Dual-color time-integrated fluorescence cumulant analysis

We introduce dual-color time-integrated fluorescence cumulant analysis (TIFCA) to analyze fluorescence fluctuation spectroscopy data. Dual-color TIFCA utilizes the bivariate cumulants of the integrated fluorescent intensity from two detection channels to extract the brightness in each channel, the occupation number, and the diffusion time of fluorophores simultaneously. Detecting the fluorescence in two detector channels introduces the possibility of differentiating fluorophores based on their fluorescence spectrum. We derive an analytical expression for the bivariate factorial cumulants of photon counts for arbitrary sampling times. The statistical accuracy of each cumulant is described by its variance, which we calculate by the moments-of-moments technique. A method that takes nonideal detector effects such as dead-time and afterpulsing into account is developed and experimentally verified. We perform dual-color TIFCA analysis on simple dye solutions and a mixture of dyes to characterize the performance and accuracy of our theory. We demonstrate the robustness of dual-color TIFCA by measuring fluorescent proteins over a wide concentration range inside cells. Finally we demonstrate the sensitivity of dual-color TIFCA by resolving EGFP/EYFP binary mixtures in living cells with a single measurement.     

The dual-color photon counting histogram with non-ideal photodetectors

Dual-color photon counting histogram (PCH) analysis utilizes the photon counts in two detection channels to distinguish species by differences in brightness and color. Here we modify the existing dual-color PCH theory, which assumes ideal detectors, to include the non-ideal nature of the detector. Specifically, we address the effects of deadtime and afterpulsing. Both effects modify the shape of the dual-color PCH and thus potentially lead to incorrect values for the brightness and number of molecules if an ideal model is assumed. We use the modified theory to predict the effects of detector non-idealities on dual-color PCH as a function of concentration and brightness. In addition, we introduce a method based on moment analysis to determine the error in brightness due to non-ideal detector effects. We verify our theory experimentally by measuring a dye solution as a function of concentration and brightness. We determine the deadtime and afterpulse probability of our detectors and show that both effects play an important role in the analysis of dual-color PCH experiments. We demonstrate that resolving a mixture of CFP and YFP requires taking non-ideal detector effects into account. These corrections are also crucial for cellular measurements, as shown for GFP and RFP in mammalian cells.     

Calculation of photon-count number distributions via master equations

Fitting of photon-count number histograms is a way of analysis of fluorescence intensity fluctuations, a successor to fluorescence correlation spectroscopy. First versions of the theory for calculating photon-count number distributions have assumed constant emission intensity by a molecule during a counting time interval. For a long time a question has remained unanswered: to what extent is this assumption violated in experiments? Here we present a theory of photon-count number distributions that takes account of intensity fluctuations during a counting time interval. Theoretical count-number distributions are calculated via a numerical solution of Master equations (ME), which is a set of differential equations describing diffusion, singlet-triplet transitions, and photon emission. Detector afterpulsing and dead-time corrections are also included. The ME-theory is tested by fitting a series of photon-count number histograms corresponding to different lengths of the counting time interval. Compared to the first version of fluorescence intensity multiple distribution analysis theory introduced in 2000, the fit quality is significantly improved. It is discussed how a theory of photon-count number distributions, which assumes constant emission intensity during a counting time interval, may also yield a good fit quality. We argue that the spatial brightness distribution used in calculations of the fit curve is not the true spatial brightness distribution. Instead, a number of dynamic processes, which cause fluorescence intensity fluctuations, are indirectly taken into account via the profile adjustment parameters.     

The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors

Fluorescence fluctuation spectroscopy utilizes the signal fluctuations of single molecules for studying biological processes. Information about the biological system is extracted from the raw data by statistical methods such as used in fluctuation correlation spectroscopy or photon counting histogram (PCH) analysis. Since detectors are never ideal, it is crucial to understand the influence of photodetectors on signal statistics to correctly interpret the experimental data. Here we focus on the effects of afterpulsing and detector dead-time on PCH statistics. We determine the dead-time and afterpulse probability for our detectors experimentally and show that afterpulsing can be neglected for most experiments. Dead-time effects on the PCH are concentration-dependent and become significant when more than one molecule is present in the excitation volume. We develop a new PCH theory that includes dead-time effects and verify it experimentally. Additionally, we derive a simple analytical expression that accurately predicts the effect of dead-time on the molecular brightness. Corrections for non-ideal detector effects extend the useful concentration range of PCH experiments and are crucial for the interpretation of titration and dilution experiments.     

Quantitative Brightness Analysis of Fluorescence Intensity Fluctuations in E. Coli

The brightness measured by fluorescence fluctuation spectroscopy specifies the average stoichiometry of a labeled protein in a sample. Here we extended brightness analysis, which has been mainly applied in eukaryotic cells, to prokaryotic cells with E. coli serving as a model system. The small size of the E. coli cell introduces unique challenges for applying brightness analysis that are addressed in this work. Photobleaching leads to a depletion of fluorophores and a reduction of the brightness of protein complexes. In addition, the E. coli cell and the point spread function of the instrument only partially overlap, which influences intensity fluctuations. To address these challenges we developed MSQ analysis, which is based on the mean Q-value of segmented photon count data, and combined it with the analysis of axial scans through the E. coli cell. The MSQ method recovers brightness, concentration, and diffusion time of soluble proteins in E. coli. We applied MSQ to measure the brightness of EGFP in E. coli and compared it to solution measurements. We further used MSQ analysis to determine the oligomeric state of nuclear transport factor 2 labeled with EGFP expressed in E. coli cells. The results obtained demonstrate the feasibility of quantifying the stoichiometry of proteins by brightness analysis in a prokaryotic cell.     

Fluorescence intensity multiple distributions analysis: concurrent determination of diffusion times and molecular brightness

Fluorescence correlation spectroscopy (FCS) has proven to be a powerful technique with single-molecule sensitivity. Recently, it has found a complement in the form of fluorescence intensity distribution analysis (FIDA). Here we introduce a fluorescence fluctuation method that combines the features of both techniques. It is based on the global analysis of a set of photon count number histograms, recorded with multiple widths of counting time intervals simultaneously. This fluorescence intensity multiple distributions analysis (FIMDA) distinguishes fluorescent species on the basis of both the specific molecular brightness and the translational diffusion time. The combined information, extracted from a single measurement, increases the readout effectively by one dimension and thus breaks the individual limits of FCS and FIDA. In this paper a theory is introduced that describes the dependence of photon count number distributions on diffusion coefficients. The theory is applied to a series of photon count number histograms corresponding to different widths of counting time intervals. Although the ability of the method to determine specific brightness values, diffusion times, and concentrations from mixtures is demonstrated on simulated data, its experimental utilization is shown by the determination of the binding constant of a protein-ligand interaction exemplifying its broad applicability in the life sciences.     

Cumulant analysis in fluorescence fluctuation spectroscopy

A novel technique for the analysis of fluorescence fluctuation experiments is introduced. Fluorescence cumulant analysis (FCA) exploits the factorial cumulants of the photon counts and resolves heterogeneous samples based on differences in brightness. A simple analytical model connects the cumulants of the photon counts with the brightness epsilon and the number of molecules N in the optical observation volume for each fluorescent species. To provide the tools for a rigorous error analysis of FCA, expressions for the variance of factorial cumulants are developed and tested. We compare theory with experiment by analyzing dye mixtures and simple fluorophore solutions with FCA. A comparison of FCA with photon-counting histogram (PCH) analysis, a related technique, shows that both methods give identical results within experimental uncertainty. Both FCA and PCH are restricted to data sampling times that are short compared to the diffusion time of molecules through the observation volume of the instrument. But FCA theory, in contrast to PCH, can be extended to treat arbitrary sampling times. Here, we derive analytical expressions for the second factorial cumulant as a function of the sampling time and demonstrate that the theory successfully models fluorescence fluctuation data.     

Sensory and intrinsic coordination of movement

A recently generalized theory of perceptual guidance (general tau theory) was used to analyse coordination in skilled movement. The theory posits that (i) guiding movement entails controlling closure of spatial and/or force gaps between effectors and goals, by sensing and regulating the tau s of the gaps (the time-to-closure at current closure rate), (ii) a principal way of coordinating movements is keeping the tau s of different gaps in constant ratio (known as tau-coupling), and (iii) intrinsically paced movements are guided and coordinated by tau-coupling onto a tau-guide, tau g, generated in the nervous system and described by the equation tau g = 0.5 (t-T 2/t) where T is the duration of the body movement and t is the time from the start of the movement. Kinematic analysis of hand to mouth movements by human adults, with eyes open or closed, indicated that hand guidance was achieved by maintaining, during 80 85% of the movement, the tau-couplings tau alpha-tau r and tau r-tau g, where tau r is tau of the hand-mouth gap, tau alpha is tau of the angular gap to be closed by steering the hand and tau g is an intrinsic tau-guide.     

-deltaG(AB) and pH dependence of the electron transfer from P(+)Q(A)(-)Q(B) toP(+)Q(A)Q(B)(-) in Rhodobacter sphaeroides reaction centers

The electron transfer from the reduced primary quinone (Q(A)(-)) to the secondary quinone (Q(B)) can occur in two phases with a well-characterized 100 micros component (tau(2)) and a faster process occurring in less than 10 micros (tau(1)). The fast reaction is clearly seen when the native ubiquinone-10 at Q(A) is replaced with naphthoquinones. The dependence of tau(1) on the free-energy difference between the P(+)Q(A)(-)Q(B) and P(+)Q(A)Q(B)(-) states (-) and on the pH was measured using naphthoquinones with different electrochemical midpoint potentials as Q(A) in Rhodobacter sphaeroides reaction centers (RCs) and in RCs where - is changed by mutation of M265 in the Q(A) site from Ile to Thr (M265IT). Q(B) was ubiquinone (UQ(B)) in all cases. Electron transfer was measured by using the absorption differences of the naphthosemiquinone at Q(A) and the ubisemiquinone at Q(B) between 390 and 500 nm. As - was changed from -90 to -250 meV tau(1) decreased from 29 to 0.2 micros. The free-energy dependence of tau(1) provides a reorganization energy of 850 +/- 100 meV for the electron transfer from Q(A)(-) to Q(B). The slower reaction at tau(2) is free-energy independent, so processes other than electron transfer determine the observed rate. The fraction of the reaction at tau(1) increases with increasing driving force and is 100% of the reaction when - is approximately 100 meV more favorable than in the native RCs with ubiquinone as Q(A). The fast phase, tau(1), is pH independent from pH 6 to 11 while tau(2) slows above pH 9. As the Q(A) isoprene tail length is increased from 2 to 10 isoprene units the fraction at tau(1) decreases. However, tau(1), tau(2), and the fraction of the reaction in each phase are independent of the tail length of UQ(B).     

Fluorescence fluctuation spectroscopy in the presence of immobile fluorophores

Fluorescence contributions from immobile sources present a challenge for fluorescence fluctuation spectroscopy (FFS) because the absence of signal fluctuations from stationary fluorophores leads to a biased analysis. This is especially of concern for cellular FFS studies on proteins that interact with immobile structures. Here we present a method that correctly analyzes FFS experiments in the presence of immobile sources by exploiting selective photobleaching of immobile fluorophores. The fluorescence decay due to photobleaching of the immobile species is modeled taking into account the nonuniform illumination volume. The experimentally observed decay curve serves to separate the mobile and immobile fluorescence contribution, which is used to calculate the molecular brightness from the FFS data. We experimentally verify this approach in vitro using the fluorescent protein EGFP as our immobilized species and a diffusing dye of a different color as the mobile one. For this special case, we also use an alternative method of determining the brightness by spectrally resolving the two species. By conducting a dilution study, we show that the correct parameters are obtained using either technique for a wide range of mobile fractions. To demonstrate the application of our technique in living cells, we perform experiments using the histone core protein H2B fused with EGFP expressed in COS-1 cells. We successfully recovered the brightness of the mobile fraction of H2B-EGFP.     

Kinetics of intramembrane charge movement and conductance activation of batrachotoxin-modified sodium channels in frog node of Ranvier

Sodium current and intramembrane gating charge movement (Q) were monitored in voltage-clamped frog node of Ranvier after modification of all sodium channels by batrachotoxin (BTX). Sodium current activation followed a single-exponential time course, provided a delay was interposed between the onset of the step ON depolarization and that of the current change. The delay decreased with increased ON depolarization and, for a constant ON depolarization, increased with prehyperpolarization. ON charge movement followed a single-exponential time course with time constants tau Q,ON slightly larger than tau Na, ON. For pulses between -70 and -50 mV, tau Q,ON/tau Na,ON = 1.14 +/- 0.08. The OFF charge movement and OFF sodium current tails after a depolarizing pulse followed single-exponential time courses, with tau Q, OFF larger than tau Na, OFF. tau Q,OFF/tau Na,OFF increased with OFF voltage from 1 near -100 mV to 2 near -160 mV. At a set OFF potential (-120 mV), both tau Q,OFF and tau Na,OFF increased with ON pulse duration. The delay in INa activation and the effect of ON pulse duration on tau Q,OFF and tau Na,OFF are inconsistent with a simple two-state, single-transition model for the gating of batrachotoxin-modified sodium channels.     

Molecular Brightness Characterization of EGFP In Vivo by Fluorescence Fluctuation Spectroscopy

We characterize the molecular properties of autofluorescence and transiently expressed EGFP in the nucleus and in the cytoplasm of HeLa cells by fluorescence correlation spectroscopy (FCS) and by photon counting histogram (PCH) analysis. PCH has been characterized and applied in vitro, but its potential for in vivo studies needs to be explored. Thus, this study mainly focuses on the characterization of PCH analysis in vivo. The strength of PCH lies in its ability to distinguish biomolecules by their molecular brightness value. Because the concept of molecular brightness is crucial for PCH analysis, we study the molecular brightness of EGFP and determine the statistical accuracy of its measurement under in vivo conditions. We started by characterizing the influence of autofluorescence on EGFP measurements. We found a molecular brightness of EGFP that is a factor of 10 higher than the brightness of the autofluorescence. Moment analysis demonstrates that the contribution of autofluorescence to fluorescence fluctuation experiments is negligible at EGFP concentrations of one protein per excitation volume. The molecular brightness of EGFP measured in the nucleus, the cytoplasm, and in vitro are identical and our study demonstrates that molecular brightness is a very stable and predictable quantity for cellular measurements. In addition to PCH, we also analyzed the autocorrelation function of EGFP. The diffusion coefficient of EGFP is a factor of 3 lower in vivo than compared to in vitro, and a simple diffusion process describes the autocorrelation function. We found that in the nucleus the fluorescence intensity is stable as a function of time, while measurements in the cytoplasm display fluorescence intensity drifts that complicate the data analysis. We introduce and discuss an analysis method that minimizes the influence of the intensity drifts on PCH analysis. This method allows us to recover the correct molecular brightness of EGFP even in the presence of drifts of the fluorescence intensity signal. We found the molecular brightness of EGFP to be a very robust parameter, and anticipate the use of PCH analysis for the study of oligomerization processes in vivo.     

Time-integrated fluorescence cumulant analysis in fluorescence fluctuation spectroscopy

We introduce a new analysis technique for fluorescence fluctuation data. Time-integrated fluorescence cumulant analysis (TIFCA) extracts information from the cumulants of the integrated fluorescence intensity. TIFCA builds on our earlier FCA theory, but in contrast to FCA or photon counting histogram (PCH) analysis is valid for arbitrary sampling times. The motivation for long sampling times lies in the improvement of the signal/noise ratio of the data. Because FCA and PCH theory are not valid in this regime, we first derive a theoretical model of cumulant functions for arbitrary sampling times. TIFCA is the first exact theory that describes the effects of sampling time on fluorescence fluctuation experiments. We calculate factorial cumulants of the photon counts for various sampling times by rebinning of the original data. Fits of the data to models determine the brightness, the occupation number, and the diffusion time of each species. To provide the tools for a rigorous error analysis of TIFCA, expressions for the variance of cumulants are developed and tested. We demonstrate that over a limited range rebinning reduces the relative error of higher order cumulants, and therefore improves the signal/noise ratio. The first four cumulant functions are explicitly calculated and are applied to simple dye systems to test the validity of TIFCA and demonstrate its ability to resolve species.     

Dual-color photon counting histogram analysis of mRFP1 and EGFP in living cells

We investigate the potential of dual-color photon counting histogram (PCH) analysis to resolve fluorescent protein mixtures directly inside cells. Because of their small spectral overlap, we have chosen to look at the fluorescent proteins EGFP and mRFP1. We experimentally demonstrate that dual-color PCH quantitatively resolves a mixture of EGFP and mRFP1 in cells from a single measurement. To mimic the effect of protein association, we constructed a fusion protein of EGFP and mRFP1 (denoted EGFP-mRFP1). Fluorescence resonant energy transfer within the fusion protein alters the dual-channel brightness of the fluorophores. We describe a model for fluorescence resonant energy transfer effects on the brightness and incorporate it into dual-color PCH analysis. The model is verified using fluorescence lifetime measurements. Dual-color PCH analysis demonstrated that not all of the expressed EGFP-mRFP1 fusion proteins contained a fluorescent mRFP1 molecule. Fluorescence lifetime and emission spectra measurements confirmed this surprising result. Additional experiments show that the missing fluorescent fraction of mRFP1 is consistent with a dark state population of mRFP1. We successfully resolved this mixture of fusion proteins with a single dual-color PCH measurement. These results highlight the potential of dual-color PCH to directly detect and quantify protein mixtures in living cells.     

Fluorescence fluctuation analysis for the study of interactions between oligonucleotides and polycationic polymers

The interactions between a cationic polymer, poly(2-dimethylamino)ethyl methacrylate (pDMAEMA), and negatively charged rhodamine-labeled 25-mer phosphodiester oligonucleotides (Rh-ONs) were studied by fluorescence fluctuation spectroscopy and other techniques. The composition of the pDMAEMA/Rh-ON complexes was investigated as a function of the charge ratio (+/-) by increasing the pDMAEMA concentration and keeping the Rh-ON concentration constant. We applied two different methods for analyzing the fluorescence fluctuation profiles of the pDMAEMA/Rh-ON complexes, which depended on their composition. First, we analyzed the data with the photon counting histogram (PCH) technique, which determines the molecular brightness and the concentration of fluorophores (Chen et al, 1999). A particular challenge for the data analysis is the occurrence of sudden fluorescence bursts in the fluorescence fluctuation profiles, which are linked to the appearance of multimolecular complexes (i. e. when several Rh-ONs were present in one complex). A quantitative interpretation of the analysis for the complexes remains challenging and is connected to the rarity of the fluorescent bursts, which do not provide sufficient data statistics. To specifically address the problem of the fluorescent bursts we employed a method described by Van Craenenbroeck et al. (1999). This method, applicable only when data were integrated over much longer time bins, allowed us to estimate the number of fluorescence bursts which could be considered as a relative measure of the amount of multimolecular complexes present. When monomolecular complexes were formed, i. e. at high values of the charge ratio, highly intense fluorescence peaks were not present and the interpretation of the PCH analysis was more straightforward. The molecular brightness of the species (epsilon), as revealed from PCH analysis, was greater than epsilon for the free Rh-ONs, indicating that the Rh-ONs were attached to pDMAEMA chains.     

Alzheimer mouse brain tissue measured by time resolved fluorescence spectroscopy using single‐ and multi‐photon excitation of label free native molecules

Time resolved spectroscopic measurements with single‐photon and multi‐photon excitation of native molecules were performed ex vivo on brain tissues from an Alzheimer's disease (AD) and a wild type (WT) mouse model using a streak camera. The fluorescence decay times of native NADH and FAD show a longer relaxation time in AD than in WT tissue, suggesting less non‐radiative processes in AD. The longer emission time of AD may be attributed to the coupling of the key native building block molecules to the amyloid‐tau and/or to the caging of the native fluorophores by the deposition of amyloid‐beta or tau plaques and neurofibrillary tangles that affect the local non‐radiative interactions.

     

Visual filling-in for computing perceptual surface properties

 The visual system is constantly confronted with the problem of integrating local signals into more global arrangements. This arises from the nature of early cell responses, whether they signal localized measures of luminance, motion, retinal position differences, or discontinuities. Consequently, from sparse, local measurements, the visual system must somehow generate the most likely hypothesis that is consistent with them. In this paper, we study the problem of determining achromatic surface properties, namely brightness. Mechanisms of brightness filling-in have been described by qualitative as well as quantitative models, such as by the one proposed by Cohen and Grossberg [Cohen and Grossberg (1984) Percept Psychophys 36: 428–456]. We demonstrate that filling-in from contrast estimates leads to a regularized solution for the computational problem of generating brightness representations from sparse estimates. This provides deeper insights into the nature of filling-in processes and the underlying objective function one wishes to compute. This particularly guided the proposal of a new modified version of filling-in, namely confidence-based filling-in which generates more robust brightness representations. Our investigation relates the modeling of perceptual data for biological vision to the mathematical frameworks of regularization theory and linear spatially variant diffusion. It therefore unifies different research directions that have so far coexisted in different scientific communities. Received: 11 March 1999 / Accepted in revised form: 14 March 2001     

The Covalent Trimethoprim Chemical Tag Facilitates Single Molecule Imaging with Organic Fluorophores

Chemical tags can be used to selectively label proteins with fluorophores that have high photon outputs. By permitting straightforward single molecule (SM) detection and imaging with organic fluorophores, chemical tags have the potential to advance SM imaging as a routine experimental tool for studying biological mechanism. However, there has been little characterization of the photophysical consequences of using chemical tags with organic fluorophores. Here, we examine the effect the covalent trimethoprim chemical tag (A-TMP-tag) has on the SM imaging performance of the fluorophores, Atto655 and Alexa647, by evaluating the photophysical properties of these fluorophores and their A-TMP-tag conjugates. We measure SM photon flux, survival lifetime, and total photon output under conditions that mimic the live cell environment and demonstrate that the A-TMP-tag complements the advantageous SM imaging properties of Atto655 and Alexa647. We also measure the ensemble properties of quantum yield and photostability lifetime, revealing a correlation between SM and ensemble properties. Taken together, these findings establish a systematic method for evaluating the impact chemical tags have on fluorophores for SM imaging and demonstrate that the A-TMP-tag with Atto655 and Alexa647 are promising reagents for biological imaging.     

Dual-color photon-counting histogram

We report on the development of dual-color photon-counting histogram (PCH) analysis. Dual-color PCH is an extension of regular PCH and considers the photon counts received in two detection channels instead of one. Because each detection channel records a different color, dual-color PCH distinguishes fluorescent species not only by differences in their brightness, but also according to their color. The additional discrimination by color increases the sensitivity of PCH in resolving a mixture of species considerably. Most dual-color fluorescence fluctuation experiments are performed on fluorophores with overlapping emission spectra. This overlap results in spectral cross talk between the detector channels, which reduces resolvability. Here, we demonstrate that dual-color PCH is able to resolve binary dye mixtures in the presence of cross talk from a single measurement without any additional information about the sample. We discuss the effect of sampling time on the fit parameters of dual-color PCH. Differences between dual-color fluorescence correlation spectroscopy and dual-color PCH will also be addressed. We quantitatively resolve a mixture of the two fluorescent proteins CFP and YFP, which is challenging because of the strong spectral overlap of their emission spectra. Dichroic mirrors are needed to direct the light into the two detection channels. We quantify the influence of these filters on dual-color PCH analysis and determine the optimal transition wavelength of the dichroic mirror for the CFP-YFP pair.     

A glutamine to glutamate mutation at position 170 (Q170E) in the rabbit Na+/glucose cotransporter, rSGLT1, enhances binding affinity for Na+

Using cysteine mutagenesis and chemical modification by methanethiosulfonate derivatives, it was demonstrated that the external putative loop, joining transmembrane segments (TM's) IV-V of rabbit Na+/glucose cotransporter, rSGLT1, forms part of a Na+ binding and voltage sensing domain. Within this region, exposure to cationic (2-aminoethyl)methanethiosulfonate hydrobromide (MTSEA) inhibited F163C, A166C, and L173C, but anionic sodium (2-sulfonatoethyl)methanethiosulfonate (MTSES) had no effect. Unexpectedly, MTSEA had no effect on Q170C; however, MTSES profoundly altered Q170C charge transfer and turnover, leaving Na+ and sugar binding affinity unchanged, but mutation of glutamine to anionic glutamate (Q170E) shifted V(0.5) to positive potentials, suggesting enhanced Na+ affinity. To clarify the role of glutamine 170 in Na+ interaction, we embarked on a more detailed investigation of Q170E using the two-microelectrode voltage clamping in Xenopus oocytes. Compared to wild-type (wt) rSGLT1, Q170E exhibits (i) a 2-fold decrease in methyl alpha-D-glucopyranoside affinity (-150 to -90 mV), (ii) a 5-fold increase in Na+ affinity (-150 to -100 mV) with less voltage dependency, (iii) reduced Na+ leak, and (iv) two transient current decay constants (tau(fast), tau(slow)) compared to three (tau(fast), tau(medium), tau(slow)) for wt, and computer simulation of Q170E pre-steady-state currents with a four-state kinetic model yields parameters similar to wt SGLT1, except for a reduced Na+ debinding rate constant compared to wt. Taken together, the data strengthen the conclusion that residue 170 lies in the Na+ pathway and provide the first evidence that it participates in determining Na+ binding.