The magnetocaloric effect on nickel

The original data of Weiss and Forrer are reanalyzed with the aim to obtain a precise relation between the observed temperature rise and the magnetic field strength at temperatures both above and below the Curie temperature. The application of nonlinear least squares analysis reveals that a simple dependence of the temperature rise upon the magnetic field strength does not give a good fit. A more complex expression is therefore used, employing two different exponents (as adjustable parameters) for the magnetic field strength. The exponent 2, required in the original theory of Weiss, appears only in the paramagnetic region, while exponent 3 applies in the ferromagnetic region. The second exponent, valid at high fields, is close to 1 in the ferromagnetic region and near 0.7 in the paramagnetic region (lower values are obtained for some temperatures, but are shown to be of low significance).     

Improved magnetization alignment schemes for spin-lock relaxation experiments

A pair of pulse schemes that spin-lock magnetization efficiently are presented. The design of the sequences benefited from a particularly simple relation that is derived describing to first order the evolution of any magnetization component due to the application of an off-resonance 90° pulse. The sequences are shown theoretically and experimentally to significantly outperform the 90°-delay-90° element that is often used in current applications. It is shown that alignment of magnetization to within 1° of the effective field can be obtained over a bandwidth extending between [−ω_SL, ω_SL], where ω_SL is the strength of the spin-lock field using a simple scheme that is an order of magnitude shorter than an adiabatic pulse that might also be used for a similar purpose. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Neural crest cell galvanotaxis: new data and a novel approach to the analysis of both galvanotaxis and chemotaxis

The galvanotaxis response of neural crest cells that had migrated out of the neural tube of a 56-hr-old quail embryo onto glass coverslips was observed using time-lapse video microscopy. These cells exhibit a track velocity of about 7 microns/min and actively translocate toward the negative pole of an imposed DC electric field. This nonrandom migration could be detected for fields as low as 7 mV/mm (0.4 mV/cell length). We find that this directional migration is independent of the speed of migration and have generated a rather simple mathematical equation that fits these data. We find that the number of cells that translocate at a given angle, phi, with respect to the field is given by the equation N(phi) = exp(a0 + a1cos phi), where a1 is linearly proportional to the electric field strength for fields less than 390 mV/mm with a constant of proportionality equal to KG, the galvanotaxis constant. We show that KG = (150 mV/mm)-1, and at this field strength the cellular response is approximately half maximal. This approach to cellular translocation data analysis is generalizable to other directed movements such as chemotaxis and allows the direct comparison of different types of directed movements This analysis requires that the response of every cell, rather than averages of cellular responses, is reported. Once an equation for N(phi) is derived, several characteristics of the cellular response can be determined. Specifically, we describe 1) the critical field strength (390 mV/mm) below which the cellular response exhibits a simple, linear dependence on field strength (for larger field strengths, an inhibitory constant can be used to fit the data, suggesting that larger field strengths influence a second cellular target that inhibits the first); and 2) the amount of information the cell must obtain in order to generate the observed asymmetry in the translocation distribution (for a field strength of 100 mV/mm, 0.3 bits of information is required).     

A simple molecular model for thermophilic adaptation of functional nucleic acids

RNA molecules have numerous functions including catalysis and small molecule recognition, which typically arise from a tertiary structure. There is increasing interest in mechanisms for the thermostability of functional RNA molecules. Sosnick, Pan, and co-workers introduced the notion of "functional stability" as the free energy of the tertiary (functional) state relative to the next most stable (nonfunctional) state. We investigated the extent to which secondary structure stability influences the functional stability of nucleic acids. Intramolecularly folding DNA triplexes containing alternating T*AT and C+*GC base triples were used as a three-state model for the folding of nucleic acids with functional tertiary structures. A four-base-pair tunable region was included adjacent to the triplex-forming portion of the helix to allow secondary structure strength to be modulated. The degree of folding cooperativity was controlled by pH, with high cooperativity maintained by lower pH (5.5), and no cooperativity by higher pH (7.0). We find a linear relationship between functional free energy and the free energy of the secondary structure element adjacent to tertiary interactions, but only when folding is cooperative. We translate the definition of functional stability into equations and perform simulations of the thermodynamic data, which lend support to this model. The ability to increase the melting temperature of tertiary structure by strengthening base-pairing interactions separate from tertiary interactions provides a simple means for evolving thermostability in functional RNAs.     

Sequence-dependent twist-stretch coupling in DNA

Recent single-molecule micromanipulation experiments on DNA subject to small distortion revealed positive coupling between DNA stretching and twisting—for instance, DNA elongates when overtwisted. Here we propose a method to calculate the twist-stretch coupling constant specific to a DNA fragment of a given sequence. The method employs a sequence-dependent dinucleotide force field and is based on constrained minimization of the fragment's deformation energy. Using a force field inferred from atomistic molecular dynamics simulations, we obtain the twist-stretch coupling for random sequence to be 0.30 nm/turn, close to experimental values. An exhaustive calculation for all oligomers of nine basepairs yields values between 0.14 and 0.45 nm/turn, positively correlated with the contents of pyrimidine-purine steps in the sequence. Our method is simple to use and allows one to explore the hypothesis that some sequences may be optimized for twist-stretch coupling.     

Contact order dependent protein folding rates: kinetic consequences of a cooperative interplay between favorable nonlocal interactions and local conformational preferences

Physical mechanisms underlying the empirical correlation between relative contact order (CO) and folding rate among naturally occurring small single-domain proteins are investigated by evaluating postulated interaction schemes for a set of three-dimensional 27mer lattice protein models with 97 different CO values. Many-body interactions are constructed such that contact energies become more favorable when short chain segments sequentially adjacent to the contacting residues adopt native-like conformations. At a given interaction strength, this scheme leads to folding rates that are logarithmically well correlated with CO (correlation coefficient r = 0.914) and span more than 2.5 orders of magnitude, whereas folding rates of the corresponding Gō models with additive contact energies have much less logarithmic correlation with CO and span only approximately one order of magnitude. The present protein chain models also exhibit calorimetric cooperativity and linear chevron plots similar to that observed experimentally for proteins with apparent simple two-state folding/unfolding kinetics. Thus, our findings suggest that CO-dependent folding rates of real proteins may arise partly from a significant positive coupling between nonlocal contact favorabilities and local conformational preferences.     

Fundamental considerations in the effect of molecular weight on the glass transition of the gelatin/cosolute system

Four molecular fractions of gelatin produced by alkaline hydrolysis of collagen were investigated in the presence of cosolute to record the mechanical properties of the glass transition in high-solid preparations. Dynamic oscillatory and stress relaxation moduli in shear were recorded from 40°C to temperatures as low as -60°C. The small-deformation behavior of these linear polymers was separated by the method of reduced variables into a basic function of time alone and a basic function of temperature alone. The former allowed the reduction of isothermal runs into a master curve covering 17 orders of magnitude in the time domain. The latter follows the passage from the rubbery plateau through the glass transition region to the glassy state seen in the variation of shift factor, a(T) , as a function of temperature. The mechanical glass transition temperature (T(g) ) is pinpointed at the operational threshold of the free volume theory and the predictions of the reaction rate theory. Additional insights into molecular dynamics are obtained via the coupling model of cooperativity, which introduces the concept of coupling constant or interaction strength of local segmental motions that govern structural relaxation at the vicinity of T(g) . The molecular weight of the four gelatin fractions appears to have a profound effect on the transition temperature or coupling constant of vitrified matrices, as does the protein chemistry in relation to that of amorphous synthetic polymers or gelling polysaccharides.     

Biotic interaction strength and the intensity of selection

Although the ecological and evolutionary impacts of species interactions have been the foci of much research, the relationship between the strength of species interactions and the intensity of selection has been investigated only rarely. I develop a simple model demonstrating how the opportunity for selection varies with interaction strength, and then use the relationship between the maximum value of the selection differential and the opportunity for selection (Arnold & Wade 1984) to evaluate how selection differentials vary in relation to species interaction strength. This model predicts an initial deceleration and then an accelerating increase in the intensity of selection with increasing strength of antagonistic interactions and with decreasing strength of mutualistic interactions. Empirical data from several studies provide support for this model. These results further support an evolutionary mechanism for some striking patterns of evolutionary diversification including the latitudinal species gradient, and should be relevant to studies of eco‐evolutionary dynamics.     

A stochastic model for the sigmoidal behaviour of cooperative biological systems

A stochastic model for cooperative transitions in biological systems based on a Markov chain is proposed. This model requires only two parameters, the mean probability, p, and the coupling capacity, Deltap, which measure the probability of forming a new weak bond depending on the number of similar bonds already formed and it is also responsible for the transition. In this paper we show how the model works for a large number of identical molecules and how it can be useful for studying the noise around the centre of the transition where, increasing the degree of cooperativity, i.e. the number n in the well-known Hill equation, the width of the noise increases along with its fractal dimension. A simple relationship between the degree of cooperativity and the parameter Deltap is proposed, suggesting that the cooperativity of real biological transitions is related to the coupling capacity Deltap of the present model.     

Quaternary-transformation-induced changes at the heme in deoxyhemoglobins

Quaternary-structure-induced differences in both the high- and low-frequency regions of the resonance Raman spectrum of the heme have been detected in a variety of hemoglobins. These differences may be the result of (1) changes in the amino acid sequence, induced by genetic and chemical modifications, and (2) alterations in the quaternary structure. For samples in solution in low ionic strength buffers, differences in the 1357-cm-1 line (an electron-density-sensitive vibrational mode) correlate with differences in the 216-cm-1 line (the iron-histidine stretching mode). Thus, changes in the iron-histidine bond and changes in the pi-electron density of the porphyrin depend upon a common heme-globin interaction. The quaternary-structure-induced changes in the vibrational modes associated with the heme demonstrate that there is extensive communication between the heme and the globin and impact on models for the energetics of cooperativity. The local interactions of the iron-histidine mode are energetically small and destabilize the deoxy heme in the T structure with respect to the R structure. Therefore, these interactions must be larger in the ligated protein than in the deoxy protein to obtain a negative free energy of cooperativity. Additionally, our data imply that the deprotonation of the proximal histidine does not play a major role in the energetics of cooperativity. On the other hand, models for cooperativity that require conformational changes in the iron-histidine bond or direct interaction between the porphyrin and the protein are qualitatively consistent with the observed variation of heme electronic structure in concert with protein quaternary structure.     

Modeling protein density of states: additive hydrophobic effects are insufficient for calorimetric two-state cooperativity

A well-established experimental criterion for two-state thermodynamic cooperativity in protein folding is that the van't Hoff enthalpy DeltaH(vH) around the transition midpoint is equal, or very nearly so, to the calorimetric enthalpy DeltaH(cal) of the entire transition. This condition is satisfied by many small proteins. We use simple lattice models to provide a statistical mechanical framework to elucidate how this calorimetric two-state picture may be reconciled with the hierarchical multistate scenario emerging from recent hydrogen exchange experiments. We investigate the feasibility of using inverse Laplace transforms to recover the underlying density of states (i.e., enthalpy distribution) from calorimetric data. We find that the constraint imposed by DeltaH(vH)/DeltaH(cal) approximately 1 on densities of states of proteins is often more stringent than other "two-state" criteria proposed in recent theoretical studies. In conjunction with reasonable assumptions, the calorimetric two-state condition implies a narrow distribution of denatured-state enthalpies relative to the overall enthalpy difference between the native and the denatured conformations. This requirement does not always correlate with simple definitions of "sharpness" of a transition and has important ramifications for theoretical modeling. We find that protein models that assume capillarity cooperativity can exhibit overall calorimetric two-state-like behaviors. However, common heteropolymer models based on additive hydrophobic-like interactions, including highly specific two-dimensional Gō models, fail to produce proteinlike DeltaH(vH)/DeltaH(cal) approximately 1. A simple model is constructed to illustrate a proposed scenario in which physically plausible local and nonlocal cooperative terms, which mimic helical cooperativity and environment-dependent hydrogen bonding strength, can lead to thermodynamic behaviors closer to experiment. Our results suggest that proteinlike thermodynamic cooperativity may require a cooperative interplay between local and nonlocal interactions. The prospect of using calorimetric data to constrain Z-scores of knowledge-based potentials is discussed.     

Redox interactions in cytochrome c oxidase: from the "neoclassical" toward "modern" models.

Because of recent experimental data on the redox characteristics of cytochrome c oxidase and renewed interest in the role of cooperativity in energy coupling, the question of redox cooperativity in cytochrome c oxidase is reexamined. Extensive redox cooperativity between more than two redox centers, some of which are spectrally invisible, may be expected for this electron transfer coupled proton pump. Such cooperativity, however, cannot be revealed by the traditional potentiometric experiments based on a difference in absorbance between two wavelengths. Multiwavelength analyses utilizing singular value decomposition and second derivatives of absorbance vs. wavelength have revealed a stronger cooperativity than consistent with the "neoclassical" model, which allowed only for weak negative cooperativity between two equipotential one-electron centers. A thermodynamic analysis of redox cooperativity is developed, which includes the possibilities of strong cooperative redox interactions, the involvement of invisible redox centers, conformational changes, and monomer/dimer equilibrations. The experimental observation of an oxidation of one of the cytochromes (a3) with a decrease in applied redox potential is shown to require both strong negative cooperativity and the participation of more than two one-electron centers. A number of "modern" models are developed using the analytical approaches described in this paper. By testing with experimental data, some of these models are falsified, whereas some are retained with suggestions for further testing.     

Beta 1-subunits are required for regulation of coupling between Ca2+ transients and Ca2+-activated K+ (BK) channels by protein kinase C

Colonic myocytes have spontaneous, localized, Ins (1,4,5) trisphosphate (IP3) receptor-dependent Ca2+ transients that couple to the activation of Ca2+-dependent K+ channels and spontaneous transient outward currents (STOCs). We previously reported that the coupling strength between spontaneous Ca2+ transients and large conductance Ca2+ activated K+ (BK) channels is regulated by Ca2+ influx through nonselective cation channels and activation of protein kinase C (PKC). Here, we used confocal microscopy and the patch-clamp technique to further investigate the coupling between localized Ca2+ transients and STOCs in colonic myocytes from animals lacking the regulatory beta1-subunit of BK channels. Myocytes from beta1-knockout (beta1-/-) animals loaded with fluo 4 showed typical localized Ca2+ transients, but the STOCs coupled to these events were of abnormally low amplitude. Reduction in external Ca2+ or application of inhibitors of nonselective cation channels (SKF-96365) caused no significant change in the amplitude or frequency of STOCs. Likewise, an inhibitor of PKC, GF 109203X, had no significant effect on STOCs. Single-channel recording from BK channels showed that application of an activator (PMA) and an inhibitor (GF 109203X) of PKC did not affect BK channel openings in myocytes of beta1-/- mice. These data show that PKC-dependent regulation of coupling strength between Ca2+ transients and STOCs in colonic myocytes depends upon the interaction between alpha- and beta1-subunits.     

Magnetization and electron paramagnetic resonance studies of reduced uteroferrin and its "EPR-silent" phosphate complex

The exchange coupling of reduced uteroferrin has been measured (19.8(5) cm-1 S1.S2) using recently developed techniques for studying metalloprotein magnetization. A spin Hamiltonian describing the coupled binuclear Fe(II).Fe(III) center has been used to fit the low and high field magnetization data, the EPR g values, and the highly anisotropic effective hyperfine tensor of the ferric site. The exchange coupling of the phosphate complex of reduced uteroferrin has also been measured (6.0(5) cm-1 S1.S2) using the same techniques. The smaller exchange coupling of the phosphate complex is comparable with the zero field splittings of the iron sites. This results in increased sensitivity of the system g values (found by calculation from the spin Hamiltonian) to variations of the zero field splitting parameters arising from heterogeneities in the protein microenvironment. Consequently, there is a very significant (9-fold) increase in the "effective g strain" of the system compared to the situation in the absence of phosphate. This, together with the larger g anisotropy (g = (1.06, 1.51, 2.27)), gives rise to an EPR signal for the phosphate complex of reduced uteroferrin which is extremely broad and difficult to detect but which has now been identified for the first time.     

Hemoglobin-membrane interaction at physiological ionic strength and temperature

The spin-label electron paramagnetic resonance (EPR) technique has been used to study the interaction between human hemoglobin and erythrocyte membranes as a function of temperature and ionic strength. We show, for the first time, experimental evidence for the existence of the interaction at physiological pH, ionic strength and temperature. In addition to the pH dependence that we have previously reported, the interactions are also temperature and ionic strength dependent. Using a simple two-state equilibrium model to analyze the EPR data, we obtain an equilibrium dissociation constant of about 8.1 +/- 5.6 X 10(-5) M for hemoglobin-membrane systems in 5 mM phosphate with 150 mM NaCl at pH 7.4 and 37 degrees C.     

The relationship between light intensity and photosynthesis—A simple mathematical model

Summary A summary is given of two papers, presented by the authors at a seminar held for members of the Netherlands Hydrobiological Society. A simple model for photosynthesis is described that leads to a new relation between production rate and light intensity. This relation gives a better fit to experimental data than previous ones and allows relatively easy statistical evaluation of its parameters. It can be intergrated analytically for calculation of total photosynthesis per unit area, if the light intensity above water and extinction are known.     

Effects of excluded surface area and adsorbate clustering on surface adsorption of proteins I. Equilibrium models

Statistical-thermodynamic models for the equilibrium adsorption of proteins onto homogeneous, locally planar surfaces are presented. An extension of earlier work [R.C. Chatelier, A.P. Minton, Biophys. J. 71 (1996) 2367], the models presented here allow for the formation of a broadly heterogeneous population of adsorbate clusters in addition to excluded volume interactions between all adsorbate species. Calculations are carried out for three simple models for the structure of adsorbate, illustrating similarities and differences in the equilibrium properties of maximally compact clusters, minimally compact clusters and isomerizing clusters. Depending upon the strength of attractive interactions between adsorbate molecules, the resulting equilibrium isotherms may exhibit negative cooperativity, positive cooperativity, essentially no apparent cooperativity, or a mixture of positive cooperativity at low surface density and negative cooperativity at high surface density of adsorbate. The condition of apparent lack of cooperativity, which might naively be interpreted as evidence of a lack of interaction between adsorbate molecules, actually conceals a balance between attractive and repulsive interactions and extensive clustering of adsorbate.     

Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon.

Transient membrane permeabilization by application of high electric field intensity pulses on cells (electropermeabilization) depends on several physical parameters associated with the technique (pulse intensity, number, and duration). In the present study, electropermeabilization is studied in terms of flow of diffusing molecules between cells and external medium. Direct quantification of the phenomenon shows that electric field intensity is a critical parameter in the induction of permeabilization. Electric field intensity must be higher than a critical threshold to make the membrane permeable. This critical threshold depends on the cell size. Extent of permeabilization (i.e., the flow rate across the membrane) is then controlled by both pulse number and duration. Increasing electric field intensity above the critical threshold needed for permeabilization results in an increase membrane area able to be permeabilized but not due to an increase in the specific permeability of the field alterated area. The electroinduced permeabilization is transient and disappears progressively after the application of the electric field pulses. Its life time is under the control of the electric field parameters. The rate constant of the annealing phase is shown to be dependent on both pulse duration and number, but is independent of electric field intensity which creates the permeabilization. The phenomenon is described in terms of membrane organization transition between the natural impermeable state and the electro-induced permeable state, phenomenon only locally induced for electric field intensities above a critical threshold and expanding in relation to both pulse number and duration.