Jon Widom—A Friend of JBSD and the Albany Conversation

Abstract

We consider kinetics of the cooperative melting of DNA sections situated at the edge of the helix. Accurate calculations based on the real sequences of such sections demonstrate that their internal heterogeneity has a drastic effect on the melting kinetics. Allowance for the internal heterogeneity increases the relaxation time by several orders of magnitude as compared with a model based on the assumption of equal base-pair stability within a section. The relaxation times obtained are in good agreement with the experimental data of Suyama and Wada (A. Suyama and A. Wada. Biopolymers, 23,409 (1989)). An analysis of the melting process revealed some simple sequence characteristics that determine its rate. An examination of the temperature dependence of the relaxation time led to a distinct interpretation of the apparent activation energies of the denaturation and renaturation. The relaxation time proved to reach its maximum near the equilibrium melting point of the section examined.     

The kinetics of DNA helix-coil subtransitions

The kinetic analysis of individual helix-coil subtransitions were performed by comparing melting and renaturation profiles obtained at different temperature change rates. The duration of the three transition stages and its dependence on temperature and ionic strength were determined for a T7 phage DNA fragment. The obtained temperature dependence of the melting time for a stretch flanked by melted regions is in quantitative agreement with that predicted by the theory of slow processes (V.V. Anshelevich, A.V. Vologodskii, A.V. Lukashin, M.D. Frank-Kamenetskii, Biopolymers 23, 39 (1984)). The reasons are discussed for the increasing relaxation time of this stretch in the middle of its transition with decreasing ionic strength. The zipping kinetics of a melted region under essentially nonequilibrium conditions was examined for T7 fragment and pAO3 DNAs. The obtained temperature dependence of the zipping time is in quantitative agreement with calculations based on the theory of slow processes. The renaturation times of stretches flanked by helical regions proved fairly small even at a low ionic strength. These times are several orders of magnitude smaller than the renaturation times of the same stretches with one helical boundary. A formal application of the theory of slow processes failed to account for the small renaturation times of stretches that are zipped from both ends. This is probably due to the non-allowance for the changing entropy of the loop linking two helix-coil boundaries migrating towards each other. Slow processes have been revealed in the intramolecular melting of Col E1 DNA at a high ionic strength. The reason for the long relaxation time of one subtransition is the large size of the loop that separates the melting stretch from the helical part of the molecule. This result can be accounted for by the theory of slow processes.     

Relaxation kinetics of denaturation of DNA

The one-dimensional Ising model, with nearest-neighbor correlations only, used earlier in equilibrium studies of melting of DNA is extended to study the relaxation kinetics of copolymeric synthetic DNA near the melting temperature. An exponential kinetics, in agreement with the observations, has been found.     

The Kinetics of DNA Helix-Coil Subtransitions

Abstract

The kinetic analysis of individual helix-coil subtransitions was performed by comparing melting and renaturation profiles obtained at different temperature change rates. The duration of the three transition stages and its dependence on temperature and ionic strength were determined for a T7 phage DNA fragment. The obtained temperature dependence of the melting time for a stretch flanked by melted regions is in quantitative agreement with that predicted by the theory of slow processes (V.V. Anshelevich, A.V. Vologodskii, A.V. Lukashin, M.D. Frank-Kamenetskii, Biopolymers 23, 39 (1984)). The reasons are discussed for the increasing relaxation time of this stretch in the middle of its transition with decreasing ionic strength.

The zipping kinetics of a melted region under essentially nonequilibrium conditions was examined for T7 fragment and pAO3 DNAs. The obtained temperature dependence of the zipping time is in quantitative agreement with calculations based on the theory of slow processes.

The renaturation times of stretches flanked by helical regions proved fairly small even at a low ionic strength. These times are several orders of magnitude smaller than the renaturation times of the same stretches with one helical boundary. A formal application of the theory of slow processes failed to account for the small renaturation times of stretches that are zipped from both ends. This is probably due to the non-allowance for the changing entropy of the loop linking two helix-coil boundaries migrating towards each other.

Slow processes have been revealed in the intramolecular melting of Col E1 DNA at a high ionic strength. The reason for the long relaxation time of one subtransition is the large size of the loop that separates the melting stretch from the helical part of the molecule. This result can be accounted for by the theory of slow processes.     

Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape

An acid-destabilized form of apomyoglobin, the so-called E state, consists of a set of heterogeneous structures that are all characterized by a stable hydrophobic core composed of 30-40 residues at the intersection of the A, G, and H helices of the protein, with little other secondary structure and no other tertiary structure. Relaxation kinetics studies were carried out to characterize the dynamics of core melting and formation in this protein. The unfolding and/or refolding response is induced by a laser-induced temperature jump between the folded and unfolded forms of E, and structural changes are monitored using the infrared amide I' absorbance at 1648-1651 cm(-1) that reports on the formation of solvent-protected, native-like helix in the core and by fluorescence emission changes from apomyoglobin's Trp14, a measure of burial of the indole group of this residue. The fluorescence kinetics data are monoexponential with a relaxation time of 14 micros. However, infrared kinetics data are best fit to a biexponential function with relaxation times of 14 and 59 micros. These relaxation times are very fast, close to the limits placed on folding reactions by diffusion. The 14 micros relaxation time is weakly temperature dependent and thus represents a pathway that is energetically downhill. The appearance of this relaxation time in both the fluorescence and infrared measurements indicates that this folding event proceeds by a concomitant formation of compact secondary and tertiary structures. The 59 micros relaxation time is much more strongly temperature dependent and has no fluorescence counterpart, indicating an activated process with a large energy barrier wherein nonspecific hydrophobic interactions between helix A and the G and H helices cause some helix burial but Trp14 remains solvent exposed. These results are best fit by a multiple-pathway kinetic model when U collapses to form the various folded core structures of E. Thus, the results suggest very robust dynamics for core formation involving multiple folding pathways and provide significant insight into the primary processes of protein folding.     

Probing the kinetic cooperativity of beta-sheet folding perpendicular to the strand direction

In an attempt to determine how the folding dynamics of multistranded beta-sheets vary with the strand number, we have studied the temperature-induced relaxation kinetics of a four-stranded beta-sheet, DPDPDP. Our results show that the thermally induced relaxation of DPDPDP occurs on the nanosecond time scale; however, a comparison of the current results with those obtained on a sequence-related, three-stranded beta-sheet suggests that increasing the strand number from three to four increases the folding free energy barrier by a minimum of 0.8 kcal/mol, depending on the folding mechanism. Therefore, these results together suggest that the relaxation kinetics of DPDPDP can be analyzed according to a two-state model even though its folding may actually involve parallel (but degenerate or nearly degenerate) kinetic pathways. The apparent, two-state folding time of DPDPDP is determined to be approximately 0.44 micros at the thermal melting temperature, which makes it one of the fastest folders known to date.     

Unwinding kinetics of cooperatively melting regions in DNA

Unwinding of a single cooperatively melting region of ColE1 DNA is investigated by a slow temperature jump in formamide–neutral buffer mixed solvent. The semilogarithmic plots of unwinding relaxation curves show a marked terminal linear region following the fast decay, which occurred within the temperature rise time (1 ～ 2 s). This longest relaxation is ascribed to the total unwinding of a single cooperatively melting region. The longest relaxation time, τ₁, is uniquely determined by the final equilibrium state and becomes shorter as the final temperature increases. Decrease in ionic strength makes τ₁ and its fractional amplitude increase, and the relaxation almost approaches single-exponential decay. The facts that (1) τ₁ of a single cooperatively melting region whose unwinding suffers larger frictional resistance does not always unwind more slowly, as was shown by the observations of τ₁'s of almost the same cooperatively melting region located at different positions on two linearized ColEl DNAs and of τ₁'s of two cooperatively melting regions on the same linearized ColEl DNA; (2) τ₁ has strong dependence on the equilibrium state after a temperature jump; and (3) the observed τ₁ is much longer than the expected time of the frictional barrier all demonstrate that the τ₁ is limited by chemical but not hydrodynamic processes. The detailed unwinding process of a single cooperatively melting region, elucidated by evidence of a negative apparent activation energy of the rewinding process and by extensive computer simulation of the equilibrium melting process, suggests that the local heterogeneity of G+C content in a cooperatively melting region, as well as its averaged G+C content, strongly affects its unwinding rate. The present study of a single cooperatively melting region is found to be useful to improve our understanding of the detailed mechanism of complex unwinding of large natural DNAs, in which many cooperatively melting regions unwind.     

Relaxation kinetics and the glassiness of proteins: the case of bovine pancreatic trypsin inhibitor

Folded proteins may be regarded as soft active matter under physiological conditions. The densely packed hydrophobic interior, the relatively molten hydrophilic exterior, and the spacer connecting these put together a large number of locally homogeneous regions. For the case of the bovine pancreatic trypsin inhibitor, with the aid of molecular dynamics simulations, we have demonstrated that the kinetics of the relaxation of the internal motions is highly concerted, manifesting the protein's heterogeneity, which may arise from variations in density, local packing, or the local energy landscape. This behavior is characterized in a stretched exponential decay described by an exponent of approximately 0.4 at physiological temperatures. Due to the trapped conformations, configurational entropy becomes smaller, and the associated stretch exponent drops to half of its value below the glass transition range. The temperature dependence of the inverse relaxation time closely follows the Vogel-Tamman-Fulcher expression when the protein is biologically active.     

Studies on chromophore coupling in isolated phycobiliproteins: III. Picosecond excited state kinetics and time-resolved fluorescence spectra of different allophycocyanins from Mastigocladus laminosus

The excited state kinetics of three different allophycocyanin (AP) complexes has been studied by picosecond fluorescence spectroscopy. Both the fluorescence kinetics and the decay-associated fluorescence spectra of the different complexes can be understood on the basis of a structural model for AP which uses (a) an analogy to the known x-ray determined structure of C-phycocyanin, (b) the biochemical analogies of AP and C-phycocyanin, and (c) the biochemical composition of AP-B (AP-681). A model is developed that describes the excited state kinetics as a mixture of internal conversion processes within a coupled exciton pair and energy transfer processes between exciton pairs. We found excited state relaxation times in the range of 13 ps (AP with linker peptide) up to 66 ps (AP-B). The trimeric aggregates AP 660 and AP 665 show one fast relaxation component each, as was expected on the basis of their symmetry properties. The lower symmetry of AP-B (AP-681) gives rise to two fast lifetime components (τ₁ = 23 ps and τ₂ = 66 ps) which are attributed to internal conversion and/or energy transfer between excitonic states formed by the coupling of symmetrically and spectrally nonequivalent chromophores. It is proposed that the internal conversion between exciton states of strongly coupled chromophores fulfills the requirements of the small energy gap limit. Thus, internal conversion rates in the order of tens of picoseconds are feasible. The influence of the interaction of the linker peptide on the properties of the AP trimer are manifested in the fluorescence kinetics. Lack of the linker peptide in AP 660 gives rise to a heterogeneity in the chromophore conformations and chromophore-chromophore interactions.     

Two-state folding over a weak free-energy barrier

We present a Monte Carlo study of a model protein with 54 amino acids that folds directly to its native three-helix-bundle state without forming any well-defined intermediate state. The free-energy barrier separating the native and unfolded states of this protein is found to be weak, even at the folding temperature. Nevertheless, we find that melting curves to a good approximation can be described in terms of a simple two-state system, and that the relaxation behavior is close to single exponential. The motion along individual reaction coordinates is roughly diffusive on timescales beyond the reconfiguration time for a single helix. A simple estimate based on diffusion in a square-well potential predicts the relaxation time within a factor of two.     

Rearrangement of partially ordered stacked conformations contributes to the rugged energy landscape of a small RNA hairpin

We have studied the fast relaxation kinetics of a small RNA hairpin tetraloop using time-resolved infrared spectroscopy. A laser-induced temperature jump initiated the relaxation by rapidly perturbing the thermal equilibrium of the sample. We probed the relaxation kinetics at two different wavenumbers, 1574 and 1669 cm (-1). The latter is due to the C6O6 carbonyl stretch of the base guanine and is a direct measure of guanine base pairing. The former is assigned to a ring vibration of guanine and tracks structure by sensing base stacking interactions. Overall, the kinetics at 1574 cm (-1) are faster than those observed at 1669 cm (-1). When relaxation occurs at the melting temperature, the kinetics at both wavenumbers are biexponential. When relaxation occurs at a temperature that is higher than the melting temperature, the data at 1669 cm (-1) are still biexponential while only a single fast phase is resolved in the data at 1574 cm (-1). The fast phases are in the range of microseconds, while the slower phases are in the range of tens of microseconds. At both wavenumbers, a portion of the relaxation is not resolved, indicating the existence of a very fast, sub-100 ns phase. Our results provide additional evidence that small, fast folding hairpin loops are characterized by a rugged energy landscape. Furthermore, our data suggest that single-strand stacking interactions and stacking interactions in the loop contribute significantly to the ruggedness of the energy landscape. This work also demonstrates the utility of time-resolved infrared spectroscopy in studying RNA folding.     

Melting-profile analysis of thermal stability of thermolysin. A formulation of temperature-scanning kinetics.

The melting-profile method consists of a continuous observation of a structural parameter while the temperature of the sample is raised at a constant rate [Fugita, S. C., & Imahori, K. (1974) IN Peptides, Polypeptides and Proteins (Blout, E. R., Bovey, F. A., Goodman, M., & Lotan, N., Eds.) p 217, Wiley, New York, N.Y.]. An analytical solution to the melting profile was formulated for the two-state irreversible process and called temperature-scanning kinetics. The theory was tested with thermolysin with consistent results, and the thermodynamic parameters of thermal denaturation were calculated: deltaH identical to = 80.3 kcal/mol, deltaS identical to = 153 eu. These values agreed with the corresponding values obtained from the classical constant-temperature relaxation kinetics. The possibilities of temperature-scanning kinetics are discussed.     

The best sections method of studying mass extinctions

Phanerozoic mass extinctions have been studied primarily by analysing global diversity patterns compiled from the published literature. However, such compilations are beset by problems of incorrect correlation, imprecise age assignments and changing taxonomy. An alternative approach is to analyse mass extinctions by the ‘best sections’ method. This method identifies abundantly fossiliferous, well‐studied, stratigraphically dense and temporally extensive fossil records in strata that contain geochemical and other relevant non‐palaeontological data from a single depositional basin or geographically restricted outcrop area as the ‘best sections’ by which to analyse extinctions. A strength of the best sections method is that it allows the extinctions identified to be compared directly to changes in facies and other factors recorded in the best section. And, the hypothesis of a widespread extinction based on an extinction seen in a best section can be tested by its presence or absence in temporally equivalent sections. What we need are more field‐based studies of the best sections that encompass mass extinctions (real and hypothetical) and less of a reliance on literature‐based diversity compilations to produce a more reliable and comprehensive understanding of the history of extinctions.     

Specific features of the structural organization of the mitochondrial genome in RAT liver

Summary The nature of intramolecular heterogeneity of mtDNA in the liver of white rats has been studied. The peculiarities of the melting curve, and the possibility of DNA fractionation of nucleotide compounds with hydroxylapatite (HA) column chromatography has shown the presence of sequences differing in the mean nucleotide content. A section of about 350 pairs in size repeated four times was found in the reassociation of most thermolabile fraction with a mean composition of 28% GC. These sections are well seen on the denaturation map of the recorded molecules formed in the range of temperature transition helix-coil. The distance between the centers of fusible sections (in percentage of total length) is 32.5, 32, 14.0 and 21.5.     

Ligand-induced changes in dynamics in the RT loop of the C-terminal SH3 domain of Sem-5 indicate cooperative conformational coupling

We report the effects of peptide binding on the (15)N relaxation rates and chemical shifts of the C-SH3 of Sem-5. (15)N spin-lattice relaxation time (T(1)), spin-spin relaxation time (T(2)), and ((1)H)-(15)N NOE were obtained from heteronuclear 2D NMR experiments. These parameters were then analyzed using the Lipari-Szabo model free formalism to obtain parameters that describe the internal motions of the protein. High-order parameters (S(2) > 0.8) are found in elements of regular secondary structure, whereas some residues in the loop regions show relatively low-order parameters, notably the RT loop. Peptide binding is characterized by a significant decrease in the (15)N relaxation in the RT loop. Concomitant with the change in dynamics is a cooperative change in chemical shifts. The agreement between the binding constants calculated from chemical shift differences and that obtained from ITC indicates that the binding of Sem-5 C-SH3 to its putative peptide ligand is coupled to a cooperative conformational change in which a portion of the binding site undergoes a significant reduction in conformational heterogeneity.     

Probing the folding and unfolding dynamics of secondary and tertiary structures in a three-helix bundle protein

Fast relaxation kinetics studies of the B-domain of staphylococcal protein A were performed to characterize the folding and unfolding of this small three-helix bundle protein. The relaxation kinetics were initiated using a laser-induced temperature jump and probed using time-resolved infrared spectroscopy. The kinetics monitored within the amide I' absorbance of the polypeptide backbone exhibit two distinct kinetics phases with nanosecond and microsecond relaxation times. The fast kinetics relaxation time is close to the diffusion limits placed on protein folding reactions. The fast kinetics phase is dominated by the relaxation of the solvated helix (nu = 1632 cm(-1)), which reports on the fast relaxation of the individual helices. The slow kinetics phase follows the cooperative relaxation of the native helical bundle core that is monitored by both solvated (nu = 1632 cm(-1)) and buried helical IR bands (nu = 1652 cm(-1)). The folding rates of the slow kinetics phase calculated over an extended temperature range indicate that the core formation of this protein follows a pathway that is energetically downhill. The unfolding rates are much more strongly temperature-dependent indicating an activated process with a large energy barrier. These results provide significant insight into the primary process of protein folding and suggest that fast formation of helices can drive the folding of helical proteins.     

Structure-based kinetic modeling of excited-state transfer and trapping in histidine-tagged photosystem II core complexes from synechocystis

Chlorophyll fluorescence decay kinetics in photosynthesis are dependent on processes of excitation energy transfer, charge separation, and electron transfer in photosystem II (PSII). The interpretation of fluorescence decay kinetics and their accurate simulation by an appropriate kinetic model is highly dependent upon assumptions made concerning the homogeneity and activity of PSII preparations. While relatively simple kinetic models assuming sample heterogeneity have been used to model fluorescence decay in oxygen-evolving PSII core complexes, more complex models have been applied to the electron transport impaired but more highly purified D1-D2-cyt b(559) preparations. To gain more insight into the excited-state dynamics of PSII and to characterize the origins of multicomponent fluorescence decay, we modeled the emission kinetics of purified highly active His-tagged PSII core complexes with structure-based kinetic models. The fluorescence decay kinetics of PSII complexes contained a minimum of three exponential decay components at F(0) and four components at F(m). These kinetics were not described well with the single radical pair energy level model, and the introduction of either static disorder or a dynamic relaxation of the radical pair energy level was required to simulate the fluorescence decay adequately. An unreasonably low yield of charge stabilization and wide distribution of energy levels was required for the static disorder model, and we found the assumption of dynamic relaxation of the primary radical pair to be more suitable. Comparison modeling of the fluorescence decay kinetics from PSII core complexes and D1-D2-cyt b(559) reaction centers indicated that the rates of charge separation and relaxation of the radical pair are likely altered in isolated reaction centers.     

Anisotropic properties of human cortical bone with osteogenesis imperfecta

The heterogeneity of bone shape and size variation is modulated by genetic, mechanical, nutritional, and hormonal patterning throughout its lifetime. Microstructural changes across cross sections are a result of mechanistic optimization that results over the years of evolution while being based on universal, time-invariant ingredients and patterns. Here we report changes across anatomical sections of bone with osteogenesis imperfecta (OI) that undermines the work of evolution through genetic mutation. This work examines the microstructure and molecular composition of different anatomical positions (anterior, medial, posterior, and lateral regions) in the diaphysis of an OI human tibia. The study shows that although there is no significant microstructural difference, molecular changes are observed using FTIR revealing differences in molecular composition of the four anatomical positions. In addition, the nanomechanical properties of anterior section of OI bone seem more heterogeneous. The nanomechanical properties of interstitial lamellae in all these bone samples are consistently greater than those of osteonal lamellae. The nanomechanical properties of bone depend on its anatomical section and on the measurement direction as well. Variations in molecular structure with anatomical positions and also corresponding differences in nanomechanical properties are reported. These are compared to those observed typically in healthy bone illustrating the unique influence of OI on bone multiscale behavior which results from an evolutionary process lasting for many years.     

The influence of single-strand breaks on the kinetics of denaturation of DNA

The influence of single-strand breaks on the kinetics of the relaxation of DNA in a solution of low ionic strength has been investigated by a temperature jump method. The relaxation of DNA after a jump of 0.7 °C in the melting region has been monitored by measuring the extinction at 260 nm. For essentially monodisperse T4 DNA (M = 130 × 10⁶) two distinct relaxation times have been observed, that depend markedly on the initial extent of denaturation 1 ? θ. The larger relaxation time decreases from 450 sec to about 300 sec, the smaller one from 55 see to 30 when 1 ? θ increases from 0.03 to about 0.8. The dependence of these relaxation times on the average number of single-strand breaks per molecule (p) appears to be very small up to p = 100. However, the relative contribution of the slow process decreases sharply when p increases from 0.6 to 30 and remains nearly constant for larger p. The observations are discussed in the light recent theories of the kinetics of denaturation.