Analysis of photoacoustic waveforms using the nonlinear least squares method.

Pulsed-laser photoacoustics is a technique which measures photoinduced enthalpic and volumetric changes on the nano- and microsecond timescales. Analysis of photoacoustic data generally requires deconvolution for a sum of exponentials, a procedure which has been developed extensively in the field of time-resolved fluorescence decay. Initial efforts to adapt an iterative nonlinear least squares computer program, utilizing the Marquardt algorithm, from the fluorescence field to photoacoustics indicated that significant modifications were needed. The major problem arises from the wide range of transient decay times which must be addressed by the photoacoustic technique. We describe an alternative approach to numerical convolution with exponential decays, developed to overcome the problems. Instead of using an approximation method (Simpson's rule) for evaluating the convolution integral, we construct a continuous instrumental response function by quadratic fitting of the discrete data and evaluate the convolution integral directly, without approximations. The success and limitations of this quadratic-fit convolution program are then demonstrated using simulated data. Finally, the program is applied to the analysis of experimental data to compare the resolution capabilities of two commercially available transducers. The advantages of a broadband, heavily damped transducer are shown for a standard organic photochemical system, the quenching of the triplet state of benzophenone by 2,5-dimethyl-2,4-hexadiene.     

A comparison of deconvolution techniques for stress relaxation

Stress relaxation (or equivalently creep) allows a large range of the relaxation (retardation) spectrum of materials to be examined, particularly at lower frequencies. However, higher frequency components of the relaxation curves (typically of the order of Hertz) are attenuated due to the finite time taken to strain the specimen. This higher frequency information can be recovered by deconvolution of the stress and strain during the loading period. This paper examines the use of three separate deconvolution techniques: numerical (Fourier) deconvolution, semi-analytical deconvolution using a theoretical form of the strain, and deconvolution by a linear approximation method. Both theoretical data (where the exact form of the relaxation function is known) and experimental data were used to assess the accuracy and applicability of the deconvolution methods. All of the deconvolution techniques produced a consistent improvement in the higher frequency data up to the frequencies of the order of Hertz, with the linear approximation method showing better resolution in high-frequency analysis of the theoretical data. When the different deconvolution techniques were applied to experimental data, similar results were found for all three deconvolution techniques. Deconvolution of the stress and strain during loading is a simple and practical method for the recovery of higher frequency data from stress-relaxation experiments.     

Increasing the Time Resolution of Single-Molecule Experiments with Bayesian Inference

Many time-resolved single-molecule biophysics experiments seek to characterize the kinetics of biomolecular systems exhibiting dynamics that challenge the time resolution of the given technique. Here, we present a general, computational approach to this problem that employs Bayesian inference to learn the underlying dynamics of such systems, even when they are much faster than the time resolution of the experimental technique being used. By accurately and precisely inferring rate constants, our Bayesian inference for the analysis of subtemporal resolution dynamics approach effectively enables the experimenter to super-resolve the poorly resolved dynamics that are present in their data.     

Phase transition kinetics of lipid bilayer membranes studied by time-resolved pressure perturbation calorimetry

The relaxation kinetics of aqueous lipid dispersions after a pressure jump (p-jump) was investigated using time-resolved pressure perturbation calorimetry (PPC). Analysis of the calorimetric response curves by deconvolution with the instrumental response function gives information about slow processes connected with the lipid phase transition. The lipid transition from the gel to the liquid-crystalline state was found to be a multi-step process with relaxation constants in the seconds range resolvable by time-resolved PPC and faster processes with relaxation times shorter than ca. 5 s that could not be resolved by the instrument. The faster processes comprise ca. 50% of the total heat uptake at the transition midpoint. This is the first calorimetric measurement showing the multi-step nature of the transition. The results are in good agreement with data obtained with other detection methods and with molecular modelling experiments describing the transition as a multi-step process with nucleation and growth steps.     

Physiochemical Modeling of Vesicle Dynamics upon Osmotic Upshift

We modeled the relaxation dynamics of (lipid) vesicles upon osmotic upshift, taking into account volume variation, chemical reaction kinetics, and passive transport across the membrane. We focused on the relaxation kinetics upon addition of impermeable osmolytes such as KCl and membrane-permeable solutes such as weak acids. We studied the effect of the most relevant physical parameters on the dynamic behavior of the system, as well as on the relaxation rates. We observe that 1) the dynamic complexity of the relaxation kinetics depends on the number of permeable species; 2) the permeability coefficients (P) and the weak acid strength (pK_a-values) determine the dynamic behavior of the system; 3) the vesicle size does not affect the dynamics, but only the relaxation rates of the system; and 4) heterogeneities in the vesicle size provoke stretching of the relaxation curves. The model was successfully benchmarked for determining permeability coefficients by fitting of our experimental relaxation curves and by comparison of the data with literature values (in this issue of Biophysical Journal). To describe the dynamics of yeast cells upon osmotic upshift, we extended the model to account for turgor pressure and nonosmotic volume.     

Volume and enthalpy changes in the early steps of bacteriorhodopsin photocycle studied by time-resolved photoacoustics.

We have studied the photoinduced volume changes, energetics, and kinetics in the early steps of the bacteriorhodopsin (BR) photocycle with pulsed, time-resolved photoacoustics. Our data show that there are two volume changes. The fast volume change ( < or = 200 ns) is an expansion (2.5 +/- 0.3 A3/molecule) and is observed exclusively in the purple membrane (PM), vanishing in the 3-[(3-cholamidopropyl)-dimethylammonio] -1-propane-sulfonate-sulfonate-solubilized BR sample; the slow change (approximately 1 micros) is a volume contraction (-3.7 +/- 0.3 A3/molecule). The fast expansion is assigned to the restructuring of the aggregated BR in the PM, and the 1-micros contraction to the change in hydrogen bonding of water at Asp 212 (Kandori et al. 1995. J. Am. Chem. Soc. 117:2118-2119). The formation of the K intermediate releases most of the absorbed energy as heat, with delta Hk = -36 +/- 8 kJ/mol. The activation energy of the K --> L step is 49 +/- 6 kJ/mol, but the enthalpy change is small, -4 +/- 10 kJ/mol. On the time scale we studied, the primary photochemical kinetics, enthalpy, and volume changes are not affected by substituting the solvent D2O for H2O. Comparing data on monomeric and aggregated BR, we conclude that the functional unit for the photocycle is the BR monomer, because both the kinetics (rate constant and activation energy) and the enthalpy changes are independent of its aggregation state.     

Large-scale homogeneous molecular templates for femtosecond time-resolved studies of the guest-host interaction

Self-assembled monolayer films based on iodobenzoyloxy-functionalized resorc[4]arenes were prepared on gold substrates to serve as model systems for future time-resolved studies of molecular recognition, a mechanism of outstanding importance in bioorganic systems. The film properties were tested using X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and imaging ellipsometry. An apparatus for time-resolved electron spectroscopy utilizing femtosecond soft X-ray pulses is capable of detecting iodine core-level photolines and the photoinduced dissociation after ultraviolet illumination. The developed technique holds promise for tracking the temporal evolution of chemical shifts of atomic markers as local probes for the dynamics of the guest-host interaction.     

The effect of charge-charge interactions on the kinetics of alpha-helix formation

The formation of the monomeric α-helix represents one of the simplest scenarios in protein folding; however, our current understanding of the folding dynamics of the α-helix motif is mainly based on studies of alanine-rich model peptides. To examine the effect of peptide sequence on the folding kinetics of α-helices, we studied the relaxation kinetics of a 21-residue helical peptide, Conantokin-T (Con-T), using time-resolved infrared spectroscopy in conjunction with a laser-induced temperature jump technique. Con-T is a neuroactive peptide containing a large number of charged residues that is found in the venom of the piscivorous cone snail Conus tulipa. The temperature-jump relaxation kinetics of Con-T is distinctly slower than that of previously studied alanine-based peptides, suggesting that the folding time of α-helices is sequence-dependent. Furthermore, it appears that the slower folding of Con-T can be attributed to the fact that its helical conformation is stabilized by charge-charge interactions or salt bridges. Although this finding contradicts an earlier molecular dynamics simulation, it also has implications for existing models of protein folding.     

Protein conformational relaxation following photodissociation of CO from carbonmonoxymyoglobin: picosecond circular dichroism and absorption studies

Picosecond time-resolved polarization spectroscopy is used to study relaxation dynamics in myoglobin following photoelimination of CO from carbonmonoxymyoglobin. Evolution of the transient circular dichroism signal of the N band of myoglobin (probed at 355 nm) to that characteristic of equilibrium myoglobin requires approximately 300 ps. This time scale is significantly longer than that corresponding to the photoinitiated bond cleavage. Transient linear dichroism of the Soret band and picosecond time-resolved magnetic circular dichroism measurements of the Q band demonstrate that the circular dichroism kinetics do not result from either time-dependent changes in the orientation of the transition moments of the heme ring or the doming of the heme that accompanies the out-of-plane motion of the iron. Finally, transient absorption data of the near-IR optical transition of photogenerated myoglobin suggest that the circular dichroism data are not a measure of the tilting of the proximal histidine. The circular dichroism data are discussed in terms of a relaxation in the tertiary structure of the protein following dissociation.     

The recovery of dipolar relaxation times from fluorescence decays as a tool to probe local dynamics in single tryptophan proteins

The dipolar relaxation process induced by the excitation of the single tryptophan residue of four proteins (staphylococcal nuclease, ribonuclease-T1, phosphofructokinase, and superoxide dismutase) has been studied by dynamic fluorescence measurements. A new algorithm taking into account the relaxation effect has been applied to the fluorescence decay function obtained by phase-shift and demodulation data. This approach only requires that fluorescence be collected through the whole emission spectrum, avoiding the time-consuming determination of the data at different emission wavelengths, as usual with time-resolved emission spectroscopy. The results nicely match those reported in the literature for staphylococcal nuclease and ribonuclease-T1, demonstrating the validity of the model. Furthermore, this new methodology provides an alternative explanation for the complex decay of phosphofructokinase and human superoxide dismutase suggesting the presence of a relaxation process even in proteins that lack a lifetime-dependent spectral shift. These findings may have important implications on the analysis of small-scale protein dynamics, since dielectric relaxation directly probes a local structural change around the excited state of tryptophan.     

Dynamic analysis of differential scanning calorimetry data

The apparent heat capacity function measured by high-sensitivity differential scanning calorimetry contains dynamic components of two different origins: (1) an intrinsic component arising from the finite instrument time response; and (2) a sample component arising from the kinetics of the thermal transition under study. The intrinsic instrumental component is always present and its effect on the shape of the experimental curve depends on the magnitude of the calorimeter response time. Usually, high-sensitivity instruments exhibit characteristic time constants varying from 10 to 100 s. This slow response introduces distortions in the shape of the heat capacity function especially at fast scanning rates. In addition to this instrumental component, dynamic effects due to sample relaxation processes also contribute to the shape of the experimental heat capacity profile. Since the nature and magnitude of these effects are a function of the kinetic parameters of the transition, they can be used to obtain kinetic information. This communication presents a dynamic deconvolution technique directed to remove artificial distortions in the shape of the heat capacity function measured at any scanning rate, and to obtain a kinetic characterization of a thermally induced transition. The kinetic characterization obtained by this method allows the researcher to obtain transition relaxation times as a continuous function of temperature. This technique has been applied to the thermal unfolding of ribonuclease A and the pretransition of dipalmitoylphosphatidylcholine (DPPC). In both systems the transition relaxation times are temperature dependent. For the protein system the relaxation time is very slow below the transition temperature (approximately 30 s) and very fast above Tm (less than 1 s) in agreement with direct kinetic measurements. For the pretransition of DPPC, the relaxation time is maximal at the transition midpoint and of the order of approx. 40 s.     

Methods to study protein folding by stopped-flow FT-IR

Stopped-flow mixing coupled with time-resolved Fourier transform infrared (FT-IR) spectroscopy represents a new experimental approach to explore protein folding events, which has become possible only recently with the development of appropriate techniques. Here, we discuss experimental apparatus that are capable of initiating and monitoring protein folding processes on the millisecond to minute timescale. The strongest point of the FT-IR approach as a structure-specific probe is that a complete spectrum is available for each time point of measurement. In this way, several spectral windows are accessible simultaneously for the observation of the unfolding or the formation of different secondary structure elements and also events that can be attributed to changes in tertiary structure. One specific advantage of the infrared technique is the ability to monitor directly the kinetics of processes involving beta-sheet structures, which is exceptionally difficult to do with other techniques.     

A photoacoustic calorimetric study of horse myoglobin

The dynamics of the enthalpy and volume changes for the photodissociation of CO from horse myoglobin has been studied by time-resolved photoacoustic calorimetry which measures the dynamics of enthalpy and volume changes on the nanosecond time scale. The role of the Lys 45 salt bridge in the ligand dissociation is discussed.     

Role of heme iron coordination and protein structure in the dynamics and geminate rebinding of nitric oxide to the H93G myoglobin mutant: implications for nitric oxide sensors

The influence of the heme iron coordination on nitric oxide binding dynamics was investigated for the myoglobin mutant H93G (H93G-Mb) by picosecond absorption and resonance Raman time-resolved spectroscopies. In the H93G-Mb, the glycine replacing the proximal histidine does not interact with the heme iron so that exogenous substituents like imidazole may coordinate to the iron at the proximal position. Nitrosylation of H93G-Mb leads to either 6- or 5-coordinate species depending on the imidazole concentration. At high concentrations, (imidazole)-(NO)-6-coordinate heme is formed, and the photoinduced rebinding kinetics reveal two exponential picosecond phases ( approximately 10 and approximately 100 ps) similar to those of wild type myoglobin. At low concentrations, imidazole is displaced by the trans effect leading to a (NO)-5-coordinate heme, becoming 4-coordinate immediately after photolysis as revealed from the transient Raman spectrum. In this case, NO rebinding kinetics remain bi-exponential with no change in time constant of the fast component whose amplitude increases with respect to the 6-coordinate species. Bi-exponential NO geminate rebinding in 5-coordinate H93G-Mb is in contrast with the single-exponential process reported for nitrosylated soluble guanylate cyclase (Negrerie, M., Bouzhir, L., Martin, J. L., and Liebl, U. (2001) J. Biol. Chem. 276, 46815-46821). Thus, our data show that the iron coordination state or the heme iron out-of-plane motion are not at the origin of the bi-exponential kinetics, which depends upon the protein structure, and that the 4-coordinate state favors the fast phase of NO geminate rebinding. Consequently, the heme coordination state together with the energy barriers provided by the protein structure control the dynamics and affinity for NO-binding enzymes.     

High-definition mapping of neural activity using voltage-sensitive dyes

The distribution of patterns of activity in different brain structures has been related to the encoding and processing of sensory information. Consequently, it is important to be able to image the distribution of these patterns to understand basic brain functions. The spatial resolution of voltage-sensitive dye (VSD) methods has recently been enhanced considerably by the use of video imaging techniques. The main factor that now hampers the resolution of VSD patterns is the inherent limitation of the optical systems. Unfortunately, the intrinsic characteristics of VSD images impose important limitations that restrict the use of general deconvolution techniques. To overcomes this problem, in this study an image restoration procedure has been implemented that takes into consideration the limiting characteristics of VSD signals. This technique is based on applying a set of imaging processing steps. First, the signal-to-noise (S/N) ratio of the images was improved to avoid an increase in the noise levels during the deconvolution procedures. For this purpose, a new filter technique was implemented that yielded better results than other methods currently used in optical imaging. Second, focal plane images were deconvolved using a modification of the well-known nearest-neighbor deconvolution algorithm. But to reduce the light exposure of the preparation and simplify image acquisition procedures, adjacent image planes were modeled according to the in-focus image planes and the empirical point spread function (PSF) profiles. Third, resulting focal plane responses were processed to reduce the contribution of optical responses that originate in distant image planes. This method was found to be satisfactory under simulated and real experimental conditions. By comparing the restored and unprocessed images, it was clearly demonstrated that this method can effectively remove the out-of-focus artifacts and produce focal plane images of better quality. Evaluations of the tissue optical properties allowed assessment of the maximum practical optical section thickness using this deconvolution technique in the optical system tested. Determination of the three-dimensional PSF permitted the correct application of deconvolution algorithms and the removal of the contaminating light arising from adjacent as well as distant optical planes. The implementation of this deconvolution approach in salamander olfactory bulb allowed the detailed study of the laminar distribution of voltage-sensitive changes across the bulb layer. It is concluded that (1) this deconvolution procedure is well suited to deconvolved low-contrast images and offers important advantages over other alternatives; (2) this method can be properly used only when the tissue optical properties are first determined; (3) high levels of light scattering in the tissue reduce the optical section capabilities of this technique as well as other deconvolution procedures; and (4) use of the highest numerical aperture in the objectives is advisable because this improves not only the light-collecting efficiency to detect poor-contrast images, but also the spatial frequency differences between adjacent image planes. Under this condition it is possible to overcome some of the limitations imposed by the light scattering/birefringence of the tissue.     

Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm's efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 μs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.     

Following the dynamics of changes in solvent accessibility of 16 S and 23 S rRNA during ribosomal subunit association using synchrotron-generated hydroxyl radicals

We have probed the structure and dynamics of ribosomal RNA in the Escherichia coli ribosome using equilibrium and time-resolved hydroxyl radical (OH) RNA footprinting to explore changes in the solvent-accessible surface of the rRNA with single-nucleotide resolution. The goal of these studies is to better understand the structural transitions that accompany association of the 30 S and 50 S subunits and to build a foundation for the quantitative analysis of ribosome structural dynamics during translation. Clear portraits of the subunit interface surfaces for 16 S and 23 S rRNA were obtained by constructing difference maps between the OH protection maps of the free subunits and that of the associated ribosome. In addition to inter-subunit contacts consistent with the crystal structure, additional OH protections are evident in regions at or near the subunit interface that reflect association-induced conformational changes. Comparison of these data with the comparable difference maps of the solvent-accessible surface of the rRNA calculated for the Thermus thermophilus X-ray crystal structures shows extensive agreement but also distinct differences. As a prelude to time-resolved OH footprinting studies, the reactivity profiles obtained using Fe(II)EDTA and X-ray generated OH were comprehensively compared. The reactivity patterns are similar except for a small number of nucleotides that have decreased reactivity to OH generated from Fe(II)EDTA compared to X-rays. These nucleotides are generally close to ribosomal proteins, which can quench diffusing radicals by virtue of side-chain oxidation. Synchrotron X-ray OH footprinting was used to monitor the kinetics of association of the 30 S and 50 S subunits. The rates individually measured for the inter-subunit contacts are comparable within experimental error. The application of this approach to the study of ribosome dynamics during the translation cycle is discussed.     

Accumulation of acridine amino derivatives by electron-dense granules in thrombocytes

The uptake and release of dense bodies' content were studied using fluorescent amines. Real-time measurements of fluorescence spectra by a device developed on the basis of a multichannel optical analyzer and computer technique of spectrum deconvolution made it possible to investigate the kinetics of monoamine uptake and release in intact cells.