Unzipping DNA from the condensed globule state-effects of unraveling

We have studied theoretically the unzipping of a double-stranded DNA from a condensed globule state by an external force. At constant force, we found that the double-stranded DNA unzips an at critical force Fc and the number of unzipped monomers M goes as M approximately (Fc - F)-3, for both the homogeneous and heterogeneous double-stranded DNA sequence. This is different from the case of unzipping from an extended coil state in which the number of unzipped monomers M goes as M approximately (Fc - F)-chi, where the exponent chi is either 1 or 2 depending on whether the double-stranded DNA sequence is homogeneous or heterogeneous, respectively. In the case of unzipping at constant extension, we found that for a double-stranded DNA with a very large number N of base pairs, the force remains almost constant as a function of the extension, before the unraveling transition, at which the force drops abruptly to zero. Right at the unraveling transition, the number of base pairs remaining in the condensed globule state is still very large and goes as N(3/4), in agreement with theoretical predictions of the unraveling transition of polymers stretched by an external force.     

Assembly of Collagen Matrices as a Phase Transition Revealed by Structural and Rheologic Studies

We have studied the structural and viscoelastic properties of assembling networks of the extracellular matrix protein type-I collagen by means of phase contrast microscopy and rotating disk rheometry. The initial stage of the assembly is a nucleation process of collagen monomers associating to randomly distributed branched clusters with extensions of several microns. Eventually a sol-gel transition takes place, which is due to the interconnection of these clusters. We analyzed this transition in terms of percolation theory. The viscoelastic parameters (storage modulus G′ and loss modulus G″) were measured as a function of time for five different frequencies ranging from ω = 0.2 rad/s to 6.9 rad/s. We found that at the gel point both G′ and G″ obey a scaling law , with the critical exponent Δ = 0.7 and a critical loss angle being independent of frequency as predicted by percolation theory. Gelation of collagen thus represents a second order phase transition.     

A Three-State Model with Loop Entropy for the Overstretching Transition of DNA

We introduce a three-state model for a single DNA chain under tension that distinguishes among B-DNA, S-DNA, and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ∼ -c ln n for the entropy of a loop of length n. Force extension curves are derived exactly by employing a generalized Poland-Scheraga approach and then compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows us to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy (entering as a domain-wall energy between paired and unpaired bases) and the loop entropy are separated. Therefore, we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.     

Effect of ionic strength of a solution on the protonation of DNA molecule

The influence of the ionic strength of solution on the DNA molecule protonation was studied by means of circular dichroism (CD), spectrophotometric and potentiometric titration methods over a wide range of the supporting electrolyte concentrations [( NaCl] = 0.0005 divided by 4 M). Consideration of the obtained CD spectra shown that the acidation of the solution induces two cooperative structural transitions in the double stranded DNA molecule in the pre-denaturation pH region. Further decrease in the solution pH results in acidic melting of the DNA molecule. Analysis of the potentiometric data shows that diluted DNA solutions exhibit marked buffer capacity at pH greater than 4.2. A concept of local pH dependent on the electrostatic potential in the vicinity of the polyion was used for interpreting the obtained results. A phase diagram, which describes the polymorphic transformations of the protonated macromolecule, was constructed in terms of pHloc and -log[Na+]. Consideration of this phase diagram allows to hypothesize that: 1) in the neutral diluted DNA solution with a very low supporting electrolyte content the macromolecule exists in a polymorphic state; 2) at [NaCl] greater than or equal to 0.001 M the acid-base equilibrium in the DNA molecule is invariant in respect to the ionic strength of the solution.     

Single-molecule mechanical identification and sequencing

High-throughput, low-cost DNA sequencing has emerged as one of the challenges of the postgenomic era. Here we present the proof of concept for a single-molecule platform that allows DNA identification and sequencing. In contrast to most present methods, our scheme is not based on the detection of the fluorescent nucleotides but on DNA hairpin length. By pulling on magnetic beads tethered by a DNA hairpin to the surface, the molecule can be unzipped. In this open state it can hybridize with complementary oligonucleotides, which transiently block the hairpin rezipping when the pulling force is reduced. By measuring from the surface to the bead of a blocked hairpin, one can determine the position of the hybrid along the molecule with nearly single-base precision. Our approach can be used to identify a DNA fragment of known sequence in a mix of various fragments and to sequence an unknown DNA fragment by hybridization or ligation.     

Intraspecific temperature dependence of the scaling of metabolic rate with body mass in fishes and its ecological implications

Metabolism constitutes a fundamental property of all organisms. Metabolic rate is commonly described to scale as a power function of body size and exponentially with temperature, thereby treating the effects of body size and temperature independently. Mounting evidence shows that the scaling of metabolic rate with body mass itself depends on temperature. Across‐species analyses in fishes suggest that the mass‐scaling exponent decreases with increasing temperature. However, whether this relationship holds at the within‐species level has rarely been tested. Here, we re‐analyse data on the metabolic rates of four freshwater fish species, two coregonids and two cyprinids, that cover wide ranges of body masses and their naturally experienced temperatures. We show that the standard metabolic rate of the coregonids is best fit when accounting for a linear temperature dependence of the scaling of metabolic rate with body mass, whereas a constant mass‐scaling exponent is supported in case of the cyprinids. Our study shows that phenotypic responses to temperature can result in temperature‐dependent scaling relationships at the species level and that these responses differ between taxa. Together with previous findings, these results indicate that evolutionarily adaptive and phenotypically plastic responses to temperature affect the scaling of metabolic rate with body mass in fishes.     

Structural support, not insulation, is the primary driver for avian cup-shaped nest design

The nest micro-environment is a widely studied area of avian biology, however, the contribution of nest conductance (the inverse of insulation) to the energetics of the incubating adult and offspring has largely been overlooked. Surface-specific thermal conductance (W °C(-1) cm(-2)) has been related to nest dimensions, wall porosity, height above-ground and altitude, but the most relevant measure is total conductance (G, W °C(-1)). This study is the first to analyse conductance allometrically with adult body mass (M, g), according to the form G = aM(b). We propose three alternative hypotheses to explain the scaling of conductance. The exponent may emerge from: heat loss scaling (M(0.48)) in which G scales with the same exponent as thermal conductance of the adult bird, isometric scaling (M(0.33)) in which nest shape is held constant as parent mass increases, and structural scaling (M(0.25)) in which nests are designed to support a given adult mass. Data from 213 cup-shaped nests, from 36 Australian species weighing 8-360 g, show conductance is proportional to M(0.25). This allometric exponent is significantly different from those expected for heat loss and isometric scaling and confirms the hypothesis that structural support for the eggs and incubating parent is the primary factor driving nest design.     

PHYLOGENETICALLY INFORMED ANALYSIS OF THE ALLOMETRY OF MAMMALIAN BASAL METABOLIC RATE SUPPORTS NEITHER GEOMETRIC NOR QUARTER-POWER SCALING

The form of the relationship between the basal metabolic rate (BMR) and body mass (M) of mammals has been at issue for almost seven decades, with debate focusing on the value of the scaling exponent ( b , where BMR ∝ M^b ) and the relative merits of b = 0.67 (geometric scaling) and b = 0.75 (quarter-power scaling). However, most analyses are not phylogenetically informed (PI) and therefore fail to account for the shared evolutionary history of the species they consider. Here, we reanalyze the most rigorously selected and comprehensive mammalian BMR dataset presently available, and investigate the effects of data selection and phylogenetic method (phylogenetic generalized least squares and independent contrasts) on estimation of the scaling exponent relating mammalian BMR to M. Contrary to the results of a non-PI analysis of these data, which found an exponent of 0.67–0.69, we find that most of the PI scaling exponents are significantly different from both 0.67 and 0.75. Similarly, the scaling exponents differ between lineages, and these exponents are also often different from 0.67 or 0.75. Thus, we conclude that no single value of b adequately characterizes the allometric relationship between body mass and BMR.     

Respiration in the burrowing brittlestar, Hemipholis elongata say (Echinodermata, Ophiuroidea): a study of the effects of environmental variables on oxygen uptake

The burrowing brittlestar Hemipholis elongata (Say) maintains a constant M(O2)of 3.79+/-1.47 micromol O(2) g(-1) h(-1) (for 0.2-0.3 g animals, mean+/-S.D., n=7), measured in the burrow, over a broad range of PO(2). Below the critical PO(2) of 37 mm Hg, M(O(2)) becomes dependent on the oxygen tension. M(O2) is a function of the size of H. elongata; the scaling exponent is 0. 83 and is similar to those reported for other echinoderms. The M(O2) of H. elongata is unaffected by removal from the burrow, by hypercapnia, by exposure to hydrogen sulfide, or by temperature change in the range from 20 to 32 degrees C. The relative insensitivity of H. elongata to these factors may be an adaptation to life in the highly variable estuarine and tidal creek environments where the animals are frequently found.     

Geometrical constraints in the scaling relationships between genome size, cell size and cell cycle length in herbaceous plants

Plant nuclear genome size (GS) varies over three orders of magnitude and is correlated with cell size and growth rate. We explore whether these relationships can be owing to geometrical scaling constraints. These would produce an isometric GS-cell volume relationship, with the GS-cell diameter relationship with the exponent of 1/3. In the GS-cell division relationship, duration of processes limited by membrane transport would scale at the 1/3 exponent, whereas those limited by metabolism would show no relationship. We tested these predictions by estimating scaling exponents from 11 published datasets on differentiated and meristematic cells in diploid herbaceous plants. We found scaling of GS-cell size to almost perfectly match the prediction. The scaling exponent of the relationship between GS and cell cycle duration did not match the prediction. However, this relationship consists of two components: (i) S phase duration, which depends on GS, and has the predicted 1/3 exponent, and (ii) a GS-independent threshold reflecting the duration of the G1 and G2 phases. The matches we found for the relationships between GS and both cell size and S phase duration are signatures of geometrical scaling. We propose that a similar approach can be used to examine GS effects at tissue and whole plant levels.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Critical jump sizes in DNA-protein interactions

Interaction of a protein molecule with a specific-site on the DNA lattice can be modeled as an unbiased random jump process. Here we show that there exists a critical jump size (kc) beyond which site-specific association of a protein molecule with a DNA lattice cannot be facilitated. The maximum achievable association rate is predicted to be approximately 10(10) mol-1 s-1. This critical jump size scales with the total length of DNA lattice (N) as kc proportional, variantN2/3. Beyond kc the mean first passage time MFPT (denoted as T) required for the protein molecule to target the specific-site follows a linear scaling law as T proportional, variantN rather than the usual T proportional, variantN2 scaling law. On the basis of these results we argue that the evolution of the super coiled structures of the genomic DNA must be a consequence of the existence of this critical jump sizes. We finally show that the random jump method of searching for the specific-site by the protein molecule on the DNA lattice itself introduce an abstract linear type potential favoring the site-specific association rate.     

Evolution of opinions on social networks in the presence of competing committed groups

Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the group''s opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about of the population (with the findings being qualitatively similar for sparse networks as well). Here we study the more general case of opinion evolution when two groups committed to distinct, competing opinions and , and constituting fractions and of the total population respectively, are present in the network. We show for stylized social networks (including Erdös-Rényi random graphs and Barabási-Albert scale-free networks) that the phase diagram of this system in parameter space consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. These two regions are separated by two fold-bifurcation (spinodal) lines which meet tangentially and terminate at a cusp (critical point). We provide further insights to the phase diagram and to the nature of the underlying phase transitions by investigating the model on infinite (mean-field limit), finite complete graphs and finite sparse networks. For the latter case, we also derive the scaling exponent associated with the exponential growth of switching times as a function of the distance from the critical point.     

A Linear Biopolymer in the Vicinity of the Triple Point The Homopolymer Case

Abstract

This is a theoretical study of a situation where each residue of a linear biopolymer may adopt one of three conformational states. Such a situation exists in the case of DNA, since it may be in helical A, B,…, Z forms as well as the melted state. In the vicinity of the triple point in the phase diagram three states, e.g. the A form, the B form and the denatured state, co-exist within a given molecule. We present an exact analytical solution of the simplest homopolymer model. Theory predicts that the presence of two helical states in one molecule should affect the helix-coil transition in two ways. The melting temperature experiences an upward shift and the melting range width is increased, by a factor of √2 as a maximum.     

Competition between supercoils and toroids in single molecule DNA condensation

The condensation of free DNA into toroidal structures in the presence of multivalent ions and polypeptides is well known. Recent single molecule experiments have shown that condensation into toroids occurs even when the DNA molecule is subjected to tensile forces. Here we show that the combined tension and torsion of DNA in the presence of condensing agents dramatically modifies this picture by introducing supercoiled DNA as a competing structure in addition to toroids. We combine a fluctuating elastic rod model of DNA with phenomenological models for DNA interaction in the presence of condensing agents to compute the minimum energy configuration for given tension and end-rotations. We show that for each tension there is a critical number of end-rotations above which the supercoiled solution is preferred and below which toroids are the preferred state. Our results closely match recent extension rotation experiments on DNA in the presence of spermine and other condensing agents. Motivated by this, we construct a phase diagram for the preferred DNA states as a function of tension and applied end-rotations and identify a region where new experiments or simulations are needed to determine the preferred state.     

Scaling analysis of the concentration dependence on elasticity of agarose gel

Since the critical exponent of the elastic modulus is related to the spatial dimension and the critical exponent of the correlation length, depending on the characteristics of elasticity, we experimentally evaluated both the elastic modulus of a sol-gel transition system and also the correlation length. We could determine the correlation length of agarose gel by the dynamic light scattering method; it was well described by the power law as a function of the deviation from the sol-gel transition point. Three scaling laws between the critical exponent of the correlation length (v) and that of the elastic shear modulus (t) were compared, and the critical exponent of the elastic modulus was described by the equation of de Gennes expression (t=1+v(d-2), where d is the spatial dimension). This result suggests that agarose fibers are stiff enough to show scalar elasticity.     

Osmotic observations on chemically cross-linked DNA gels in physiological salt solutions

Neutralized DNA gels exhibit a reversible volume transition when CaCl2 is added to the surrounding aqueous NaCl solution. In this paper, a systematic study of the osmotic and mechanical properties of Na-DNA gels is presented to determine, qualitatively and quantitatively, the effect of Ca-Na exchange on the volume transition. It is found that in the absence of CaCl2 the DNA gels exhibit osmotic behavior similar to that of DNA solutions with reduced DNA concentration. At low CaCl2 concentration, the gel volume gradually decreases as the CaCl2 concentration increases. Below the volume transition, the concentration dependence of the osmotic pressure can be satisfactorily described by a Flory-Huggins-type equation. The Ca2+ ions primarily affect the third-order interaction term, which strongly increases upon the introduction of Ca2+ ions. The second-order interaction term only slightly depends on the CaCl2 concentration. It is demonstrated that DNA gels cross-linked in solutions containing CaCl2 exhibit reduced osmotic mixing pressure. The concentration dependence of the shear modulus of DNA gels can be described by a single power law. The scaling exponent is practically independent of the NaCl concentration and increases with increasing CaCl2 content.     

Pre-power stroke cross bridges contribute to force during stretch of skeletal muscle myofibrils

When activated skeletal muscle is stretched, force increases in two phases. This study tested the hypothesis that the increase in stretch force during the first phase is produced by pre-power stroke cross bridges. Myofibrils were activated in sarcomere lengths (SLs) between 2.2 and 2.5 microm, and stretched by approximately 5-15 per cent SL. When stretch was performed at 1 microms-1SL-1, the transition between the two phases occurred at a critical stretch (SLc) of 8.4+/-0.85 nm half-sarcomere (hs)-1 and the force (critical force; Fc) was 1.62+/-0.24 times the isometric force (n=23). At stretches performed at a similar velocity (1 microms-1SL-1), 2,3-butanedione monoxime (BDM; 1 mM) that biases cross bridges into pre-power stroke states decreased the isometric force to 21.45+/-9.22 per cent, but increased the relative Fc to 2.35+/-0.34 times the isometric force and increased the SLc to 14.6+/-0.6 nm hs-1 (n=23), suggesting that pre-power stroke cross bridges are largely responsible for stretch forces.     

DNA length tunes the fluidity of DNA-based condensates

Living organisms typically store their genomic DNA in a condensed form. Mechanistically, DNA condensation can be driven by macromolecular crowding, multivalent cations, or positively charged proteins. At low DNA concentration, condensation triggers the conformational change of individual DNA molecules into a compacted state, with distinct morphologies. Above a critical DNA concentration, condensation goes along with phase separation into a DNA-dilute and a DNA-dense phase. The latter DNA-dense phase can have different material properties and has been reported to be rather liquid-like or solid-like depending on the characteristics of the DNA and the solvent composition. Here, we systematically assess the influence of DNA length on the properties of the resulting condensates. We show that short DNA molecules with sizes below 1 kb can form dynamic liquid-like assemblies when condensation is triggered by polyethylene glycol and magnesium ions, binding of linker histone H1, or nucleosome reconstitution in combination with linker histone H1. With increasing DNA length, molecules preferentially condense into less dynamic more solid-like assemblies, with phage λ-DNA with 48.5 kb forming mostly solid-like assemblies under the conditions assessed here. The transition from liquid-like to solid-like condensates appears to be gradual, with DNA molecules of roughly 1–10 kb forming condensates with intermediate properties. Titration experiments with linker histone H1 suggest that the fluidity of condensates depends on the net number of attractive interactions established by each DNA molecule. We conclude that DNA molecules that are much shorter than a typical human gene are able to undergo liquid-liquid phase separation, whereas longer DNA molecules phase separate by default into rather solid-like condensates. We speculate that the local distribution of condensing factors can modulate the effective length of chromosomal domains in the cell. We anticipate that the link between DNA length and fluidity established here will improve our understanding of biomolecular condensates involving DNA.