Formation and development of photosynthetic units in repigmenting Rhodopseudomonas sphaeroides wild type and "Phofil" mutant strain.

The formation of the photosynthetic apparatus in the wild type Rhodopseudomonas sphaeroides and in the "Phofil" mutant was investigated by analyzing absorption and fluorescence parameters and the kinetics of fluorescence induction. Repigmentation was induced by transfer of bleached cells to semi-aerobic culture conditions. 1. In the "Phofil" mutant, functional photosynthetic units appear at pigment cellular contents which depend on the physiological state of the inoculum. The unadapted mutant can reach the functional units stage at a cellular pigment level 20 times lower than that of the wild type, although the size and composition of the units are identical in both strains. This rules out the hypothesis of photosynthetic units forming by random integration of pigments into the membrane. Moreover, the fact that units are separate at this stage (as shown by the exponential shape of fluorescence induction kinetics) suggests that the units' formation proceeds from discrete predetermined membrane sites. 2. In repigmentng wild type cells, the multistep assembly of bacteriochlorophyll complexes appears correlated to their organization in photosynthetic units as follows: (i) During a first stage, B-875 is mostly synthesized, while the efficiency of transfer increases, suggesting that the pigments are initially interpersed at comparatively large average distances from each other in the bleached membrane. (ii) After 1.5 h of repigmentation, the transfer and trapping efficiencies reach a maximum. The units (26 B-875 + 11 B-850 per center) are still separate, as shown by exponential fluorescence kinetics. (iii) The increase in the units' size then essentially proceeds through B-850 incorporation. Energy transfer between units occurs at a comparatively late stage, i.e., 5 h repigmentation.     

Entropic barriers, transition states, funnels, and exponential protein folding kinetics: a simple model

This paper presents an analytically tractable model that captures the most elementary aspect of the protein folding problem, namely that both the energy and the entropy decrease as a protein folds. In this model, the system diffuses within a sphere in the presence of an attractive spherically symmetric potential. The native state is represented by a small sphere in the center, and the remaining space is identified with unfolded states. The folding temperature, the time-dependence of the populations, and the relaxation rate are calculated, and the folding dynamics is analyzed for both golf-course and funnel-like energy landscapes. This simple model allows us to illustrate a surprising number of concepts including entropic barriers, transition states, funnels, and the origin of single exponential relaxation kinetics.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

A large collapsed-state RNA can exhibit simple exponential single-molecule dynamics

The process of large RNA folding is believed to proceed from many collapsed structures to a unique functional structure requiring precise organization of nucleotides. The diversity of possible structures and stabilities of large RNAs could result in non-exponential folding kinetics (e.g. stretched exponential) under conditions where the molecules have not achieved their native state. We describe a single-molecule fluorescence resonance energy transfer (FRET) study of the collapsed-state region of the free energy landscape of the catalytic domain of RNase P RNA from Bacillus stearothermophilus (C_thermo). Ensemble measurements have shown that this 260 residue RNA folds cooperatively to its native state at ≥1 mM Mg²⁺, but little is known about the conformational dynamics at lower ionic strength. Our measurements of equilibrium conformational fluctuations reveal simple exponential kinetics that reflect a small number of discrete states instead of the expected inhomogeneous dynamics. The distribution of discrete dwell times, collected from an “ensemble” of 300 single molecules at each of a series of Mg²⁺ concentrations, fit well to a double exponential, which indicates that the RNA conformational changes can be described as a four-state system. This finding is somewhat unexpected under [Mg²⁺] conditions in which this RNA does not achieve its native state. Observation of discrete well-defined conformations in this large RNA that are stable on the seconds timescale at low [Mg²⁺] (<0.1 mM) suggests that even at low ionic strength, with a tremendous number of possible (weak) interactions, a few critical interactions may produce deep energy wells that allow for rapid averaging of motions within each well, and yield kinetics that are relatively simple.     

Transition from exponential to linear photoautotrophic growth changes the physiology of <Emphasis Type="Italic">Synechocystis</Emphasis> sp. PCC 6803

Phototrophic microorganisms like cyanobacteria show growth curves in batch culture that differ from the corresponding growth curves of chemotrophic bacteria. Instead of the usual three phases, i.e., lag-, log-, and stationary phase, phototrophs display four distinct phases. The extra growth phase is a phase of linear, light-limited growth that follows the exponential phase and is often ignored as being different. Results of this study demonstrate marked growth phase-dependent alterations in the photophysiology of the cyanobacterium Synechocystis sp. PCC 6803 between cells harvested from the exponential and the linear growth phase. Notable differences are a gradual shift in the energy transfer of the light-harvesting phycobilisomes to the photosystems and a distinct change in the redox state of the plastoquinone pool. These differences will likely affect the result of physiological studies and the efficiency of product formation of Synechocystis in biotechnological applications. Our study also demonstrates that the length of the period of exponential growth can be extended by a gradually stronger incident light intensity that matches the increase of the cell density of the culture.     

Kinetics of gram-negative bacterial cell elongation as measured by using the large rod "Lineola longa"

Photomicrographic data were collected to measure the kinetics of elongation of "Lineola longa," a large gram-negative rod ranging from 5 to 10 microns long, during the exponential phase of growth. Its large size makes this organism especially well suited for light microscopic observations. Because this organism is aerobic, it was necessary to ensure a saturating supply of oxygen during growth. Oxygen was supplied by using Chlorella species, in a Wheaton microculture slide, as an oxygen donor separated from the bacteria by a thin layer of agar. In another set of experiments, water-saturated air replaced Chlorella species, with similar results. Statistical analysis of the data showed that "L. longa" elongates in an exponential manner. Minicell-like structures, small spherical cells lacking DNA, were occasionally seen to be produced by aberrant septation. These minicells were seen most often at the end of the exponential-growth phase. A model of cell growth is proposed to account for these observations.     

A fractional calculus approach to self-similar protein dynamics.

Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.     

Squeezed exponential kinetics to describe a nonglassy downhill folding as observed in a lattice protein model

We previously studied the so-called strange kinetics in the two-dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27-mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two-state-like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or "shrunken") exponential function, exp [-(t/tau)beta] with beta > 1, at temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the nonglassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single-domain proteins may follow the squeezed exponential kinetics at about the room temperature.     

Solvation effects and driving forces for protein thermodynamic and kinetic cooperativity: how adequate is native-centric topological modeling?

What energetic and solvation effects underlie the remarkable two-state thermodynamics and folding/unfolding kinetics of small single-domain proteins? To address this question, we investigate the folding and unfolding of a hierarchy of continuum Langevin dynamics models of chymotrypsin inhibitor 2. We find that residue-based additive Gō-like contact energies, although native-centric, are by themselves insufficient for protein-like calorimetric two-state cooperativity. Further native biases by local conformational preferences are necessary for protein-like thermodynamics. Kinetically, however, even models with both contact and local native-centric energies do not produce simple two-state chevron plots. Thus a model protein's thermodynamic cooperativity is not sufficient for simple two-state kinetics. The models tested appear to have increasing internal friction with increasing native stability, leading to chevron rollovers that typify kinetics that are commonly referred to as non-two-state. The free energy profiles of these models are found to be sensitive to the choice of native contacts and the presumed spatial ranges of the contact interactions. Motivated by explicit-water considerations, we explore recent treatments of solvent granularity that incorporate desolvation free energy barriers into effective implicit-solvent intraprotein interactions. This additional feature reduces both folding and unfolding rates vis-à-vis that of the corresponding models without desolvation barriers, but the kinetics remain non-two-state. Taken together, our observations suggest that interaction mechanisms more intricate than simple Gō-like constructs and pairwise additive solvation-like contributions are needed to rationalize some of the most basic generic protein properties. Therefore, as experimental constraints on protein chain models, requiring a consistent account of protein-like thermodynamic and kinetic cooperativity can be more stringent and productive for some applications than simply requiring a model heteropolymer to fold to a target structure.     

Picosecond time-resolved energy transfer in Porphyridium cruentum. Part I. In the intact alga

The wavelength-resolved fluorescence emission kinetics of the accessory pigments and chlorophyll a in Porphyridium cruentum have been studied by pico-second laser spectroscopy. Direct excitation of the pigment B-phycoerythrin with a 530 nm, 6 ps pulse produced fluorescence emission from all of the pigments as a result of energy transfer between the pigments to the reaction centre of Photosystem II. The emission from B-phycoerythrin at 576 nm follows a nonexponential decay law with a mean fluorescence lifetime of 70 ps, whereas the fluorescence from R-phycocyanin (640 nm), allophycocyanin (660 nm) and chlorophyll a (685 nm) all appeared to follow an exponential decay law with lifetimes of 90 ps, 118 ps and 175 ps respectively. Upon closure of the Photosystem II reaction centres with 3-(3,4-dichlorophenyl)-1,1-dimethylurea and preillumination the chlorophyll a decay became non-exponential, having a long component with an apparent lifetime of 840 ps. The fluorescence from the latter three pigments all showed finite risetimes to the maximum emission intensity of 12 ps for R-phycocyanin, 24 ps for allophycocyanin and 50 ps for chlorophyll a. A kinetic analysis of these results indicates that energy transfer between the pigments is at least 99% efficient and is governed by an exp --At1/2 transfer function. The apparent exponential behaviour of the fluorescence decay functions of the latter three pigments is shown to be a direct result of the energy transfer kinetics, as are the observed risetimes in the fluorescence emissions.     

Probe-dependent and nonexponential relaxation kinetics: unreliable signatures of downhill protein folding

The theoretical suggestion that some proteins may encounter no significant free energy barriers during their folding raises an important question: What experimental signature does this downhill folding produce? Several authors have argued that nonexponential (and especially stretched exponential) or probe‐dependent kinetics represent useful experimental signatures of a downhill free energy surface. Here we examine more closely the connection between unusual kinetics and downhill energy surfaces. Simulation of diffusive relaxation dynamics on a variety of generically downhill, two‐dimensional free energy surfaces shows that these surfaces do not necessarily produce either probe‐dependent or significantly nonexponential kinetics. Conversely, we find that two‐dimensional surfaces with significant (>3k_B T) energy barriers can readily give rise to nonexponential and probe‐dependent kinetics. These results show that downhill folding does not constitute a necessary or sufficient condition for nonexponential and/or probe‐dependent folding kinetics. One cannot easily prove or disprove that a protein folds downhill simply by studying its relaxation kinetics. Proteins 2007. © 2007 Wiley‐Liss, Inc.     

Experimental characterization of the folding kinetics of the notch ankyrin domain

Proteins constructed from linear arrays of tandem repeats provide a simplified architecture for understanding protein folding. Here, we examine the folding kinetics of the ankyrin repeat domain from the Drosophila Notch receptor, which consists of six folded ankyrin modules and a seventh partly disordered N-terminal ankyrin repeat sequence. Both the refolding and unfolding kinetics are best described as a sum of two exponential phases. The slow, minor refolding phase is limited by prolyl isomerization in the denatured state (D). The minor unfolding phase, which appears as a lag during fluorescence-detected unfolding, is consistent with an on-pathway intermediate (I). This intermediate, although not directly detected during refolding, is shown to be populated by interrupted refolding experiments. When plotted against urea, the rate constants for the major unfolding and refolding phases define a single non-linear v-shaped chevron, as does the minor unfolding phase. These two chevrons, along with unfolding amplitudes, are well-fitted by a sequential three-state model, which yields rate constants for the individual steps in folding and unfolding. Based on these fitted parameters, the D to I step is rate-limiting, and closely matches the major observed refolding phase at low denaturant concentrations. I appears to be midway between N and D in folding free energy and denaturant sensitivity, but has Trp fluorescence properties close to N. Although the Notch ankyrin domain has a simple architecture, folding is slow, with the limiting refolding rate constant as much as seven orders of magnitude smaller than expected from topological predictions.     

Consideration of the Possibility that the slow step in protein denaturation reactions is due to cis-trans isomerism of proline residues.

A model is proposed to account for the observation that the denaturation of small proteins apparently occurs in two kinetic phases. It is suggested that only one of these phases--the fast one--is actually an unfolding process. The slow phase is assumed to arise from the cis-trans isomerism of proline residues in the denaturated protein. From model compound data, it is shown that the expected rate for isomerism is in satisfactory agreement with the rates actually observed for protein folding. It is also shown that a simple model of protein unfolding based on the isomerism concept is very successful in accounting for many known experimental characteristics of the kinetics and thermodynamic of protein denaturation. Thus, the model is able to predict that two kinetic phases will be seen in the transition region while none are seen in the base-line regions, that both the fast and slow refolding phases lead to the native protein as the product, that the fast phase becomes the only observable phase for jumps ending far in the denatured base-line region, that most or all small proteins show a limiting low-temperature activation energy of ca. 20,000 cal, and that the relaxtion time for the slow phase seen in cytochrome c denaturation is much shorter than for all other small proteins. By utilizing "double-jump" experiments, it is shown directly that the slow phase is not part of the unfolding process but that it corresponds to a transition among two or more denatured forms which have identical spectroscopic (286.5 nm) properties. Thus, the slow relaxation is "invisible" except in the transition region where it couples to the fast unfolding equilibrium. Finally, since the present model assumes that only one of the major kinetic phases seen in denaturation reactions is concerned with the denaturation process per se, it is in agreement with numerous thermodynamic studies which show consistency with the two-state model for unfolding.     

Delays in inactivation development and activation kinetics in myxicola giant axons

Na inactivation was studied in Myxicola (two-pulse procedure, 6-ms gap between conditioning and test pulses). Inactivation developed with an initial delay (range 130-817 microseconds) followed by a simple exponential decline (time constant tau c). Delays (deviations from a simple exponential) are seen only for brief conditioning pulses were gNa is slightly activated. Hodgkin-Huxley kinetics with series resistance, Rs, predict deviations from a simple exponential only for conditioning pulses that substantially activate gNa. Reducing INa fivefold (Tris substitution) had no effect on either tau c or delay. Delay in not generated by Rs or by contamination from activation development. The slowest time constant in Na tails is approximately 1 ms (Goldman and Hahin, 1978) and the gap was 6 ms. Shortening the gap to 2 ms had no effect on either tau c or delay. Delay is a true property of the channel. Delay decreased with more positive conditioning potentials, and also decreased approximately proportionally with time to peak gNa during the conditioning pulse, as expected for sequentially coupled activation and inactivation. In a few cases the difference between Na current values for brief conditioning pulses and the tau c exponential could be measured. Difference values decayed exponentially with time constant tau m. The inactivation time course is described by a model that assumes a process with the kinetics of gNa activation as a precursor to inactivation.     

A study of mass transfer kinetics in an enantiomeric separation system using a polymeric imprinted stationary phase

Chromatographic data pertaining to the enantioseparation of L- and D-phenylalanine anilide (PA) on a polymeric stationary phase imprinted with L-PA were studied from the viewpoints of phase equilibrium, mass transfer kinetics, and the thermodynamic properties of this enantiomeric separation system. The concentration dependence of the lumped mass transfer rate coefficient (k(m,L)) previously published was analyzed to obtain new information concerning the mass transfer characteristics in this chiral separation system. It was shown that intraparticle diffusion contributed much more to k(m,L) than adsorption/desorption. The positive concentration dependence of k(m,L) seemed to be interpreted by considering that of the surface diffusion coefficient, itself explained by the heterogeneous surface model. The characteristic features of the phase equilibrium, the mass transfer kinetics, and the thermodynamics of the enantiomeric separation system probably result from the adsorption energy distribution on the surface of the imprinted phase having an exponential decay.     

Transfer of long-chain fluorescent free fatty acids between unilamellar vesicles

Movement of free fatty acids (ffa) between small unilamellar vesicles (SUV) was studied by measuring the transfer of fluorescent n-(9-anthroyloxy)-labeled analogues (AOffa) between donor and acceptor vesicles. Donors were composed of egg phosphatidylcholine (PC) loaded with 1-2 mol % AOffa, and acceptors were egg PC containing 10-12 mol % N-(7-nitro-2,1,3-benzoxadiazol-4-yl)phosphatidylethanolamine (NBD-PE). The fluorescence of AO added directly to acceptor SUV was greater than 98% quenched by energy transfer to NBD. Thus, AOffa movement from donor to acceptor was monitored by the time-dependent decrease in AO fluorescence. The transfer of the short-chain AOffa, although too fast to be resolved by the methods used here, is consistent with studies that find transfer rates on the order of milliseconds and kinetics which are first order. In contrast, transfer rates for the long-chain AOffa are more than 2 orders of magnitude slower, and the kinetics of the transfer process are best described by the sum of two exponentials plus a constant. The ffa ionization state was also found to be an important determinant of transfer rate. The charged species transferred an average of 10-fold faster than the protonated ffa. The ffa pKa in the membrane is 9, as calculated from the pH dependence of transfer. Similar to results found for other lipids, long-chain AOffa are transferred via water rather than a collision-mediated process. The aqueous phase route of AOffa intermembrane transfer is indicated by the lack of effect on transfer of large alterations in the product of donor and acceptor phospholipid concentrations. Moreover, the transfer rate is decreased as [NaCl] is increased from 0.1 to 4 M. This effect of ionic strength is probably due not only to a decrease in the aqueous phase partition of the AOffa but also to an alteration in bilayer structure, as measured by fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene. The observed kinetics are consistent with a model in which the transfer involves two steps: transbilayer movement between the inner and outer bilayer leaflets, followed by transfer from the outer leaflet to the aqueous phase (off rate). Within the framework of this model, the observed slow rate is primarily determined by the rate of transbilayer movement, and the observed fast rate is approximately equal to the off rate. The off rate is about 10-fold faster than the rate of transbilayer movement.     

Combined fluorescence and photovoltage studies on chlorosome containing bacteria

Energy transfer kinetics, primary charge separation, antenna size and excitonic connectivity of photosynthetic units (PSU) in whole cells of Chloroflexus aurantiacus were studied at room temperature by ps-fluorescence and ps-photovoltage as well as by stationary fluorescence-spectroscopy and fluorescence induction measurements. The fluorescence decay kinetics measured at different wavelengths are in accordance with the currently accepted sequential energy transfer from the chlorosomes via the baseplates to the B808–866 complexes and the final trapping in the RC with time constants of 19 ± 2 ps, 40 ± 4 ps and 90 ± 9 ps, respectively. However, the quantitative analysis of fluorescence spectra and the occurrence of slow phases in the fluorescence decays reveal that in whole cells a significant fraction of BChl c in the chlorosome and of BChl a in the baseplate is unconnected. The photovoltage kinetics consisted of two electrogenic phases with time constants of 118 ± 5 ps and 326 ± 35 ps and comparable electrogenicities. The first phase is ascribed to trapping from the B808-866 complexes by P+H_A- formation and the second one to charge stabilization on a quinone acceptor. Fluorescence induction curves displayed a pronounced sigmoidicity, indicating efficient lateral energy transfer between neighbored PSUs and a dense packing of 19 reaction centers (RC) beneath one chlorosome. A quantitative analysis of the fluorescence-induction curves at different excitation wavelengths allows the estimation of pigment stoichiometries (i.e. antenna sizes): BChl c/RC 794 and B808/RC 15.     

Apparent heterogeneity in the response of quiescent swiss 3T3 cells to serum growth factors: implications for the transition probability model and parallels with "cellular senescence" and "competence"

When subconfluent, Swiss 3T3 cells made quiescent by serum deprivation are stimulated with low concentrations of serum (ca. 1%), only a proportion of them (roughly 50%) enter S phase despite daily replacement with fresh, low-serum medium. The cells that fail to enter S phase are not incapable of doing so, since most of them initiate DNA synthesis after transfer to 10% serum. It would appear that individual cells vary in their growth factor requirements. Using time-lapse cinemicroscopy a few of the cells that respond to low serum were seen to give rise to several generations of progeny, while the majority of cells failed to divide at all, or divided once at most. Despite this, differences between cells in growth factor requirements do not seem to be heritable in the long term, since attempts to enrich for responding cells by prolonged culture in 1% serum have been unsuccessful. Rather, it would appear that the capacity to respond to low serum is an unstable property lost after a few generations in low serum. The loss of responsiveness shows parallels with "cellular senescence" and could conceivably result from decay of the platelet-derived growth factor-induced state of "competence." But regardless of why some cells respond to low serum while others do not, it is clear that the kinetics of entry into S phase after serum stimulation of quiescent 3T3 cells are not strictly first-order, since the labelling index plateaus after roughly 3 days at values substantially below 100%. As such, the kinetics, though not contradicting the transition probability model, cannot be taken to support it as was previously thought.     

Electron transfer kinetics in photosynthetic reaction centers embedded in trehalose glasses: trapping of conformational substates at room temperature.

We report on room temperature electron transfer in the reaction center (RC) complex purified from Rhodobacter sphaeroides. The protein was embedded in trehalose-water systems of different trehalose/water ratios. This enabled us to get new insights on the relationship between RC conformational dynamics and long-range electron transfer. In particular, we measured the kinetics of electron transfer from the primary reduced quinone acceptor (Q(A)(-)) to the primary photo oxidized donor (P(+)), by time-resolved absorption spectroscopy, as a function of the matrix composition. The composition was evaluated either by weighing (liquid samples) or by near infrared spectroscopy (highly viscous or solid glasses). Deconvolution of the observed, nonexponential kinetics required a continuous spectrum of rate constants. The average rate constant ( = 8.7 s(-1) in a 28% (w/w) trehalose solution) increases smoothly by increasing the trehalose/water ratio. In solid glasses, at trehalose/water ratios > or = 97%, an abrupt increase is observed ( = 26.6 s(-1) in the driest solid sample). A dramatic broadening of the rate distribution function parallels the above sudden increase. Both effects fully revert upon rehydration of the glass. We compared the kinetics observed at room temperature in extensively dried water-trehalose matrices with the ones measured in glycerol-water mixtures at cryogenic temperatures and conclude that, in solid trehalose-water glasses, the thermal fluctuations among conformational substates are inhibited. This was inferred from the large broadening of the rate constant distribution for electron transfer obtained in solid glasses, which was due to the free energy distribution barriers having become quasi static. Accordingly, the RC relaxation from dark-adapted to light-adapted conformation, which follows primary charge separation at room temperature, is progressively hindered over the time scale of P(+)Q(A)(-) charge recombination, upon decreasing the water content. In solid trehalose-water glasses the electron transfer process resulted much more affected than in RC dried in the absence of sugar. This indicated a larger hindering of the internal dynamics in trehalose-coated RC, notwithstanding the larger amount of residual water present in comparison with samples dried in the absence of sugar.