Single-molecule protein folding: Diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2

We report single-molecule folding studies of a small, single-domain protein, chymotrypsin inhibitor 2 (CI2). CI2 is an excellent model system for protein folding studies and has been extensively studied, both experimentally (at the ensemble level) and theoretically. Conformationally assisted ligation methodology was used to synthesize the proteins and site-specifically label them with donor and acceptor dyes. Folded and denatured subpopulations were observed by fluorescence resonance energy transfer (FRET) measurements on freely diffusing single protein molecules. Properties of these subpopulations were directly monitored as a function of guanidinium chloride concentration. It is shown that new information about different aspects of the protein folding reaction can be extracted from such subpopulation properties. Shifts in the mean transfer efficiencies are discussed, FRET efficiency distributions are translated into potentials, and denaturation curves are directly plotted from the areas of the FRET peaks. Changes in stability caused by mutation also are measured by comparing pseudo wild-type CI2 with a destabilized mutant (K17G). Current limitations and future possibilities and prospects for single-pair FRET protein folding investigations are discussed.

Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

Facilitated diffusion of fructose via the phosphoenolpyruvate/glucose phosphotransferase system of Escherichia coli

From mutants of Escherichia coli unable to utilize fructose via the phosphoenolpyruvate/glycose phosphotransferase system (PTS), further mutants were selected that grow on fructose as the sole carbon source, albeit with relatively low affinity for that hexose (Km for growth ≈8 mM but with Vmax for generation time ≈1 h 10 min); the fructose thus taken into the cells is phosphorylated to fructose 6-phosphate by ATP and a cytosolic fructo(manno)kinase (Mak). The gene effecting the translocation of fructose was identified by Hfr-mediated conjugations and by phage-mediated transduction as specifying an isoform of the membrane-spanning enzyme IIGlc of the PTS, which we designate ptsG-F. Exconjugants that had acquired ptsG+ from Hfr strains used for mapping (designated ptsG-I) grew very poorly on fructose (Vmax ≈7 h 20 min), even though they were rich in Mak activity. A mutant of E. coli also rich in Mak but unable to grow on glucose by virtue of transposon-mediated inactivations both of ptsG and of the genes specifying enzyme IIMan (manXYZ) was restored to growth on glucose by plasmids containing either ptsG-F or ptsG-I, but only the former restored growth on fructose. Sequence analysis showed that the difference between these two forms of ptsG, which was reflected also by differences in the rates at which they translocated mannose and glucose analogs such as methyl α-glucoside and 2-deoxyglucose, resided in a substitution of G in ptsG-I by T in ptsG-F in the first position of codon 12, with consequent replacement of valine by phenylalanine in the deduced amino acid sequence.

Diffusion of nitric oxide can facilitate cerebellar learning: A simulation study

The gaseous second messenger nitric oxide (NO), which readily diffuses in brain tissue, has been implicated in cerebellar long-term depression (LTD), a form of synaptic plasticity thought to be involved in cerebellar learning. Can NO diffusion facilitate cerebellar learning? The inferior olive (IO) cells, which provide the error signals necessary for modifying the granule cell–Purkinje cell (PC) synapses by LTD, fire at ultra-low firing rates in vivo, rarely more than 2–4 spikes within a second. In this paper, we show that NO diffusion can improve the transmission of sporadic IO error signals to PCs within cerebellar cortical functional units, or microzones. To relate NO diffusion to adaptive behavior, we add NO diffusion and a “volumic” LTD learning rule, i.e., a learning rule that depends both on the synaptic activity and on the NO concentration at the synapse, to a cerebellar model for arm movement control. Our results show that biologically plausible diffusion leads to an increase in information transfer of the error signals to the PCs when the IO firing rate is ultra-low. This, in turn, enhances cerebellar learning as shown by improved performance in an arm-reaching task.

Intranuclear diffusion and hybridization state of oligonucleotides measured by fluorescence correlation spectroscopy in living cells

Fluorescein-labeled oligodeoxynucleotides (oligos) were introduced into cultured rat myoblasts, and their molecular movements inside the nucleus were studied by fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). FCS revealed that a large fraction of both intranuclear oligo(dT) (43%) and oligo(dA) (77%) moves rapidly with a diffusion coefficient of 4 × 10−7 cm2/s. Interestingly, this rate of intranuclear oligo movement is similar to their diffusion rates measured in aqueous solution. In addition, we detected a large fraction (45%) of the intranuclear oligo(dT), but not oligo(dA), diffusing at slower rates (≤1 × 10−7 cm2/s). The amount of this slower-moving oligo(dT) was greatly reduced if the oligo(dT) was prehybridized in solution with (unlabeled) oligo(dA) prior to introduction to cells, presumably because the oligo(dT) was then unavailable for subsequent hybridization to endogenous poly(A) RNA. The FCS-measured diffusion rate for much of the slower oligo(dT) population approximated the diffusion rate in aqueous solution of oligo(dT) hybridized to a large polyadenylated RNA (1.0 × 10−7 cm2/s). Moreover, this intranuclear movement rate falls within the range of calculated diffusion rates for an average-sized heterogeneous nuclear ribonucleoprotein particle in aqueous solution. A subfraction of oligo(dT) (15%) moved over 10-fold more slowly, suggesting it was bound to very large macromolecular complexes. Average diffusion coefficients obtained from FRAP experiments were in agreement with the FCS data. These results demonstrate that oligos can move about within the nucleus at rates comparable to those in aqueous solution and further suggest that this is true for large ribonucleoprotein complexes as well.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

Radial and longitudinal diffusion of myoglobin in single living heart and skeletal muscle cells

We have used a fluorescence recovery after photobleaching (FRAP) technique to measure radial diffusion of myoglobin and other proteins in single skeletal and cardiac muscle cells. We compare the radial diffusivities, Dr (i.e., diffusion perpendicular to the long fiber axis), with longitudinal ones, Dl (i.e., parallel to the long fiber axis), both measured by the same technique, for myoglobin (17 kDa), lactalbumin (14 kDa), and ovalbumin (45 kDa). At 22°C, Dl for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes. Dl for lactalbumin is similar in both cell types. Dr for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes and, again, similar for lactalbumin. Dl and Dr for ovalbumin are 0.5 × 10−7 cm2/s. In the case of myoglobin, both Dl and Dr at 37°C are about 80% higher than at 22°C. We conclude that intracellular diffusivity of myoglobin and other proteins (i) is very low in striated muscle cells, ≈1/10 of the value in dilute protein solution, (ii) is not markedly different in longitudinal and radial direction, and (iii) is identical in heart and skeletal muscle. A Krogh cylinder model calculation holding for steady-state tissue oxygenation predicts that, based on these myoglobin diffusivities, myoglobin-facilitated oxygen diffusion contributes 4% to the overall intracellular oxygen transport of maximally exercising skeletal muscle and less than 2% to that of heart under conditions of high work load.

Co-Permeability of 3H-Labeled Water and 14C-Labeled Organic Acids across Isolated Plant Cuticles1 : Investigating Cuticular Paths of Diffusion and Predicting Cuticular Transpiration

Penetration of 3H-labeled water (3H2O) and the 14C-labeled organic acids benzoic acid ([14C]BA), salicylic acid ([14C]SA), and 2,4-dichlorophenoxyacetic acid ([14C]2,4-D) were measured simultaneously in isolated cuticular membranes of Prunus laurocerasus L., Ginkgo biloba L., and Juglans regia L. For each of the three pairs of compounds (3H2O/[14C]BA, 3H2O/[14C]SA, and 3H2O/[14C]2,4-D) rates of cuticular water penetration were highly correlated with the rates of penetration of the organic acids. Therefore, water and organic acids penetrated the cuticles by the same routes. With the combination 3H2O/[14C]BA, co-permeability was measured with isolated cuticles of nine other plant species. Permeances of 3H2O of all 12 investigated species were highly correlated with the permeances of [14C]BA (r2 = 0.95). Thus, cuticular transpiration can be predicted from BA permeance. The application of this experimental method, together with the established prediction equation, offers the opportunity to answer several important questions about cuticular transport physiology in future investigations.

Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperature-dependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.

Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding.

How fast can a protein fold? The rate of polypeptide collapse to a compact state sets an upper limit to the rate of folding. Collapse may in turn be limited by the rate of intrachain diffusion. To address this question, we have determined the rate at which two regions of an unfolded protein are brought into contact by diffusion. Our nanosecond-resolved spectroscopy shows that under strongly denaturing conditions, regions of unfolded cytochrome separated by approximately 50 residues diffuse together in 35-40 microseconds. This result leads to an estimate of approximately (1 microsecond)-1 as the upper limit for the rate of protein folding.

Intracellular pH in adipocytes: effects of free fatty acid diffusion across the plasma membrane, lipolytic agonists, and insulin.

The main function of white adipose tissue is to store nutrient energy in the form of triglycerides. The mechanism by which free fatty acids (FFA) move into and out of the adipocyte has not been resolved. We show here that changes in intracellular pH (pH1) in adipocytes correlate with the movement of FFA across cellular membranes as predicted by the Kamp and Hamilton model of passive diffusion of FFA. Exposure of fat cells to lipolytic agents or external FFA results is a rapid intracellular acidification that is reversed by metabolism of the FFA or its removal by albumin. In contrast, insulin causes an alkalinization of the cell, consistent with its main function to promote esterification. Inhibition of Na+/H+ exchange in adipocytes does not prevent the changes in pHi caused by FFA, lipolytic agents, or insulin. A fatty acid dimer, which diffuses into the cell but is not metabolized, causes an irreversible acidification. Taken together, the data suggest that changes in pHi occur in adipocytes in response to the passive diffusion of un-ionized FFA (flip-flop) into and out of the cell and in response to their metabolism and production within the cell. These changes in pHi may, in turn, modulate hormonal signaling and metabolism with significant impact on cell function.

Multicomponent diffusion in polymeric liquids.

It is shown how the phase-space kinetic theory of polymeric liquid mixtures leads to a set of extended Maxwell-Stefan equations describing multicomponent diffusion. This expression reduces to standard results for dilute solutions and for undiluted polymers. The polymer molecules are modeled as flexible bead-spring structures. To obtain the Maxwell-Stefan equations, the usual expression for the hydrodynamic drag force on a bead, used in previous kinetic theories, must be replaced by a new expression that accounts explicitly for bead-bead interactions between different molecules.

Miniature endplate current rise times less than 100 microseconds from improved dual recordings can be modeled with passive acetylcholine diffusion from a synaptic vesicle.

We recorded miniature endplate currents (mEPCs) using simultaneous voltage clamp and extracellular methods, allowing correction for time course measurement errors. We obtained a 20-80% rise time (tr) of approximately 80 micros at 22 degrees C, shorter than any previously reported values, and tr variability (SD) with an upper limit of 25-30 micros. Extracellular electrode pressure can increase tr and its variability by 2- to 3-fold. Using Monte Carlo simulations, we modeled passive acetylcholine diffusion through a vesicle fusion pore expanding radially at 25 nm x ms(-1) (rapid, from endplate omega figure appearance) or 0.275 nm x ms(-1) (slow, from mast cell exocytosis). Simulated mEPCs obtained with rapid expansion reproduced tr and the overall shape of our experimental mEPCs, and were similar to simulated mEPCs obtained with instant acetylcholine release. We conclude that passive transmitter diffusion, coupled with rapid expansion of the fusion pore, is sufficient to explain the time course of experimentally measured synaptic currents with trs of less than 100 micros.