Slow knot formation by suppressed self-reptation in a collapsed polymer chain.

Chain-expansion processes from knotted globules have been measured for poly(methyl methacrylate) (PMMA) in the mixed solvent tert-butyl alcohol (TBA) + water (2.5 vol %) by static light scattering. The solution was quenched from the Θ temperature of 41.5 °C to 37.0 °C, aged there for a time period t(p,) and then returned rapidly to the Θ temperature. The chain-expansion process was determined as a time evolution of the expansion factor α(2) after the temperature increase. The measurement was carried out by changing the aging time t(p) from 240 to 7200 min, and the molecular weight from M(w) = 4.0 × 10(6) to 1.5 × 10(7), by taking advantage of the extremely slow chain aggregation in the solution. The chain-expansion process obtained for M(w) = 1.22 × 10(7) became slow with increasing t(p), which revealed the knot formation in single globules. The characteristic time of the chain expansion from globules aged for t(p) = 7200 min was found to depend on the molecular weight as M(w)(2.7). This exponent, which is close to 3, demonstrated a disentanglement process due to self-reptation. The present data were compared with the previous data of the chain expansion from compact globules aged at 25.0 °C. The comparison made at M(w) = 1.22 × 10(7) and at the same values of t(p) revealed that the chain expansion from the globules aged at 25.0 °C was much faster than that from the globules at 37.0 °C, indicating a lower knot density in the more compact globules. It was conjectured that the knot formation due to self-reptation would be suppressed in a compact globule because an entire conformational change required by knot formation would become difficult to occur in the confined space of high segment concentration, particularly for a long polymer chain. The chain collapse of PMMA in the mixed solvent has been observed to occur extremely slowly at the later stage. This slow process was explained by the suppressed self-reptation.

Comparison of the kinetics of chain aggregation and chain collapse in dilute polymer solutions.

The rates of chain aggregation of poly(methyl methacrylate) (PMMA) in acetonitrile (AcN) and in the mixed solvent of AcN+water (10 vol%) were determined by static light scattering and compared with the rates of chain collapse [Maki, J. Chem. Phys. 126, 134901 (2007)]. Dilute solutions of PMMA with the molecular weight m{w}=6.4 x 10{6} and in the concentration range of (0.8-5)x10;{-4}gcm;{3} were quenched below the cloud point, and the weight-average molecular weight M{w} and z -average square radius of gyration S;{2}_{z} for clusters of PMMA chains were measured as a function of the time t after the quench and the concentration c . The measurement of chain aggregation was carried out up to the cluster size of M{w}m{w} approximately 30 , which required time periods of hours to several days depending on the concentration and solvent. The chain aggregation in AcN+water occurred much faster than that in AcN. The growth of clusters in both the solvents was represented by the exponential function as M{w} approximately e;{gct} and S;{2}_{z} approximately e{hct} , where g and h represent the intrinsic rate of chain aggregation. The ratio sigma of the intrinsic rate in AcN+water to that in AcN was estimated to be 9 by taking a rough average of the ratios 9.4 obtained from g and 8.8 from h . This value is comparable to the ratio 11 of the rate of chain collapse of PMMA in AcN+water (10 vol%) to that in AcN. This close value of the ratios indicates that the nature of solvent would affect the rates of chain collapse and chain aggregation through a similar mechanism.

Transition from a chain-collapse process to a chain-aggregation process of poly(methyl methacrylate) in a mixed solvent.

The transition from a chain-collapse process to a chain-aggregation process was studied by static light scattering on poly(methyl methacrylate) of the molecular weight mw=1.22x10(7) in the mixed solvent tert-butyl alcohol+water (2.5 vol%). The concentration c of the solutions ranged from 0.5 to 2.5x10(-4) g/cm3 and the measurement was carried out at appropriate time intervals up to the time t(h)=3250 after the quench to 35.0 degrees C which was a few degrees below the phase separation temperature. The molecular weight Mw and mean-square radius of gyrationz were estimated from each scattering curve determined at the finite concentrations. At the initial stage of 100 h, z decreased rapidly with the time t indicating the chain collapse, while at the later stage of 3000 h, z increased very slowly indicating the chain aggregation. The chain-collapse process and chain-aggregation process could be analyzed separately, though the two processes overlapped appreciably at the higher concentrations. The former process depended slightly on the concentration, while the latter process showed the exponential growth of ln Mw approximately ct and lnz approximately ct. In the plot of lnz versus ln Mw, the chain-collapse process was depicted by different lines depending on the concentration, while the chain-aggregation process was described by a single straight line. The transition from the former to the latter process occurred distinctly near 200 h after the quench irrespective of the concentration.

Kinetics of chain collapse in dilute polymer solutions: molecular weight and solvent dependences.

The molecular weight and solvent dependences of the characteristic time of chain collapse were studied for poly(methyl methacrylate) (PMMA) of the molecular weight Mw=6.4x10(6) and 1.14x10(7) in pure acetonitrile (AcN) and in the mixed solvent of AcN+water (10 vol %). The size of PMMA chains was measured as a function of the time after the quench by static light scattering and the chain collapse processes were expressed by the plot of the expansion factor alpha2 vs ln t. The chain collapse in the mixed solvent AcN+water (10 vol %) was found to occur much faster than that in pure AcN, though the measurement of the former collapse process required several hours. In order to make a comparison between the rates of chain collapses, the fast chain collapse process was superposed on the slow one by scaling the time of the fast process as gammat. The scale factor gamma was determined by comparing the chain collapse processes of nearly the same equilibrium expansion factor with each other. Accordingly, the superposition of the collapse for Mw=6.4x10(6) on that for Mw=1.14x10(7) yielded gammam=4.0+/-0.6 for the process in AcN+water and 5.5+/-0.6 in AcN. The superposition of the chain collapse process in AcN+water on that in AcN yielded gammas=9.5+/-1.4 for Mw=6.4x10(6) and 12.0+/-1.8 for Mw=1.14x10(7). This analysis suggests that gammam and gammas are constant independent of each other. Thus, by assuming the molecular weight dependence of gammam approximately Mz, the characteristic time tauexp of chain collapse was conjectured as tauexp approximately kappaMz, where kappa reflects the nature of solvent species. The ratio of kappa for PMMA in AcN to that in AcN+water is given by gammas. The exponent was estimated to be z=2.4+/-0.7 for AcN+water and 3.0+/-0.7 for AcN. These values are compatible with the theoretical prediction z=3 based on a phenomenological model, though the observed characteristic times are longer by several orders of magnitude than those of the theoretical prediction.

Mathematical description of stress relaxation of bovine femoral cortical bone.

In 1993 we proposed an empirical formula for describing the relaxation modulus of cortical bone based on the results of stress relaxation experiments performed for 1 x 10(5) sec: [E(t) = E0{A exp[ -(t/tau1)beta] + (1 - A) exp(-t/tau2)}, (0 < A, beta <1 and tau1 << tau2) where E0 is the initial value of the relaxation modulus, A is the portion of the first term, tau1 and tau2 are characteristic relaxation times, and beta is a shape factor [Sasaki et al., J. Biomechanics 26 (1993), 1369]. Although the relaxation properties of bone under various external conditions were described well by the above equation, recent experimental results have indicated some limitations in its application. In order to construct an empirical formula for the relaxation modulus of cortical bone that has a high degree of completeness, stress relaxation experiments were performed for 6 x 10(5) seconds. The second term in the equation was determined as an apparently linear portion in a log E(t) vs t plot at t>1 x 10(4) sec. The same plot for experiments performed for 6 x 10(5) seconds revealed that the linear portion corresponding to the second term was in fact a curve with a large radius of curvature. On the basis of this fact, we proposed a second improved empirical equation E(t) = E0{A exp [ -(t/tau1)beta] + (1 - A) exp[-(t/tau2)gamma]}, (0

Molecular weight effect on liquid crystalline gel formation of curdlan.

Curdlan dissolved in alkaline solution forms a unique gel consisting of liquid crystalline gel (LCG) and amorphous gel (AG) in alternating layers by a dialysis into aqueous calcium chloride. The unique structure has been investigated by measuring the birefringence of the gel Deltan, the ratio q of the thickness of LCG layer delta to the gel radius R, and the calcium content in the gel C(Ca) in a wide range of molecular weights of fractionated Curdlan, as well as unfractionated Curdlan as a control. With increasing molecular weight of Curdlan, Deltan increased and q = delta/R decreased, and both became saturated at high molecular weight. Deltan and q for unfractionated Curdlan were smaller and larger, respectively, than those for fractionated Curdlan. C(Ca) was constant irrespective of molecular weight and its distribution, which means that the abundance of calcium ions per glucose unit in the gel does not depend on the degree of orientation of mesogens. These results suggest that the amorphous phase appears when the size of the Curdlan molecules is larger than the average intermolecular distance, resulting from the random coil to triple helix transformation of Curdlan molecules associated with lowering hydroxide anion concentration in the dialysis process.

Memory effect in the chain-collapse process in a dilute polymer solution.

The effect of temperature perturbation on a single-chain-collapse process was studied for poly(methyl methacrylate) with the molecular weight M(w)=1.05 x 10(7) in the mixed solvent of tert-butyl alcohol+water (2.5 vol %). In the chain-collapse process after a quench from the theta; temperature to a temperature T(1), the temperature was changed from T(1) to T(2) at the time t(1) after the quench and returned to T(1) at the time t(1)+t(2). In the three stages at T(1), T(2), and T(1), measurements of the mean-square radius of gyration of polymer chains were carried out by static light scattering and the chain-collapse process was represented by the expansion factor as a function of time. An effect of chain aggregation on the measurements was negligibly small because of the very slow phase separation. For the negative temperature perturbation (T(1)>T(2)), the chain-collapse processes observed in the first and third stages were connected smoothly and agreed with the collapse process due to a single-stage quench to T(1). A memory of the chain collapse in the first stage at T(1) was found to persist into the third stage at the same temperature T(1) without being affected by the temperature perturbation of T(2) during t(2). The memory effect was observed irrespective of the time period of t(2). The positive temperature perturbation (T(1)

Anisotropic viscoelastic properties of cortical bone.

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted): E(t)=E0 (A1 exp[-(t/tau1)beta]+(1-A1) exp[-(t/tau2)gamma]), [0 < A1, beta, gamma < 1], where E0 is the initial modulus value E0. Tau1 and tau2(>>tau1) are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and beta and gamma are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.

Elongational flow studies on conformational change in DNA induced by DNA-binding protein HU.

Interaction of DNA-binding protein HU from Bacillus stearothermophilis (HUBst) with coliphage T2 DNA was investigated by observing an elongational flow-induced birefringence, Deltan, of a T2-phage DNA aqueous solution at various HU concentrations. Localized flow birefringence was observed in the pure elongational flow region, and the strain rate dependence of Deltan had a critical strain rate epsilon;(c) for the appearance of flow birefringence at all of the HU concentrations examined, indicating that a coil-stretch transition occurred at epsilon;(c) in each DNA-HU system. For strain rates larger than epsilon;(c), Deltan increased rapidly and then gradually, approaching a plateau value. The value of epsilon;(c) increased with an increase in HU concentration. Analysis based on the relationship between epsilon; (c) and the Rouse-Zimm relaxation time revealed that the increase in epsilon;(c)with increase in HU can be explained by the decrease in the size of the DNA-HU complex. The plateau birefringence value, Deltan(p), decreased at small HU concentrations but did not change at larger HU concentrations. Considering that Deltan(p) is related to the orientational order parameter of segments, it was concluded that there were at least two stages in the process of compaction of DNA induced by HU.

The solution structure of apocalmodulin from Saccharomyces cerevisiae implies a mechanism for its unique Ca2+ binding property.

We have determined the solution structure of calmodulin (CaM) from yeast (Saccharomyces cerevisiae) (yCaM) in the apo state by using NMR spectroscopy. yCaM is 60% identical in its amino acid sequence with other CaMs, and exhibits its unique biological features. yCaM consists of two similar globular domains (N- and C-domain) containing three Ca(2+)-binding motifs, EF-hands, in accordance with the observed 3 mol of Ca(2+) binding. In the solution structure of yCaM, the conformation of the N-domain conforms well to the one of the expressed N-terminal half-domains of yCaM [Ishida, H., et al. (2000) Biochemistry 39, 13660-13668]. The conformation of the C-domain basically consists of a pair of helix-loop-helix motifs, though a segment corresponding to the forth Ca(2+)-binding site of CaM deviates in its primary structure from a typical EF-hand motif and loses the ability to bind Ca(2+). Thus, the resulting conformation of each domain is essentially identical to the corresponding domain of CaM in the apo state. A flexible linker connects the two domains as observed for CaM. Any evidence for the previously reported interdomain interaction in yCaM was not observed in the solution structure of the apo state. Hence, the interdomain interaction possibly occurs in the course of Ca(2+) binding and generates a cooperative Ca(2+) binding among all three sites. Preliminary studies on a mutant protein of yCaM, E104Q, revealed that the Ca(2+)-bound N-domain interacts with the apo C-domain and induces a large conformational change in the C-domain.

1H, 15N and 13C resonance assignments of yeast Saccharomyces cerevisiae calmodulin in the Ca2+-free state.

Calmodulin (CaM) is a small Ca2+-binding protein, which has been found in all of eucaryotic cells examined. CaMs isolated from various species have highly conserved amino acid sequence (more than 90% identical), and show the same biological functions. CaM isolated from the baker's yeast (Saccharomyces cerevisiae) (yCaM), however, shares only 60% identity in the amino acid sequence with CaM from vertebrate, and shows quite distinct conformational and biochemical properties compared with those of CaM from other species. The conformational details of yCaM, however, have not been revealed yet. We achieved the chemical shift assignments of yCaM (146 amino acids) in the apo-state using uniformly 15N- and 13C-labeled protein. Consequently, the resonances of 95% atoms in the backbone amides were successfully assigned.

Coexistence curve near the tricritical point in ternary polymer solutions.

Two-phase coexistence curves were measured for ternary solutions of bimodal polystyrene in methylcyclohexane with the molecular weight ratio near the tricritical value 23. Coexistence curves were determined by the refractive index method on a diagram of temperature versus volume fraction of total polystyrene. The diameter was strongly curved near the top. The double logarithmic plots of volume fraction difference between two coexisting phases versus reduced temperature yielded the critical exponent beta=0.250+/-0.005 for the tricritical solution and, 0.412+/-0.005 and 0.383+/-0.016 for solutions not far from the tricritical one. The former value could be compared with the classical tricritical exponent beta=1 / 4 and the latter values near 0.40 could be explained by a crossover between the ordinary critical exponent 0.32 or the tricritical exponents 1 / 4 and the classical exponent 1 / 2.

Compact form of DNA induced by DNA-binding protein HU.

Interaction of DNA-binding protein HU from Bacillus stearothermophilus (HUBst) with coliphage T2 DNA was investigated by means of a single-duplex DNA chain visualization method using fluorescence microscopy. Fluorescence microscopic images of coliphage T2 DNA molecules were observed as a function of HUBst concentration. The average fluorescence image size of T2 DNA decreased with increase in HUBst concentration to a size comparable to that of a DNA globule induced by polyethylene glycol (PEG) and multivalent cation (MVC). The change to globule-like DNA proceeded gradually and monotonously, in contrast to the coil-globule transition of DNA induced by PEG and MVC. The histogram of the fluorescence image length was essentially a single-modal one throughout the process of conformational change. These results indicate that the process of shrinking of DNA from a random coil to a globule-like one is not of a transitional nature. The interaction of HUBst with DNA and the mechanism of shrinkage are concluded to be different from those of PEG-induced and MVC-induced coil-globule transition of DNA.

Atomic force microscopic studies on the structure of bovine femoral cortical bone at the collagen fibril-mineral level.

The structure of cortical bone at the collagen-mineral level was investigated by means of atomic force microscopy. Surfaces of the specimens treated with collagenase and ethylenediaminetetraacetic acid (EDTA) were examined. Images of blob-like objects observed in intact specimen became clearly outlined after collagenase treatment; the sizes of the blob decreased, suggesting that each blob had been fragmented by the collagenase treatment. Following EDTA treatment of an intact specimen, an image of thread-like objects appeared; the thread was partly constructed by trains of blobs and the other parts of the threads had a periodic pattern along its longer axis. The period was almost equal to the collagen D-period of the Hodge-Petruska model, indicating that the threads are collagen fibrils and that the blobs are related to the mineral phase in bone. It was concluded that minerals were deposited on and along collagen fibrils. A decorated collagen fibril model for the spatial relationship between mineral and collagen fibril was proposed. According to our model, the mineral inside the collagen fibril is about one forth of the extrafibrillar mineral.