that the associated assembly scenario of such single-stranded spherelike RNA viruses resembles that of cylindrical RNA viruses, such as tobacco mosaic viruses.

Charge transfer, symmetry, and dissipation in donor-acceptor molecules

We study charge transfer between donor-acceptor molecules subject to a mirror symmetry constraint in the presence of a dissipative environment. The symmetry requirement leads to the breakdown of the standard single reaction coordinate description, and to a new charge transfer model, in the limit of low temperature, based on two independent reaction coordinates of equal relevance. We discuss implications of these results to charge transfer between DNA base pairs, whose geometrical configuration is modified by the addition of the migrating charge in conformity with the discussed symmetry constraint.

The nuclear pore complex mystery and anomalous diffusion in reversible gels

The exchange of macromolecules between the cytoplasm and the nucleus of eukaryotic cells takes place through the nuclear pore complex (NPC), which contains a selective permeability barrier. Experiments on the physical properties of this barrier appear to be in conflict with current physical understanding of the rheology of reversible gels. This paper proposes that the NPC gel is anomalous and characterized by connectivity fluctuations. It develops a simplified model to demonstrate the possibility of enhanced diffusion constants of macromolecules trapped in such a gel.

Cavitation of Langmuir monolayers

Cavitation in liquid expanded and liquid condensed Langmuir monolayers induced by laser heating or microbubble coalescence is studied experimentally using fluorescence and Brewster angle microscopy. The kinetics of hole closure of two-dimensional (2D) gaseous cavitation bubbles exhibits a decelerated dynamics for cavities surrounded by a liquid expanded phase and an accelerated dynamics for cavities in a liquid condensed phase. Most of the cavities in liquid condensed phases possess a nonconvex shape and do not close. The results are compared with theoretical predictions derived for 2D cavitation of liquid monolayers of different surface shear viscosities, and for solid monolayers with diffusive flux of vacancies and interstitials. While part of the theory is in qualitative agreement with the experiment, the experimentally observed hole persistence within the liquid condensed phases and the hole closure within liquid expanded phases remains to be explained. The technique of microbubble coalescence might be particularly useful for the study of the rheological properties of hexatic phases.

Helfrich repulsion and dynamical phase separation of multicomponent lipid bilayers

Thermal fluctuations of surfactant bilayers in an aqueous solution produce an effective, long-range repulsion that can lead to a continuous unbinding transition. We report on an optical interferometry study of the thermal fluctuations of multicomponent bilayers close to the unbinding transition. We find that, in contrast to the case of single-component bilayers, the thermal fluctuation spectrum of multicomponent bilayers does not agree with a continuous unbinding transition but instead indicates the proximity of an unbinding tricritical point.

Mechanical force generation by G proteins

GTP-hydrolyzing G proteins are molecular switches that play a critical role in cell signaling processes. Here we use molecular dynamics simulations to show that Ras, a monomeric G protein, can generate mechanical force upon hydrolysis. The generated force levels are comparable to those produced by ATP-hydrolyzing motor proteins, consistent with the structural similarities of the catalytic region of motor proteins and G proteins. The force transduction mechanism is based on an irreversible structural change, produced by the hydrolysis, which triggers thermal switching between force-generating substates through changes in the configurational space of the protein.

Effects of torsional strain on thermal denaturation of DNA

A class of simple statistical mechanical models for DNA melting, first proposed by Poland and Scheraga, has been demonstrated to exhibit a first or second order thermodynamic singularity, notwithstanding the intrinsic one-dimensional nature of the problem. In the present paper we consider the case of circular DNA and show that the inclusion of twist elastic energy in the Poland-Scheraga models leads either to suppression of the thermodynamic singularity or to a weak, third order singularity. Such behavior may also be present in linear DNA under mechanical influences that preclude the release of torsional strain.

Liquid crystals of polyelectrolyte networks

The Onsager theory of nematic liquid crystals is extended to rigid polyelectrolytes cross-linked by polyvalent ions. Recent synchrotron x-ray diffraction experiments showed that dilute, birefringent networks are formed under these conditions. The application of Onsager theory to this system leads to the prediction of the existence of a range of exotic mesophases such as the "cubatic," the "tetratic," and the "trigatic." The exotic network phases appear on the border of regions of phase coexistence of network phase with isotropic material (at low polyvalent ion concentration) and with dense bundles (at high polyvalent ion concentration).

DNA folding: structural and mechanical properties of the two-angle model for chromatin

We present a theoretical analysis of the structural and mechanical properties of the 30-nm chromatin fiber. Our study is based on the two-angle model introduced by Woodcock et al. (Woodcock, C. L., S. A. Grigoryev, R. A. Horowitz, and N. Whitaker. 1993. Proc. Natl. Acad. Sci. USA. 90:9021-9025) that describes the chromatin fiber geometry in terms of the entry-exit angle of the nucleosomal DNA and the rotational setting of the neighboring nucleosomes with respect to each other. We analytically explore the different structures that arise from this building principle, and demonstrate that the geometry with the highest density is close to the one found in native chromatin fibers under physiological conditions. On the basis of this model we calculate mechanical properties of the fiber under stretching. We obtain expressions for the stress-strain characteristics that show good agreement with the results of recent stretching experiments (Cui, Y., and C. Bustamante. 2000. Proc. Natl. Acad. Sci. USA. 97:127-132) and computer simulations (Katritch, V., C. Bustamante, and W. K. Olson. 2000. J. Mol. Biol. 295:29-40), and which provide simple physical insights into correlations between the structural and elastic properties of chromatin.