Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states

Abstract

In living cells, biochemical reaction networks often function in nonequilibrium steady states. Under these conditions, the networks necessarily have cyclic reaction kinetics that are maintained by sustained constant input and output, i.e., pumping. To differentiate this state from an equilibrium state without flux, we propose a microscopic method based on concentration fluctuation measurements, via fluorescence correlation spectroscopy, and statistical analyses of high-order correlations and cross correlations beyond the standard fluorescence correlation spectroscopy autocorrelation. We show that, for equilibrium systems with time reversibility, the correlation functions possess certain symmetries, the violation of which is a measure of steady-state fluxes in reaction cycles. This result demonstrates the theoretical basis for experimentally measuring reaction fluxes in a biochemical network in situ and the importance of single-molecule measurements in providing fundamental information on nonequilibrium steadystates in biochemistry. recent study on enzyme kinetics of single horseradish peroxidase molecules has observed an oscillatory timecorrelation function, suggesting an irreversible, nonequilibrium nature of the biochemical reaction (4). In single-molecule enzymology (5, 6), the consecutive turnover of substrates to products catalyzed by a single enzyme molecule is recorded in terms of the fluorescence of enzyme-substrate or enzymeproduct complexes. One essential feature of such a measurement is that the concentrations of the substrate, [S], and the product, [P], are approximately constant over the course of the entire experiment. Thus, although the enzyme molecule is subject to stochastic fluctuations, on average it participates in a stationary process with a net circular flux. The flux is zero if and only if the substrate and product concentrations satisfy conditions of [P]͞[S] ϭ K eq , where K eq is the equilibrium constant for the reaction S º P, both in the presence and absence of the enzyme. In this unique situation, the reaction is at a chemical equilibrium.

Three-point frequency fluctuation correlation functions of the OH stretch in liquid water

“…The two-point frequency fluctuation correlation function, c 2 ͑t͒ is then given by 45 c 2 ͑t͒ = ͗͑t͒͑0͒͘ ͑B2͒…”

Communications: Can one identify nonequilibrium in a three-state system by analyzing two-state trajectories?

“…Only if all three states are visible, such as in dual-color fluorescence correlation spectroscopy, one can discriminate between equilibrium and nonequilibrium steady states. 23,24 We consider a three-state Markov system with states i =1,2,3 and transition rates k ij . The dynamics of the probability p i ͑t͒ to be in state i at time t then is governed by the master equation…”

Study of molecular events in cells by fluorescence correlation spectroscopy

“…FCS experiments demonstrated that enzymatic activity of HRP on a single-molecule level varies broadly. To examine the origins of distributed kinetics in a single HRP [52] Fractal analysis of fluorescence time series as a method to investigate anomalous diffusion [53] Bias in FCS measurements [54] Development toward application in highly heterogeneous systems [55] Experimental artefacts in confocal FCS [56] Concentration fluctuations in an oscillating chemical reaction system [57] Standard deviation and accuracy in FCS [58] High-order and dual-color correlation to probe non-equilibrium steady states [59] Correction of artefacts in FCS measurements arising due to afterpulsing [60] Unavoidable artefacts in FCS measurements due to photophysical properties of the fluorophore [61] DNA structure and interactions Dynamics of bubble formation in double-stranded DNA [62] Dynamics of NCp7-mediated nucleic acid destabilization [63] Formation and dissociation of the polyethylenimine/DNA complex [64] Association of oligonucleotides with positively charged liposomes [65] DNA looping by NgoMIV restriction endonuclease [66] Dynamics of large semiflexible DNA chains [67] Transport of nucleosome core particles in semidilute DNA solutions [68] Rates of Mg 2+ and Na + dependent conformational changes in a single RNA molecule [69] Denaturation of dsDNA by p53 [70] Protein structure, interactions and function Gag-Gag interactions during retrovirus assembly [71] Stability of drug-induced tubulin rings [72] Precipitation and size distribution of the Abeta(1)(-)(40) amyloid beta peptide in solutions [73] Thermodynamic analysis of ssDNA-protein interaction [74] Conformational dynamics and folding of the intestinal fatty acid binding protein [75] Transportation of large transporting complex of tubulin [76] Thrombin-induced fibrin polymerization [77] p53 binding to double-stranded DNA oligonucleotides [78] Ligand-receptor binding and diffusion Binding of protoberberine type 2 alcaloids on the GABA A binding site [79] Induction of seed germin...…”

“…Another important point in determining local concentrations and diffusion rates is that we may begin to understand on a quantitative level how molecular crowding, local differences in pH, ionic strength and redox potentials influence the course of biochemical reactions [123,124]. By distinguishing non-equilibrium steady states maintained through a continuous exchange of energy and matter from equilibrium states without flux [59] and by studying the interplay of diffusion and chemical kinetics in living cells, we may come closer to understanding how non-linear processes in non-equilibrium cellular environments lead to biological complexity: how it is possible to escape limitation by diffusion in the glucose phosphotransferase system in bacterial cells, and why this is not possible in eukaryotic cells [125], what critical number of molecules is required to establish cellular rhythms and how robust they are in respect to molecular noise [126,127], how physicochemical mechanisms of self-organization lead to formation of spatial receptor-ligand synaptic patterns in the intercellular junctions (observed in Tcell/antigen-presenting cell junctions with different major histocompatibility complex peptides and in natural killer cells, for example) and what their role is in cell-cell interactions [128], and how non-linear mechanisms of spatiotemporal symmetry breaking lead to pattern formation in somitogenesis [129]. Understanding these cellular mechanisms at a molecular level is not an unrealistic goal, thanks to computational power and mathematical modeling [126,127,[130][131][132].…”