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.