Temperature Dependence of the DNA Double Helix at the Nanoscale: Structure,Elasticity, and Fluctuations

Biological organisms exist over a broad temperature range of −15°C to +120°C, where many molecular processes involving DNA depend on the nanoscale properties of the double helix. Here, we present results of extensive molecular dynamics simulations of DNA oligomers at different temperatures. We show that internal basepair conformations are strongly temperature-dependent, particularly in the stretch and opening degrees of freedom whose harmonic fluctuations can be considered the initial steps of the DNA melting pathway. The basepair step elasticity contains a weaker, but detectable, entropic contribution in the roll, tilt, and rise degrees of freedom. To extend the validity of our results to the temperature interval beyond the standard melting transition relevant to extremophiles, we estimate the effects of superhelical stress on the stability of the basepair steps, as computed from the Benham model. We predict that although the average twist decreases with temperature in vitro, the stabilizing external torque in vivo results in an increase of ∼1°/bp (or a superhelical density of Δσ ?  + 0.03) in the interval 0–100°C. In the final step, we show that the experimentally observed apparent bending persistence length of torsionally unconstrained DNA can be calculated from a hybrid model that accounts for the softening of the double helix and the presence of transient denaturation bubbles. Although the latter dominate the behavior close to the melting transition, the inclusion of helix softening is important around standard physiological temperatures.     

Projected US distributions of transgenic and wildtype zebra danios, Danio rerio, based on temperature tolerance data

A genetically modified version of the south Asian, zebra danio, Danio rerio, a common aquarium fish, has become the first transgenic pet sold in the USA. Mean chronic lethal maxima of wildtype (39.8 °C, n=16$n=16$) and transgenic (39.3 °C, n=10$n=10$) zebra danios initially acclimated to 30 °C were statistically (but not dramatically) different as were mean chronic lethal minima of wildtype (5.3 °C, n=16$n=16$) and transgenic (5.6 °C, n=20$n=20$) zebra danios initially acclimated to 20 °C. These temperature tolerance values were used to estimate potential geographic distributions of the two varieties in the USA. Distributions of these D. rerio varieties in the USA should not be limited by their upper temperature tolerances, and low-temperature tolerance data suggest that both varieties are capable of overwintering in some southern and western US waters.     

Ionic microenvironmental effects on triplex DNA stabilization: Cationic counterion effects on poly(dT)·poly(dA)·poly(dT)

The structure and conformation of nucleic acids are influenced by metal ions, polyamines, and the microenvironment. In poly(purine) · poly(pyrimidine) sequences, triplex DNA formation is facilitated by metal ions, polyamines and other ligands. We studied the effects of mono- and di-valent metal ions, and ammonium salts on the stability of triple- and double-stranded structures formed from poly(dA) and poly(dT) by measuring their respective melting temperatures. In the presence of metal ions, the absorbance versus temperature profile showed two transitions: T_m1 for triplex to duplex and single stranded DNA, and T_m2 for duplex DNA melting to single stranded DNA. Monovalent cations (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺ and ₄NH⁺${{\text{NH}}_4}^{+}$) promoted triplex DNA at concentrations ≥150 mM. T_m1 varied from 49.8 °C in the presence of 150 mM Li⁺ to 30.6 °C in the presence of 150 mM K⁺. ₄NH⁺${{\text{NH}}_4}^{+}$ was very effective in stabilizing triplex DNA and its efficacy decreased with increasing substitution of the hydrogen atoms with methyl, ethyl, propyl and butyl groups. As in the case of monovalent cations, a concentration-dependent increase in T_m1 was observed with divalent ions and triplex DNA stabilization decreased in the order: Mg²⁺ > Ca²⁺ > Sr²⁺ > Ba²⁺. All positively charged cations increased the melting temperature of duplex DNA. Values of Δn (number of ions released) on triplex DNA melting were 0.46 ± 0.06 and 0.18 ± 0.02, respectively, for mono- and di-valent cations, as calculated from 1/T_m1 versus ln[M^+,2+] plots. The corresponding values for duplex DNA were 0.25 ± 0.02 and 0.12 ± 0.02, respectively, for mono- and di-valent cations. Circular dichroism spectroscopic studies showed distinct conformational changes in triplex DNA stabilized by alkali metal and ammonium ions. Our results might be useful in developing triplex forming oligonucleotide based gene silencing techniques.     

DNA,Flexibly Flexible

Investigators have constructed dsDNA molecules with several different base modifications and have characterized their bending and twisting flexibilities using atomic force microscopy, DNA ring closure, and single-molecule force spectroscopy with optical tweezers. The three methods provide persistence length measurements that agree semiquantitatively, and they show that the persistence length is surprisingly similar for all of the modified DNAs. The circular dichroism spectra of modified DNAs differ substantially. Simple explanations based on base stacking strength, polymer charge, or groove occupancy by functional groups cannot explain the results, which will guide further high-resolution theory and experiments.Real double-stranded DNA molecules differ from the idealized zero-Kelvin A, B, and Z forms. They can adopt deformed average conformations, as in bent A-tract DNA or protein-DNA complexes. The path of the DNA helix axis also varies due to thermal energy, so at very long lengths DNA behaves as a random coil. The term “long lengths” is relative to the persistence length P of the wormlike chain model. P is the average offset of the end of a chain along its initial direction, or alternatively the length over which the unit vectors μ1→ and μ2→ tangent to the helix axis lose colinearity according to〈μ1→⋅μ2→〉=〈cosθ〉=e−d12/P,where d₁₂ is the contour length from point 1 to point 2, as in Fig. 1. P can be measured by hydrodynamics (1), atomic force microscopy (AFM) (2), DNA ring closure (3) or protein-DNA looping (4), tethered particle microscopy (5), or single-molecule optical tweezers experiments (6). The long-range loss of memory of DNA direction grows out of local variations in the helix axis direction specified by roll, tilt, and twist angles that parameterize changes in the helix axis direction. For harmonic bending potentials, the bending persistence length is related to roll and tilt according toσroll2+σtilt2=2ℓ/P,where ℓ = 3.4 Å, so for P ∼ 50 nm (147 bp) the average standard deviations in the roll and tilt angles σ_roll and σ_tilt are ∼4.7°, although in real DNA, roll varies more than tilt. Similar relationships hold for twist flexibility (7).Open in a separate windowFigure 1The base modifications studied by Peters et al. (13,14) affect both Watson-Crick hydrogen bonding and groove occupancy. They used AFM, DNA ring closure, single-molecule force spectroscopy, and circular dichroism spectroscopy (not shown) to characterize the resulting changes in bending and twisting flexibility. DNA molecules are not shown to scale. To see this figure in color, go online.DNA flexibility can be studied at contour length scales from Ångstroms to microns. Flexibility at the atomic scale accessed by nuclear magnetic resonance, x-ray crystallography, cryo-electron microscopy, and molecular dynamics simulations (8) refers to many aspects of conformational variability. One active thread of research at this scale concerns interconversion among helical forms, base flipping, DNA kinking, changes in backbone torsion angles, and the sequence dependence of all of these local properties. Local fluctuations in the basepair roll, tilt, and twist angles do seem to predict the correct long-range behavior (9). A second thread asks whether the wormlike chain model holds at DNA lengths shorter than P (2,10); the active controversy concerning enhanced bendability at short lengths has recently been reviewed by Vologodskii and Frank-Kamenetskii (11). A third thread asks whether we can understand the underlying biophysical causes of long-range DNA flexibility. These presumably include base stacking, electrostatic repulsion along the backbone, changes in the counterion atmosphere (12), occupancy of the major and minor grooves by functional groups, conformational entropy, the strength of Watson-Crick hydrogen bonding, and water structure. Helical polymorphisms and the junctions between polymorphs presumably affect the sequence dependence of the persistence length.Peters et al. (13,14) have attempted to understand bending and twisting flexibility by characterizing a variety of modified nucleic acids using DNA ring closure, AFM, and optical tweezer methods, sketched in Fig. 1. In previous work (13), they used ring closure to show that major groove substituents that alter the charge on the polymer do not have substantial effects on the bending persistence length, and that the effects were not correlated in an obvious way to the stacking propensity of the modified bases. The work described in this issue of the Biophysical Journal (14) uses all three methods to demonstrate that DNA with 2-amino-adenosine (a.k.a., 2,6-diaminopurine) substituted for adenosine has an increased persistence length, whereas inosine substitution for guanosine reduces the persistence length, as would be expected if groove occupancy (or the number of Watson-Crick hydrogen bonds) affects flexibility. However, the authors did one experiment too many—when they measured the effects of the earlier major groove substituents (13) using AFM, the correlation with groove occupancy disappeared. This could be because changes in helical geometry, as evidenced by the circular dichroism spectroscopy also reported in the article, alter the grooves sufficiently to prevent a straightforward connection to flexibility.The magnitude of the effect of base modifications on P is the largest for the optical tweezers and the smallest for DNA ring closure, showing that no more than one of the experiments is perfect. The Supporting Material for both articles (13,14) offers valuable resources for the careful evaluation of experimental results and possible sources of error within and between experiments. For example, the DNA lengths and the ionic conditions required by the different methods differ. Ring closure results depend critically on the purity of the DNA and appropriate ligation conditions. Analysis of AFM results averaged several different statistical measures of decaying angular correlations and end-to-end distance, which did not individually always agree. In force spectroscopy there are variations in the bead attachment for each molecule, errors in the stretch modulus can affect the measured persistence length, force can induce DNA melting, and very few molecules can be observed. Rare kinking events proposed to explain enhanced bendability should affect the cyclization experiment most markedly; no evidence for enhanced flexibility was seen. Finally, Peters et al. (14) have observed that DNA twist and twisting flexibility seem to be more sensitive than the persistence length to base modifications.Taken as a whole, this extremely thorough series of experiments shows that we still do not understand the fundamental origins of the remarkable stiffness of double-stranded DNA. There may be compensating effects that make the dissection difficult. For example, changing the charge on the polymer may induce a corresponding adjustment in the counterion condensation atmosphere, leading to a relatively constant residual charge. Groove substituents that enhance basepair stability could enhance bendability for steric reasons. Stacking thermodynamics may not change very much for the very small bend angles at any individual basepair. Locally stiff regions may introduce nearby junctions that are flexible.The stiffness of DNA relative to other biopolymers inspired the development of DNA nanotechnology (although that field has adopted bridged synthetic constructs that are even more rigid). Further research on the biophysics, and specifically the long-range mechanical properties of DNA, will be essential as we build better models of DNA in the cell, which has evolved many proteins that act to increase apparent flexibility. The various aspects of DNA flexibility influence the protein-DNA complexes that mediate DNA’s informational role, the induction of and responses to supercoiling used for long-range communication among sites (15), and chromosome structure and genome organization.     

The conformation and orientation of copper(II)-bleomycin intercalated with DNA

EPR data are used to describe the conformation and identity of the atoms coordinated to Cu(II) in Cu(II)-bleomycin bound to oriented DNA fibers. The fibers were slowly drawn from viscous solutions of Cu(II)-bleomycin-DNA containing one Cu(II)-bleomycin to 200 basepairs. EPR measurements were made at room temperature and 90 K for different orientations of the external magnetic field with respect to the helical axes of the fibers. The g-values ($\text{g}{}_{\mathrm{}}\text{=2.21}$, g_⊥ =2.04) and the hyperfine constant ($\text{A}{}_{\mathrm{}}\text{=175}\text{G}$) are consistent with values expected for Cu(II) chelated to a square planar array of ligands. In the oriented fibers, the square planar arrays do not all have the same orientations with respect to the fiber axes. At room temperature the chelated ions have rotational freedom in which the normal to the planar array has almost complete freedom of rotation about axes perpendicular to the DNA fiber axes. The normal maintains an angle of 75° with respect to the axis, in the plane of the basepair, about which it rotates. Nine superhyperfine peaks on the high field side of the EPR spectrum were partially resolved. The number and splitting (12 G) of these superhyperfine peaks indicate that four nitrogen atoms are chelated to Cu(II) in a square planar array. These data on Cu(II)-bleomycin bound to DNA give information on the orientation of the metal-containing portion of bleomycin which lies outside the double helix.     

Effects of lycopene supplementation on antioxidant status,oxidative stress,performance and carcass characteristics in heat-stressed Japanese quail

Lycopene, a carotenoid present predominantly in tomatoes, is one of the most efficient antioxidants. This experiment was conducted to evaluate the effects of dietary lycopene supplementation on performance, carcass characteristics, biomarkers of oxidative stress (malondialdehyde (MDA) and homocysteine), and concentrations of vitamins C, E, A, cholesterol, triglyceride, and glucose in Japanese quails (Coturnix coturnix Japonica) exposed to high-ambient temperature of 34 °C. Two hundred and forty Japanese quails (10 day-old) were randomly assigned to eight treatment groups consisting of 10 replicates of three birds. The birds were kept at a temperature-controlled room at 22 °C (Thermoneutral, TN groups) or 34 °C (for 12 h/day; 09.00 am–05.00 pm; Heat stress, HS groups). Birds were fed either a basal (control) diet (TN and HS) or the basal diet supplemented with 50, 100 or 200 mg of lycopene/kg of diet. Lycopene supplementation linearly increased feed intake (P=0.05$P=0.05$), live weight gain (P=0.01$P=0.01$), feed efficiency (P=0.01$P=0.01$) and cold carcass weight (P=0.01$P=0.01$) and yield (P=0.05$P=0.05$) under heat stress conditions but did not show the same effect at thermoneutral conditions (P>0.05$P>0.05$). The interaction Serum vitamin C, E, and A (P=0.01$P=0.01$) concentrations increased linearly in birds reared at high temperature while non-significant changes occurred at TN groups. Homocysteine level in serum and malondialdehyde (MDA) levels in serum, liver, and heart (P=0.001$P=0.001$) linearly decreased in all birds of both TN and HS groups as dietary lycopene supplementation increased. Heat stress-induced increase in serum cholesterol (P=0.01$P=0.01$), triglycerides (P=0.05$P=0.05$) and glucose (P=0.01$P=0.01$) concentrations were linearly reversed by lycopene supplementation. Supplementation of lycopene increased the HDL concentration whereas, the VLDL and LDL concentrations reduced with lycopene supplementation (P=0.01$P=0.01$, linear), particularly at a dietary concentration of 200 mg/kg. Lycopene could not be detected in control birds while a linear increase was observed in the sera of lycopene supplemented birds The results of the study indicate that lycopene supplementation attenuated the increase in oxidative stress and depletion in antioxidants caused by heat stress in Japanese quails.     

Sharp bounds on the relative treatment effect for ordinal outcomes

For ordinal outcomes, the average treatment effect is often ill-defined and hard to interpret. Echoing Agresti and Kateri, we argue that the relative treatment effect can be a useful measure, especially for ordinal outcomes, which is defined as $\gamma =\text{pr}\left\{Y_i\left(1\right)>Y_i\left(0\right)\right\}-\text{pr}\left\{Y_i\left(1\right)<Y_i\left(0\right)\right\}$, with $Y_i\left(1\right)$ and $Y_i\left(0\right)$ being the potential outcomes of unit $i$ under treatment and control, respectively. Given the marginal distributions of the potential outcomes, we derive the sharp bounds on $\gamma ,$ which are identifiable parameters based on the observed data. Agresti and Kateri focused on modeling strategies under the assumption of independent potential outcomes, but we allow for arbitrary dependence.     

Kinetics of H2O2-driven catalysis by a lytic polysaccharide monooxygenase from the fungus Trichoderma reesei

Owing to their ability to break glycosidic bonds in recalcitrant crystalline polysaccharides such as cellulose, the catalysis effected by lytic polysaccharide monooxygenases (LPMOs) is of major interest. Kinetics of these reductant-dependent, monocopper enzymes is complicated by the insoluble nature of the cellulose substrate and parallel, enzyme-dependent, and enzyme-independent side reactions between the reductant and oxygen-containing cosubstrates. Here, we provide kinetic characterization of cellulose peroxygenase (oxidative cleavage of glycosidic bonds in cellulose) and reductant peroxidase (oxidation of the reductant) activities of the LPMO TrAA9A of the cellulose-degrading model fungus Trichoderma reesei. The catalytic efficiency (kcat/Km(H2O2)) of the cellulose peroxygenase reaction (k_cat = 8.5 s⁻¹, and Km(H2O2)=30μM) was an order of magnitude higher than that of the reductant (ascorbic acid) peroxidase reaction. The turnover of H₂O₂ in the ascorbic acid peroxidase reaction followed the ping-pong mechanism and led to irreversible inactivation of the enzyme with a probability of 0.0072. Using theoretical analysis, we suggest a relationship between the half-life of LPMO, the values of kinetic parameters, and the concentrations of the reactants.     

Rectal,telemetry pill and tympanic membrane thermometry during exercise heat stress

We compared the accuracy of an ingestible telemetry pill method of core temperature (T_c) measurement and an infrared tympanic membrane thermometer to values from a rectal thermistor during exercise-induced heat stress. Ten well-trained subjects completed four exercise trials consisting of 40 min constant-load exercise at 63% of maximum work rate followed by a 16.1 km time trial at 30 °C and 70% relative humidity. Temperature at rest was not different between the three methods of T_c measurement (T_re: 37.2±0.3 °C; T_p: 37.2±0.2 °C; T_ty: 37.1±0.3 °C; P=0.40$P=0.40$). Temperature rose continuously during the exercise period (ΔT_re: 2.2±0.5 °C; ΔT_p: 2.2±0.5 °C; ΔT_ty: 1.9±0.5 ±°C and there were no differences between T_re and T_p measurements at any time throughout exercise (P=0.32$P=0.32$). While there were no differences between T_re and T_ty after 10 min (P=0.11$P=0.11$) and 20 min (P=0.06$P=0.06$) of exercise, T_ty was lower than T_re after 30 min of exercise (P<0.01$P<0.01$) and remained significantly lower throughout the remainder of the exercise period. These results demonstrate that the telemetry pill system provides a valid measurement of trunk temperature during rest and exercise-induced thermal strain. T_ty was significantly lower than T_re when temperature exceeded 37.5 °C. However, whether these differences are due to selective brain cooling or imperfections in the tympanic membrane thermometer methodology remains to be determined.     

Analysis of Amylose-borate Interaction by Frontal Gel Filtration

Amylose-borate interaction has been analyzed by frontal gel chromatography, using the constituent velocity data alone. The constituent Velocity equation was reformulated in terms of elution volume for a type of interacting system described by$\text{A}+i\text{B}={\text{AB}}_i(i=1,2,3\dots n)$

Detailed examination of the binding data indicates that, in the complex formation between amylose and borate, this type of equilibria operates predominantly, if not solely. Use of the constituent elution volume equation enabled us, for the first time, to evaluate the association constant (K) and number of binding site pertaining to this system, i.e., K = 4.9 10² and n = 1. There was no evidence indicating the occurrence of the formation of inclusion complex.     

The limitations,dangers, and benefits of simple methods for testing identifiability

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading [1]) have commented on our paper in which we proposed a simple scaling method to test structural identifiability [2]. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries (we indeed indicated but not investigated the importance of generalizing the method to other symmetries). Thus, we agree that our simple method provides a necessary but not sufficient condition for identifiability, and we appreciate their careful analysis and constructive criticism.We nevertheless think that the simple method remains useful because it is so simple. Even for investigators with little training in mathematics, the method provides a necessary condition for structural identifiability that can be derived in a few minutes with pen and paper. Similarly, we have found its pedagogic strength by teaching the method to our own graduate students and colleagues. More advanced methods (such as STRIKE-GOLDD [3,4], COMBOS [5], or SIAN [6]) are typically intimidating for researchers with a background in Biology or Bioinformatics. This simple method can help those practitioners to familiarize themselves with the identifiability problem and better understand their models.Finally, it is worth noting that if scaling invariance is the only symmetry (as it was in all the cases we analyzed), our SIM remains valuable (albeit uncontrolled), and surprisingly effective for a wide variety of problems (as the extensive list collected in the Supplementary Material our paper [2]). We guess that the SIM especially fails when applied to linear models (as more potential rotations of the variables leave the system invariant), and in non-linear scenarios where some parameters are identical. For instance, the FitzHugh-Nagumo model raised by Villaverde and Massonis, x˙1(t)=c(x1(t)−x13(t)3−x2(t)+d),x˙2(t)=1c(x1(t)+a−b·x2(t)),y(t)=x1(t), could have been written as x˙1(t)=λ1x1(t)−λ2x13(t)3−λ3x2(t)+d,x˙2(t)=λ4x1(t)+a−b·x2(t),y(t)=x1(t) where λ₁ = λ₂ = λ₃ = 1/λ₄ = c. One of the reasons why our method fails, in this case, might be these additional symmetries introduced in this more elaborate notation of the model.Hence, it is worth understanding generic conditions under which the SIM method is expected to be fragile, possibly using STRIKE-GOLDD to test large families of nonlinear models.As a final remark, we appreciate that Villaverde and Massonis have shared their source code, so researchers might have a gold standard to test identifiability.     

Kinetics and Energetics of Biomolecular Folding and Binding

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation. The fit yields the key determinants of the folding and binding processes: the intrinsic on-rate and the location and height of the activation barrier.Dynamic processes in living cells are regulated through conformational changes in biomolecules—their folding into a particular shape or binding to selected partners. The ability of biomolecules to fold and to bind enables them to act as switches, assembly factors, pumps, or force- and displacement-generating motors (1). Folding and binding transitions are often hindered by a free energy barrier. Overcoming the barrier requires energy-demanding rearrangements such as displacing water from the sites of native contacts and breaking nonnative electrostatic contacts, as well as loss of configurational entropy. Once the barrier is crossed, the folded and bound states are stabilized by short-range interactions: hydrogen bonds, favorable hydrophobic effects, and electrostatic and van der Waals attractions (2).Mechanistic information about folding and binding processes is detailed in the folding and binding trajectories of individual molecules: observing an ensemble of molecules may obscure the inherent heterogeneity of these processes. Single-molecule trajectories can be induced, and monitored, by applying force to unfold/unbind a molecule and then relaxing the force until folding or binding is observed (3–5) (Fig. 1). Varying the force relaxation rate shifts the range of forces at which folding or binding occurs, thus broadening the explorable spectrum of molecular responses to force and revealing conformational changes that are otherwise too fast to detect. The measured force-dependent kinetics elucidates the role of force in physiological processes (6) and provides ways to control the timescales, and even the fate, of these processes. The force-dependent data also provides a route to understanding folding and binding in the absence of force—by extrapolating the data to zero force via a fit to a theory.Open in a separate windowFigure 1Schematic of the output from a force-relaxation experiment. The applied force is continuously relaxed from the initial value F₀ until the biomolecule folds or binds, as signified by a sharp increase in the measured force. From multiple repeats of this experiment, distributions of the folding or binding forces are collected (inset). Fitting the force distributions with the derived analytical expression yields the key parameters that determine the kinetics and energetics of folding or binding.In this letter, we derive an analytical expression for the distribution of transition forces, the major output of force-relaxation experiments that probe folding and binding processes. The expression extracts the key determinants of these processes: the on-rate and activation barrier in the absence of force. The theory is first developed in the context of biomolecular folding, and is then extended to cover the binding of a ligand tethered to a receptor. In contrast to unfolding and unbinding, the reverse processes of folding and binding require a theory that accounts for the compliance of the unfolded state, as well as the effect of the tether, to recover the true kinetic parameters of the biomolecule of interest.In a force-relaxation experiment, an unfolded biomolecule or unbound ligand-receptor complex is subject to a stretching force, which is decreased from the initial value F₀ as the pulling device approaches the sample at speed V until a folding or binding transition is observed (Fig. 1) (3–5). Define S(t) as the probability that the molecule has not yet escaped from the unfolded (implied: or unbound) state at time t. When escape is limited by one dominant barrier, S(t) follows the first-order rate equationS˙(t)≡dS(t)dt=−k←(F(t))S(t),where k_←(F(t)) is the on-rate at force F at time t. Because, prior to the transition, the applied force decreases monotonically with time, the distribution of transition forces, p(F), is related to S(t) through p(F)dF=S˙(t)dt, yieldingp(F)=−k←(F)F˙(F)e−∫F0Fk←(F′)F˙(F′)dF′.(1)Here F˙(F)≡dF(t)/dt<0 is the force relaxation rate. The proper normalization of p(F) is readily confirmed by integrating Eq. 1 from the initial force F₀ to negative infinity, the latter accounting for transitions that do not occur by the end of the experiment. Note that the expression for the distribution of folding/binding forces in Eq. 1 differs from its analog for the unfolding process (7) by the limits of integration and a negative sign, reflecting the property of a relaxation experiment to decrease the survival probability S(t) by decreasing the force. Converting the formal expression in Eq. 1 into a form suitable for fitting experimental data requires establishing functional forms for k_←(F) and F˙(F) and analytically solving the integral. These steps are accomplished below.The on-rate k_←(F) is computed by treating the conformational dynamics of the molecule as a random walk on the combined free energy profile G(x,t) = G₀(x) + G_pull(x,t) along the molecular extension x. Here G₀(x) is the intrinsic molecular potential and G_pull(x,t) is the potential of the pulling device. When G(x,t) features a high barrier on the scale of k_BT (k_B is the Boltzmann constant and T the temperature), the dynamics can be treated as diffusive. The unfolded region of the intrinsic potential for a folding process, unlike that for a barrierless process (8), can be captured by the functionG0(x)=ΔG‡ν1−ν(xx‡)11−ν−ΔG‡ν(xx‡),which has a sharp (if ν = 1/2, Fig. 2, inset) or smooth (if ν = 2/3) barrier of height ΔG^‡ and location x^‡. The potential of a pulling device of stiffness κ_S is G_pull(x,t) = κ_S/2(X₀ – Vt – x)² with an initial minimum at X₀ (corresponding to F₀). Applying Kramers formalism (9) to the combined potential G(x,t), we establish the analytical form of the on-rate at force F(t),k←(F)=k0(1+κSκU(F))1ν−12(1+νFx‡ΔG‡)1ν−1×eβΔG‡[1−(1+κSκU(F))2ν1−ν−1(1+νFx‡ΔG‡)1ν],where k₀ is the intrinsic on-rate, β ≡ (k_BT)⁻¹, andκU(F)=ν(1−ν)2ΔG‡x‡2(1+νFx‡ΔG‡)2−1νis the stiffness of the unfolded biomolecule under force F (see the Supporting Material for details on all derivations). The full nonlinear form of G_pull(x,t) was necessary in the derivation because, in contrast to the typically stiff folded state, the unfolded state may be soft (to be exact, 1/2κ_S x^‡2(F) << k_BT may not be satisfied) and thus easily deformed by the pulling device. Because of this deformation, the folding transition faces an extra contribution (regulated by the ratio κ_S/κ_U(F)) to the barrier height, typically negligible for unfolding, that decreases the on-rate in addition to the applied force F.Open in a separate windowFigure 2Contributions to the free energy profile for folding (inset) and binding (main figure). The derived expression (Eq. 2) extracts the on-rate and the location and height of the activation barrier to folding. When applied to binding data, the expression extracts the parameters of the ligand-tether-receptor (LTR) potential G˜0 (x); the proposed algorithm (Eqs. 3 and 4) removes the contribution of the tether potential G_teth(x) to recover the parameters of the intrinsic ligand-receptor (LR) potential G₀(x).The last piece required for Eq. 1, the loading rate F˙(F), is computed as the time derivative of the force F(t) on the unfolded molecule at its most probable extension at time t:F˙(F)=−κSV1+κS/κU(F).Finally, we realize that the integral in Eq. 1 can be solved analytically exactly, both for ν = 1/2 and ν = 2/3, resulting in the analytical expression for the distribution of folding forces:p(F)=k←(F)|F˙(F)|e−k←(F)β|F˙(F)|x‡(1+κSκU(F))νν−1(1+νFx‡ΔG‡)1−1ν.(2)Equation 2 can be readily applied to (normalized) histograms from force-relaxation experiments to extract the parameters of the intrinsic kinetics and energetics of folding. Being exact for ν = 1/2 and ν = 2/3, Eq. 2 is also an accurate approximation for any ν in the interval 1/2 < ν < 2/3 as long as κ_S ≲ κ_U (F) (see Fig. S1 in the Supporting Material). For simplicity, in Eq. 2 we have omitted the term containing F₀ as negligible if F₀ is large enough to prevent folding events.The solution in Eq. 2 reveals properties of the distribution of folding forces that distinguish it from its unfolding counterpart (7):

• 1.The distribution has a positive skew (Fig. 3), as intuitively expected: the rare folding events occur at high forces when the barrier is still high.Open in a separate windowFigure 3Force histograms from folding (left) and binding (right) simulations at several values of the force-relaxation speed (in nanometers per second, indicated at each histogram). Fitting the histograms with the analytical expression in Eq. 2 (lines) recovers the on-rate and activation barrier for folding or binding (2.Increasing the relaxation speed shifts the distribution to lower forces (Fig. 3): faster force relaxation leaves less time for thermal fluctuations to push the system over a high barrier, causing transitions to occur later (i.e., at lower forces), when the barrier is lower.
• 3.The stiffness κ_S and speed V enter Eq. 2 separately, providing independent routes to control the range of folding forces and thus enhance the robustness of a fit.

The application of the above framework to binding experiments on a ligand and receptor connected by a tether (3) involves an additional step—decoupling the effect of the tether—to reconstruct the parameters of ligand-receptor binding. Indeed, the parameters extracted from a fit of experimental histograms to Eq. 2 characterize the ligand-tether-receptor (LTR) potential (k˜0, x˜‡, ΔG˜‡, ν) (Fig. 2). The parameters of the natural ligand-receptor (LR) potential (k₀, x^‡, ΔG^‡) can be recovered using three characteristics of the tether: contour length L; persistence length p; and extension Δℓ of the tether along the direction of the force in the LTR transition state. The values of L and p can be determined from the force-extension curve of the tether (10); these define the tether potential G_teth(x) (Fig. 2). The value of Δℓ can be found from an unbinding experiment (7) on LTR and the geometry of the tether attachment points (see Fig. S3). Approximating the region of the LR potential between the transition and unbound states as harmonic, with no assumptions about the shape of the potential beyond x^‡, the ligand-receptor barrier parameters are thenx‡=α−1α−2x˜‡,ΔG‡=(α−1)22(α−2)x˜‡Fteth(Δℓ+x˜‡),(3)and the intrinsic unimolecular association rate isk0≈k˜0(βΔG‡)32(βΔG˜‡)1ν−12(x˜‡x‡)2eβ(ΔG˜‡−ΔG‡).(4)Here, the force value Fteth(Δℓ+x˜‡) is extracted from the force-extension curve of the tether at extension Δℓ+x˜‡ andα=2(ΔG˜‡−Gteth(Δℓ)+Gteth(Δℓ+x˜‡))x˜‡Fteth(Δℓ+x˜‡),where G_teth(x) is the wormlike-chain potential (see Eq. S13 in the Supporting Material). Equations 3–4 confirm that a tether decreases the height and width of the barrier (see Fig. 2), thus increasing the on-rate.In Fig. 3, the developed analytical framework is applied to folding and binding force histograms from Brownian dynamics simulations at parameters similar to those in the analogous experimental and computational studies (3,5,11) (for details on simulations and fitting procedure, see the Supporting Material). For the stringency of the test, the simulations account for the wormlike-chain nature of the molecular unfolded and LTR unbound states that is not explicitly accounted for in the theory. With optimized binning (12) of the histograms and a least-squares fit, Eqs. 2–4 recover the on-rate, the location and the height of the activation barrier, and the value of ν that best captures how the kinetics scale with force (

1.Multiple relaxation speeds,

2.Folding/binding events at low forces, and

3.A large number of events at each speed.

Table 1

On-rate and the location and height of the activation barrier from the fit of simulated data to the theory in Eq. 2

Physicochemical Properties and Amino Acid Composition of Alkaline Proteinase from Aspergillus sojae

Some physicochemical properties and amino acid composition of alkaline proteinase from Aspergillus sojae were found to be as follows: The isoelectric point was at pH 5.1. The molecular weight was 25,500 using the Sheraga-Mandelkern’s formula, based upon the values of the sedimentation coefficient $(s_{20,w}^{°}=\text{?}2.82\text{?}\text{S})$, the intrinsic viscosity ([η] = 0.027 dl/g), and the partial specific volume $({\displaystyle \overline{V}}\text{?}=\text{?}0.726\text{?}\text{ml}/\text{g})$. The enzyme contains 16.8% of nitrogen and is composed of 250 residues of amino acid; Asp₃₁ Glu₁₉, Gly₂₇, Ala₃₂, Val₁₈, Leu₁₄, Ile₁₄, Ser₂₈, Thr₁₈, ${\text{(}{\displaystyle \stackrel{}{{\displaystyle \stackrel{?}{\text{Cys C}}}}}\text{ys})}_1$, Met₂, Pro₆, Phe₇, Tyr₈, Trp₂, His₅, Lys₁₄, Arg₃, (amide-NH₃)₂₀.     

Isolation and Structure of Sclerothionine,a Metabolite of Sclerotinia Fungus

A new sulfur-containing imidazole compound, m.p. 218~223°C (decomp.), ${[\alpha ]}_{\text{D}}^{24}+{7.4}^{°}$ in water), C₁₁H₁₉N₃O₃S was isolated from sclerotia of Sclerotinia libertiana and named sclerothionine. The chemical structure of sclerothionine was identified with 2-hydroxyethyl-ergothioneine which was synthesized from ethylene chlorhydrine and ergothioneine.     

The MCT1 gene Glu490Asp polymorphism (rs1049434) is associated with endurance athlete status,lower blood lactate accumulation and higher maximum oxygen uptake

The purpose of this study was to explore the association of the MCT1 gene Glu490Asp polymorphism (rs1049434) with athletic status and performance of endurance athletes. A total of 1,208 Brazilians (318 endurance athletes and 890 non-athletes) and 867 Europeans (315 endurance athletes and 552 non-athletes) were evaluated in a case–control approach. Brazilian participants were classified based on self-declared ethnicity to test whether the polymorphism was different between Caucasians and Afro-descendants. Moreover, 66 Hungarian athletes underwent an incremental test until exhaustion to assess blood lactate levels, while 46 Russian athletes had their maximum oxygen uptake (V⋅O2max ) compared between genotypes. In the Brazilian cohort, the major T-allele was more frequent in Caucasian top-level competitors compared to their counterparts of lower competitive level (P = 0.039), and in Afro-descendant athletes compared to non-athletes (P = 0.015). Similarly, the T-allele was more frequent in European athletes (P = 0.029). Meta-analysis of the Brazilian and European cohorts confirmed that the T-allele is over-represented in endurance athletes (OR: 1.48, P = 0.03), especially when Afro-descendant athletes were included in the meta-analysis (OR: 1.58, P = 0.005). Furthermore, carriers of the T/T genotype accumulated less blood lactate in response to intense effort (P < 0.01) and exhibited higher V⋅O2max (P = 0.04)_. In conclusion, the Glu490Asp polymorphism was associated with endurance athletic status and performance. Our findings suggest that, although ethnic differences may exist, the presence of the major T-allele (i.e., the Glu-490 allele) favours endurance performance more than the mutant A-allele (i.e., the 490-Asp allele).