Extracting kinetic rate constants from surface plasmon resonance array systems

Surface plasmon resonance imaging systems, such as Flexchip from Biacore, are capable of monitoring hundreds of reaction spots simultaneously within a single flow cell. Interpreting the binding kinetics in a large-format flow cell presents a number of potential challenges, including accounting for mass transport effects and spot-to-spot sample depletion. We employed a combination of computer simulations and experimentation to characterize these effects across the spotted array and established that a simple two-compartment model may be used to accurately extract intrinsic rate constants from the array under mass transport-limited conditions. Using antibody systems, we demonstrate that the spot-to-spot variability in the binding kinetics was <9%. We also illustrate the advantage of globally fitting binding data from multiple spots within an array for a system that is mass transport limited.     

Analysis of a procedure for the determination of kinetic rate constants

This paper is concerned with a mathematical analysis of the modified Guggenheim procedure. Theorems concerning the solutions of the differential equations which describe the general reaction

$$E + SB\xrightarrow{{k_2 }}C + X, C\xrightarrow{{k_3 }}E + D$$     

Efficient maximum likelihood estimation of kinetic rate constants from macroscopic currents

A new method is described that accurately estimates kinetic constants, conductance and number of ion channels from macroscopic currents. The method uses both the time course and the strength of correlations between different time points of macroscopic currents and utilizes the property of semiseparability of covariance matrix for computationally efficient estimation of current likelihood and its gradient. The number of calculation steps scales linearly with the number of channel states as opposed to the cubic dependence in a previously described method. Together with the likelihood gradient evaluation, which is almost independent of the number of model parameters, the new approach allows evaluation of kinetic models with very complex topologies. We demonstrate applicability of the method to analysis of synaptic currents by estimating accurately rate constants of a 7-state model used to simulate GABAergic macroscopic currents.     

Quantification of kinetic rate constants for transcytosis of polymeric nanoparticle through blood-brain barrier

Background

Polymeric nanoparticles (PNP) have received significant amount of interests for targeted drug delivery across the blood-brain barrier (BBB). Experimental studies have revealed that PNP can transport drug molecules from microvascular blood vessels to brain parenchyma in an efficient and non-invasive way. Despite that, very little attention has been paid to theoretically quantify the transport of such nanoparticles across BBB.

On calculation of rate and dissociation constants from kinetic constants for the Ordered Bi Bi mechanism of liver alcohol dehydrogenase

Rate and dissociation constants for the Ordered Bi Bi mechanism can be incorrectly calculated if interconversion of central complexes is ignored. The problems are illustrated by an examination of the kinetics of liver alcohol dehydrogenase. Definitions of the kinetic constants in terms of rate constants for the complete mechanism are presented.     

Allowance for antibody bivalence in the determination of association rate constants by kinetic exclusion assay

This investigation completes the amendment of theoretical expressions for the characterization of antigen–antibody interactions by kinetic exclusion assay—an endeavor that has been marred by inadequate allowance for the consequences of antibody bivalence in its uptake by the affinity matrix (immobilized antigen) that is used to ascertain the fraction of free antibody sites in a solution with defined total concentrations of antigen and antibody. A simple illustration of reacted site probability considerations in action confirms that the square root of the fluorescence response ratio, R_Ag/R_o, needs to be taken in order to determine the fraction of unoccupied antibody sites, which is the parameter employed to describe the kinetics of antigen uptake in the mixture of antigen and antibody with defined initial composition. The approximately 2-fold underestimation of the association rate constant (k_a) that emanates from the usual practice of omitting the square root factor gives rise to a corresponding overestimate of the equilibrium dissociation constant (K_d)—a situation that is also encountered in the thermodynamic characterization of antigen–antibody interactions by kinetic exclusion assay.     

New constraints between kinetic parameters explain the (Un)identifiability of enzymatic rate constants

For an enzymatic reaction the rate constants in the assumed mechanism (k(1), k(-1), etc.) sometimes can be calculated from the steady-state parameter values (V(max), K(m), etc.) and sometimes cannot. When identifiability problems occur, these are obscured by redundancy occurring among the steady-state parameters. This redundancy is only partly revealed by the known Haldane relations. We found the additional constraints between the parameters. These relations allow to predict in which situation rate constants are identifiable by steady-state kinetic methods. (c) 1996 John Wiley & Sons, Inc.     

A numerical experiment on the determination of kinetic rate constants in the presence of diffusion

Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK ₁ andK _?1. A systematic analysis of the effects of errors is also presented.     

Biosensor-based estimation of kinetic and equilibrium constants

The steady-state affinity constant for the interaction of glutathione S-transferase (GST) with anti-GST immunoglobulin (IgG) was determined by solution-phase equilibrium analysis. A Biacore concentration assay for the determination of free anti-GST IgG was employed giving a Kd value of 6.83 x 10(-10) M. A simple 1:1 solution-phase, equilibrium model approximated the data well. Furthermore, saturation studies showed a maximum occupation of approximately 50%. The choice of affinity-capture ligand, used to anchor anti-GST IgG to the hydrogel, influenced the interaction curves, as evidenced by contact-time-dependent dissociation-phase curves. This was apparent when performing the analysis on anti-mouse Fc-coated surfaces. When the interaction was conducted on a protein A-coated CM5 sensor chip, the interaction conformed well to ideal behavior and was selected for kinetic analysis of the GST interaction.     

Temperature dependence of divalent cation induced fusion of phosphatidylserine liposomes: evaluation of the kinetic rate constants

The effect of temperature and divalent cation binding (Ca2+, Sr2+, Ba2+) on the kinetic rate constants of aggregation and fusion of large phosphatidylserine liposomes is measured for the first time. Fusion is monitored by the Tb3+/dipicolinate assay. Fusion rate constants increase with temperature (15-35 degrees C) in a roughly linear fashion. These rate constants are not otherwise sensitive to whether the temperature is above or below the phase transition temperature of the Ba2+ or Sr2+ complex of phosphatidylserine, as measured by differential scanning calorimetry. Hence, the isothermal transition of the acyl chains from liquid-crystalline to gel phase induced by the cations is not the driving force of the initial fusion event. The aggregation rate constants increase with temperature, and it is the temperature dependence of the energetics of close approach of the liposomes which underlies this increase. On the other hand, the aggregation becomes more reversible at higher temperatures, which has also been observed with monovalent cation induced liposome aggregation where there is no fusion. Calculations on several cases show that the potential energy minimum holding the liposome dimer aggregates together is approximately 5-6 kT deep. This result implies that the aggregation step is highly reversible; i.e., if fusion were not occurring, no stable aggregates would form.     

Estimation of kinetic rate constants from multi-channel recordings by a direct fit of the time series.

The maximum-likelihood technique for the direct estimation of rate constants from the measured patch clamp current is extended to the analysis of multi-channel recordings, including channels with subconductance levels. The algorithm utilizes a simplified approach for the calculation of the matrix exponentials of the probability matrix from the rate constants of the Markov model of the involved channel(s) by making use of the Kronecker sum and product. The extension to multi-channel analysis is tested by the application to simulated data. For these tests, three different channel models were selected: a two-state model, a three-state model with two open states of different conductance, and a three-state model with two closed states. For the simulations, time series of these models were calculated from the related first-order, finite-state, continuous-time Markov processes. Blue background noise was added, and the signals were filtered by a digital filter similar to the anti-aliasing low-pass. The tests showed that the fit algorithm revealed good estimates of the original rate constants from time series of simulated records with up to four independent and identical channels even in the case of signal-to-noise ratios being as low as 2. The number of channels in a record can be determined from the dependence of the likelihood on channel number. For large enough data sets, it takes on a maximum when the assumed channel number is equal to the "true" channel number.     

Relationships between kinetic constants and the amino acid composition of enzymes from the yeast Saccharomyces cerevisiae glycolysis pathway

The kinetic models of metabolic pathways represent a system of biochemical reactions in terms of metabolic fluxes and enzyme kinetics. Therefore, the apparent differences of metabolic fluxes might reflect distinctive kinetic characteristics, as well as sequence-dependent properties of the employed enzymes. This study aims to examine possible linkages between kinetic constants and the amino acid (AA) composition (AAC) for enzymes from the yeast Saccharomyces cerevisiae glycolytic pathway. The values of Michaelis-Menten constant (KM), turnover number (kcat), and specificity constant (ksp = kcat/KM) were taken from BRENDA (15, 17, and 16 values, respectively) and protein sequences of nine enzymes (HXK, GADH, PGK, PGM, ENO, PK, PDC, TIM, and PYC) from UniProtKB. The AAC and sequence properties were computed by ExPASy/ProtParam tool and data processed by conventional methods of multivariate statistics. Multiple linear regressions were found between the log-values of kcat (3 models, 85.74% < Radj.2 <94.11%, p < 0.00001), KM (1 model, Radj.2 = 96.70%, p < 0.00001), ksp (3 models, 96.15% < Radj.2 < 96.50%, p < 0.00001), and the sets of AA frequencies (four to six for each model) selected from enzyme sequences while assessing the potential multicollinearity between variables. It was also found that the selection of independent variables in multiple regression models may reflect certain advantages for definite AA physicochemical and structural propensities, which could affect the properties of sequences. The results support the view on the actual interdependence of catalytic, binding, and structural residues to ensure the efficiency of biocatalysts, since the kinetic constants of the yeast enzymes appear as closely related to the overall AAC of sequences.     

Estimating kinetic constants from single channel data.

The process underlying the opening and closing of ionic channels in biological or artificial lipid membranes can be modeled kinetically as a time-homogeneous Markov chain. The elements of the chain are kinetic states that can be either open or closed. A maximum likelihood procedure is described for estimating the transition rates between these states from single channel data. The method has been implemented for linear kinetic schemes of fewer than six states, and is suitable for nonstationary data in which one or more independent channels are functioning simultaneously. It also provides standard errors for all estimates of rate constants and permits testing of smoothly parameterized subhypotheses of a general model. We have illustrated our approach by analysis of single channel data simulated on a computer and have described a procedure for analysis of experimental data.     

Diffusional falsification of kinetic constants on Lineweaver-Burk plots

The effect of mass transfer resistances on the Lineweaver-Burk plots in immobilized enzyme systems has been investigated numerically and with analytical approximate solutions. While Hamilton, Gardner & Colton (1974) studied the effect of internal diffusion resistances in planar geometry, our study was extended to the combined effect of internal and external diffusion in cylindrical and spherical geometries as well. The variation of Lineweaver-Burk plots with respect to the geometries was minimized by modifying the Thiele modulus and the Biot number with the shape factor. Especially for a small Biot number all the three Lineweaver-Burk plots fell on a single line. As was discussed by Hamilton, et al (1974), the curvature of the line for large external diffusion resistances was small enough to be assumed linear, which was confirmed from the two approximate solutions for large and small substrate concentrations. Two methods for obtaining intrinsic kinetic constants were proposed: First, we obtained both maximum reaction rate and Michaelis constant by fitting experimental data to a straight line where external diffusion resistance was relatively large, and second, we obtained Michaelis constant from apparent Michaelis constant from the figure in case we knew maximum reaction rate a priori.