Two-state expansion and collapse of a polypeptide

The initial phase of folding for many proteins is presumed to be the collapse of the polypeptide chain from expanded to compact, but still denatured, conformations. Theory and simulations suggest that this collapse may be a two-state transition, characterized by barrier-crossing kinetics, while the collapse of homopolymers is continuous and multi-phasic. We have used a laser temperature-jump with fluorescence spectroscopy to measure the complete time-course of the collapse of denatured cytochrome c with nanosecond time resolution. We find the process to be exponential in time and thermally activated, with an apparent activation energy approximately 9 k(B)T (after correction for solvent viscosity). These results indicate that polypeptide collapse is kinetically a two-state transition. Because of the observed free energy barrier, the time scale of polypeptide collapse is dramatically slower than is predicted by Langevin models for homopolymer collapse.     

Two-state expansion and collapse of a polypeptide

The initial phase of folding for many proteins is presumed to be the collapse of the polypeptide chain from expanded to compact, but still denatured, conformations. Theory and simulations suggest that this collapse may be a two-state transition, characterized by barrier-crossing kinetics, while the collapse of homopolymers and random heteropolymers is continuous and multi-phasic. A new rapid-mixing flow technique has been used to resolve the late stages of polypeptide collapse, at time scales >/=45 microseconds. We have used a laser temperature-jump with fluorescence spectroscopy to resolve the complete time-course of the collapse of denatured cytochrome c with nanosecond time resolution. We find the process to be exponential in time and thermally activated, with an apparent activation energy approximately 9 k(B)T (after correction for solvent viscosity). These results indicate that polypeptide collapse is kinetically a two-state transition. Because of the observed free energy barrier, the time scale of polypeptide collapse is dramatically slower than is predicted by Langevin models for homopolymer collapse.     

Collapse Dynamics of Single Proteins Extended by Force

Single-molecule force spectroscopy has opened up new approaches to the study of protein dynamics. For example, an extended protein folding after an abrupt quench in the pulling force was shown to follow variable collapse trajectories marked by well-defined stages that departed from the expected two-state folding behavior that is commonly observed in bulk. Here, we explain these observations by developing a simple approach that models the free energy of a mechanically extended protein as a combination of an entropic elasticity term and a short-range potential representing enthalpic hydrophobic interactions. The resulting free energy of the molecule shows a force-dependent energy barrier of magnitude, ΔE = ɛ(F − F_c)^3/2, separating the enthalpic and entropic minima that vanishes at a critical force F_c. By solving the Langevin equation under conditions of a force quench, we generate folding trajectories corresponding to the diffusional collapse of an extended polypeptide. The predicted trajectories reproduce the different stages of collapse, as well as the magnitude and time course of the collapse trajectories observed experimentally in ubiquitin and I27 protein monomers. Our observations validate the force-clamp technique as a powerful approach to determining the free-energy landscape of proteins collapsing and folding from extended states.     

Observation of Continuous Contraction and a Metastable Misfolded State during the Collapse and Folding of a Small Protein

To obtain proper insight into how structure develops during a protein folding reaction, it is necessary to understand the nature and mechanism of the polypeptide chain collapse reaction, which marks the initiation of folding. Here, the time-resolved fluorescence resonance energy transfer technique, in which the decay of the fluorescence light intensity with time is used to determine the time evolution of the distribution of intra-molecular distances, has been utilized to study the folding of the small protein, monellin. It is seen that when folding begins, about one-third of the protein molecules collapse into a molten globule state (I_MG), from which they relax by continuous further contraction to transit to the native state. The larger fraction gets trapped into a metastable misfolded state. Exit from this metastable state occurs via collapse to the lower free energy I_MG state. This exit is slow, on a time scale of seconds, because of activation energy barriers. The trapped misfolded molecules as well as the I_MG molecules contract continuously and slowly as structure develops. A phenomenological model of Markovian evolution of the polymer chain undergoing folding, incorporating these features, has been developed, which fits well the experimentally observed time evolution of distance distributions. The observation that the “wrong turn” to the misfolded state has not been eliminated by evolution belies the common belief that the folding of functional protein sequences is very different from that of a random heteropolymer, and the former have been selected by evolution to fold quickly.     

On the compact form of linear duplex DNA: globular states of the uniform elastic (persistent) macromolecule

A theory of collapse of DNA considered as unifilar homopolymer is suggested. The collapse is interpreted as the coil-globule transition. Three reasons of the collapse such as the confinement in a microcavity, the influence of poor low-molecular-weight solvent and the influence of polymeric solvent were studied. The results are summed up by the stage diagrams in variables: DNA length versus the characteristics of the compaction factor (the cavity volume, the energy of attraction of DNA segments in poor low-molecular-weight solvent and the concentration of polymer added). It is shown that a sufficiently long DNA forms the spherical compact particle while the relatively short DNA forms the toroidal one. More delicate features of the tertiary structure are determined by the relative role of the bending stiffness and steric repulsions in preventing further collapse. As the compaction occurs in polymeric solvent almost all added polymer is forced out from the globule. Thus, the internal structure of the compact DNA particle in polymeric solvent is similar to that in the model of microcavity.     

Long-term potential ecosystem responses to greenhouse gas-induced thermohaline circulation collapse

Abrupt climate change, such as could occur with significant thermohaline circulation (THC) weakening, appears throughout the palaeoclimate record and in many model experiments. We examine potential responses of ecosystem structure and function to the combined influence of THC collapse and greenhouse gas increase in Central England using a broad range of temperature scenarios. We demonstrate that biological communities in the North Atlantic region could be heavily influenced by THC collapse, but that the pattern of ecosystem responses depends upon the seasonal pattern of temperature changes. Plausible THC collapse scenarios threaten the remnant habitat fragments, upon which much of England's remaining biodiversity depends, by causing shifts away from the currently dominant temperate broadleaf cold deciduous tree type. Furthermore, some ecosystem responses, particularly of energy partitioning between sensible and latent heat fluxes, constitute potentially substantial feedbacks to the local climate system. However, accurate assessment of biotic responses to THC collapse requires far better confidence of the resulting seasonal temperature cycle than climate models currently provide.     

The effect of hexadecaprenol on molecular organisation and transport properties of model membranes

The Langmuir monolayer technique and voltammetric analysis were used to investigate the properties of model lipid membranes prepared from dioleoylphosphatidylcholine (DOPC), hexadecaprenol (C80), and their mixtures. Surface pressure-molecular area isotherms, current-voltage characteristics, and membrane conductance-temperature were measured. Molecular area isobars, specific molecular areas, excess free energy of mixing, collapse pressure and collapse area were determined for lipid monolayers. Membrane conductance, activation energy of ion migration across the membrane, and membrane permeability coefficient for chloride ions were determined for lipid bilayers. Hexadecaprenol decreases the activation energy and increases membrane conductance and membrane permeability coefficient. The results of monolayer and bilayer investigations show that some electrical, transport and packing properties of lipid membranes change under the influence of hexadecaprenol. The results indicate that hexadecaprenol modulates the molecular organisation of the membrane and that the specific molecular area of polyprenol molecules depends on the relative concentration of polyprenols in membranes. We suggest that hexadecaprenol modifies lipid membranes by the formation of fluid microdomains. The results also indicate that electrical transmembrane potential can accelerate the formation of pores in lipid bilayers modified by long chain polyprenols.     

Exponential decay kinetics in "downhill" protein folding

The observation of single-exponential kinetic phases in early stages of protein folding is often interpreted as evidence that these phases are rate limited by significant energy or entropy barriers. However, although the existence of large barriers reliably implies exponential kinetics, the reverse is not necessarily true. A simple model for the hydrophobic collapse of a chain molecule demonstrates that a barrierless or "downhill" diffusional relaxation can give rise to kinetics that are practically indistinguishable from a pure exponential. Within this model, even a highly nonlinear experimental probe such as resonance energy transfer (F?rster transfer) could exhibit a large amplitude decay (greater than 90% in fluorescence) that deviates from a simple exponential by less than 0.5%. Only a detailed analysis of the dynamics is likely to reveal that a free energy barrier is absent.     

Coulomb forces control the density of the collapsed unfolded state of barstar

Although it has been recently shown that unfolded polypeptide chains undergo a collapse on transfer from denaturing to native conditions, the forces determining the dynamics and the size of the collapsed form have not yet been understood. Here, we use single-molecule fluorescence resonance energy transfer experiments on the small protein barstar to characterize the unfolded chain in guanidinium chloride (GdmCl) and urea. The unfolded protein collapses on decreasing the concentration of denaturants. Below the critical concentration of 3.5 M denaturant, the collapse in GdmCl leads to a more dense state than in urea. Since it is known that GdmCl suppresses electrostatic interactions, we infer that Coulomb forces are the dominant forces acting in the unfolded barstar under native conditions. This hypothesis is clearly buttressed by the finding of a compaction of the unfolded barstar by addition of KCl at low urea concentrations.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

The Current Collapse in AlGaN/GaN High-Electron Mobility Transistors Can Originate from the Energy Relaxation of Channel Electrons?

Influence of the energy relaxation of the channel electrons on the performance of AlGaN/GaN high-electron mobility transistors (HEMTs) has been investigated using self-consistent solution to the coupled Schrödinger equation and Poisson equation. The first quantized energy level in the inversion layer rises and the average channel electron density decreases when the channel electric field increases from 20 kV/cm to 120 kV/cm. This research also demonstrates that the energy relaxation of the channel electrons can lead to current collapse and suggests that the energy relaxation should be considered in modeling the performance of AlGaN/GaN HEMTs such as, the gate leakage current, threshold voltage, source-drain current, capacitance-voltage curve, etc.     

Characterisation of the hydrophobic collapse of polystyrene in water using free energy techniques

We characterise the hydrophobic collapse of single polystyrene chains in water using molecular dynamics simulations. Specifically, we calculate the potential of mean force for the collapse of a single polystyrene chain in water using metadynamics, comparing the results between all atomistic with coarse-grained (CG) molecular simulation. We next explore the scaling behaviour of the collapsed globular shape at the minimum energy configuration, characterised by the radius of gyration, as a function of chain length. The exponent is close to one third, consistent with that predicted for a polymer chain in bad solvent. We also explore the scaling behaviour of the solvent accessible surface area (SASA) as a function of chain length, finding a similar exponent for both all atomistic and CG simulations. Furthermore, calculation of the local water density as a function of chain length near the minimum energy configuration suggests that intermediate chain lengths are more likely to form dewetted states, as compared to shorter or longer chain lengths.     

Effect of rapid changes of the oxygenation state and other external parameters on the long-term behavior of the energy metabolism in the erythrocyte]

The red blood cell when transported through the circulatory system is exposed to a steady (approximately periodical) change of environmental conditions causing a permanent fluctuation of its important metabolic parameters. In a simple theoretical model it is demonstrated that a rapid oscillation of such parameters may stabilize a metabolic state which will collapse when this oscillation breaks off. The hypothesis is advanced that parameter oscillations caused by the physiological function of the red blood cell may be of importance for the maintenance of its energy metabolism and that the break-off of these oscillations may be a potential cause for the metabolic collapse, e.g. in stored blood.     

Catastrophic desert formation in Daisyworld

Feedback between life and its environment is ubiquitous but the strength of coupling and its global implications remain hotly debated. Abrupt changes in the abundance of life for small changes in forcing provide one indicator of regulation, for example, when vegetation-climate feedback collapses in the formation of a desert. Here we use a two-dimensional "Daisyworld" model with curvature to show that catastrophic collapse of life under gradual forcing provides a testable indicator of environmental feedback. When solar luminosity increases to a critical value, a desert forms across a wide band of the planet. The scale of collapse depends on the strength of feedback. The efficiency of temperature regulation is limited by mutation rate in an analogous manner to the limitation of adaptive fitness in evolutionary theories. The final state of the system emerging from single-site rules can be described by two global quantities: optimization of temperature regulation and maximization of diversity, which are mathematically analogous to energy and entropy in thermodynamics.     

Evidence for Initial Non-specific Polypeptide Chain Collapse During the Refolding of the SH3 Domain of PI3 Kinase

Refolding of the SH3 domain of PI3 kinase from the guanidine hydrochloride (GdnHCl)-unfolded state has been probed with millisecond (stopped flow) and sub-millisecond (continuous flow) measurements of the change in fluorescence, circular dichroism, ANS fluorescence and three-site fluorescence resonance energy transfer (FRET) efficiency. Fluorescence measurements are unable to detect structural changes preceding the rate-limiting step of folding, whereas measurements of changes in ANS fluorescence and FRET efficiency indicate that polypeptide chain collapse precedes the major structural transition. The initial chain collapse reaction is complete within 150 μs. The collapsed form at this time possesses hydrophobic clusters to which ANS binds. Each of the three measured intra-molecular distances has contracted to an extent predicted by the dependence of the FRET signal in completely unfolded protein on denaturant concentration, indicating that contraction is non-specific. The extent of contraction of each intra-molecular distance in the collapsed product of sub-millisecond folding increases continuously with a decrease in [GdnHCl]. The gradual contraction is continuous with the gradual contraction seen in completely unfolded protein, and its dependence on [GdnHCl] is not indicative of an all-or-none collapse reaction. The dependence of the extent of contraction on [GdnHCl] was similar for the three distances, indicating that chain collapse occurs in a synchronous manner across different segments of the polypeptide chain. The sub-millisecond measurements of folding in GdnHCl were unable to determine whether hydrophobic cluster formation, probed by ANS fluorescence measurement, precedes chain contraction probed by FRET. To determine whether hydrogen bonding plays a role in initial chain collapse, folding was initiated by dilution of the urea-unfolded state. The extent of contraction of at least one intra-molecular distance in the collapsed product of sub-millisecond folding in urea is similar to that seen in GdnHCl, and the initial contraction in urea too appears to be gradual.     

Seasonal changes in particulate and dissolved lipids in a eutrophic prairie lake

1. Critical periods of lipid energy transfer from phyto- to zooplankton were inferred by comparing seasonal patterns of particulate and dissolved lipid fractions in lake water with temporal changes in lipid energy reserves of the zooplankton in a hypereutrophic lake.
2. The midsummer phytoplankton community was dominated by the bloom-forming cyanobacterium Aphanizomenon flos-aquae. The collapse of the bloom was accompanied by a 2-week period of severe nitrogen deficiency after which there was a marked increase in the concentration of lipid energy reserves in the particulate (algal) fraction.
3. Areal lipid energy reserves of the dominant herbivorous zooplankton responded positively to changes in the tri-and diacylglycerol content of the particulate fraction of lake water in a species-specific manner.
4. Bacterial numbers also peaked in September concomitant with a large increase in free fatty acids in the dissolved lipid fraction probably produced by the decay of the
A. flos-aquae bloom.
5. The association between periods of nitrogen deficiency and increased energy reserve lipids in the particulate fraction supports observations made with laboratory algal cultures that periods of nutrient deficiency may intensify lipid synthesis in some algal species, thereby enhancing the rate of lipid energy transfer from phytoplankton to zooplankton.     

The interactions of cobalt(II) with mitochondria from rat liver

The interactions of Co²⁺ with mitochondria have been investigated. The results indicate that Co²⁺ inhibits ATP synthesis. Further investigations into ATP synthesis mechanisms indicated that inhibition is due to the opening of a transmembrane pore. The opening of this pore causes the collapse of the high-energy intermediate where, under a pH and a potential gradient, the energy is stored and subsequently utilized to form ATP from ADP.     

DNA condensation by multivalent cations

In the presence of multivalent cations, high molecular weight DNA undergoes a dramatic condensation to a compact, usually highly ordered toroidal structure. This review begins with an overview of DNA condensation : condensing agents, morphology, kinetics, and reversibility, and the minimum size required to form orderly condensates. It then summarizes the statistical mechanics of the collapse of stiff polymers, which shows why DNA condensation is abrupt and why toroids are favored structures. Various ways to estimate or measure intermolecular forces in DNA condensation are discussed, all of them agreeing that the free energy change per base pair is very small, on the order of 1% of thermal energy. Experimental evidence is surveyed showing that DNA condensation occurs when about 90% of its charge is neutralized by counterions. The various intermolecular forces whose interplay gives rise to DNA condensation are then reviewed. The entropy loss upon collapse of the expanded wormlike coil costs free energy, and stiffness sets limits on tight curvature. However, the dominant contributions seem to come from ions and water. Electrostatic repulsions must be overcome by high salt concentrations or by the correlated fluctuations of territorially bound multivalent cations. Hydration must be adjusted to allow a cooperative accommodation of the water structure surrounding surface groups on the DNA helices as they approach. Undulations of the DNA in its confined surroundings extend the range of the electrostatic forces. The condensing ions may also subtly modify the local structure of the double helix. © 1998 John Wiley & Sons, Inc. Biopoly 44: 269–282, 1997     

Growth cone collapse through coincident loss of actin bundles and leading edge actin without actin depolymerization

Repulsive guidance cues can either collapse the whole growth cone to arrest neurite outgrowth or cause asymmetric collapse leading to growth cone turning. How signals from repulsive cues are translated by growth cones into this morphological change through rearranging the cytoskeleton is unclear. We examined three factors that are able to induce the collapse of extending Helisoma growth cones in conditioned medium, including serotonin, myosin light chain kinase inhibitor, and phorbol ester. To study the cytoskeletal events contributing to collapse, we cultured Helisoma growth cones on polylysine in which lamellipodial collapse was prevented by substrate adhesion. We found that all three factors that induced collapse of extending growth cones also caused actin bundle loss in polylysine-attached growth cones without loss of actin meshwork. In addition, actin bundle loss correlated with specific filamentous actin redistribution away from the leading edge that is characteristic of repulsive factors. Finally, we provide direct evidence using time-lapse studies of extending growth cones that actin bundle loss paralleled collapse. Taken together, these results suggest that actin bundles could be a common cytoskeletal target of various collapsing factors, which may use different signaling pathways that converge to induce growth cone collapse.