General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: application to kinetics of open complex formation between Esigma70 RNA polymerase and lambdaP(R) promoter DNA.
(17/9350)
A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] >> [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation. (+info)
Model-independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers.
(18/9350)
The orientation of proteins in ordered biological samples can be investigated using steady-state polarized fluorescence from probes conjugated to the protein. A general limitation of this approach is that the probes typically exhibit rapid orientational motion ("wobble") with respect to the protein backbone. Here we present a method for characterizing the extent of this wobble and for removing its effects from the available information about the static orientational distribution of the probes. The analysis depends on four assumptions: 1) the probe wobble is fast compared with the nanosecond time scale of its excited-state decay; 2) the orientational distributions of the absorption and emission transition dipole moments are cylindrically symmetrical about a common axis c fixed in the protein; 3) protein motions are negligible during the excited-state decay; 4) the distribution of c is cylindrically symmetrical about the director of the experimental sample. In a muscle fiber, the director is the fiber axis, F. All of the information on the orientational order of the probe that is available from measurements of linearly polarized fluorescence is contained in five independent polarized fluorescence intensities measured with excitation and emission polarizers parallel or perpendicular to F and with the propagation axis of the detected fluorescence parallel or perpendicular to that of the excitation. The analysis then yields the average second-rank and fourth-rank order parameters ( and ) of the angular distribution of c relative to F, and and , the average second-rank order parameters of the angular distribution for wobble of the absorption and emission transition dipole moments relative to c. The method can also be applied to other cylindrically ordered systems such as oriented lipid bilayer membranes and to processes slower than fluorescence that may be observed using longer-lived optically excited states. (+info)
Model for bacteriophage T4 development in Escherichia coli.
(19/9350)
Mathematical relations for the number of mature T4 bacteriophages, both inside and after lysis of an Escherichia coli cell, as a function of time after infection by a single phage were obtained, with the following five parameters: delay time until the first T4 is completed inside the bacterium (eclipse period, nu) and its standard deviation (sigma), the rate at which the number of ripe T4 increases inside the bacterium during the rise period (alpha), and the time when the bacterium bursts (mu) and its standard deviation (beta). Burst size [B = alpha(mu - nu)], the number of phages released from an infected bacterium, is thus a dependent parameter. A least-squares program was used to derive the values of the parameters for a variety of experimental results obtained with wild-type T4 in E. coli B/r under different growth conditions and manipulations (H. Hadas, M. Einav, I. Fishov, and A. Zaritsky, Microbiology 143:179-185, 1997). A "destruction parameter" (zeta) was added to take care of the adverse effect of chloroform on phage survival. The overall agreement between the model and the experiment is quite good. The dependence of the derived parameters on growth conditions can be used to predict phage development under other experimental manipulations. (+info)
Model studies of chromatin structure based on X-ray diffraction data.
(20/9350)
Model calculations are presented in order to interpret the X-ray diffraction diagrams given by chromatin gels. It is shown that by taking into account the hydration of chromatin subunits, the problem of calculating the interference function in concentrated gels is greatly simplified. In this way it is spossible to fully interpret the influence of concentration on the position and intensity of the various rings present in the X-ray diffraction patterns. The possibilities and limitations of models based on spherical symmetry are also discussed. It is concluded that each chromatin subunit most likely contains three turns of DNA in each 200 base pairs segment surrounding a central protein core. With the method presented here it is possible to test if other models of chromatin based on different kinds of evidence are compatible with the X-ray diffraction data. (+info)
Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia.
(21/9350)
This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (DeltapO2) in the breathing gas. For a step change of DeltapO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and DeltapO2, which can be written as P(t-t1 | DeltapO2). An effective method does not exist to examine the nonlinear function P(t-t1 | DeltapO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed. (+info)
Zernike representation of corneal topography height data after nonmechanical penetrating keratoplasty.
(22/9350)
PURPOSE: To demonstrate a mathematical method for decomposition of discrete corneal topography height data into a set of Zernike polynomials and to demonstrate the clinical applicability of these computations in the postkeratoplasty cornea. METHODS: Fifty consecutive patients with either Fuchs' dystrophy (n = 20) or keratoconus (n = 30) were seen at 3 months, 6 months, and 1 year (before suture removal) and again after suture removal following nonmechanical trephination with the excimer laser. Patients were assessed using regular keratometry, corneal topography (TMS-1, simulated keratometry [SimK]), subjective refraction, and best-corrected visual acuity (VA) at each interval. A set of Zernike coefficients with radial degree 8 was calculated to fit two model surfaces: a complete representation (TOTAL) and a representation with parabolic terms only to define an approximate spherocylindrical surface (PARABOLIC). The root mean square error (RMS) was calculated comparing the corneal raw height data with TOTAL (TOTALRMS) and PARABOLIC (PARABOLICRMS). The cylinder of subjective refraction was correlated with the keratometric readings, the SimK, and the respective Zernike parameter. Visual acuity was correlated with the tilt components of the Zernike expansion. RESULTS: The measured corneal surface could be approximated by the composed surface 1 with TOTALRMS < or = 1.93 microm and by surface 2 with PARABOLICRMS < or = 3.66 microm. Mean keratometric reading after suture removal was 2.8+/-0.6 D. At all follow-up examinations, the SimK yielded higher values, whereas the keratometric reading and the refractive cylinder yielded lower values than the respective Zernike parameter. The correlation of the Zernike representation and the refractive cylinder (P = 0.02 at 3 months, P = 0.05 at 6 months and at 1 year, and P = 0.01 after suture removal) was much better than the correlation of the SimK and refractive cylinder (P = 0.3 at 3 months, P = 0.4 at 6 months, P = 0.2 at 1 year, and P = 0.1 after suture removal). Visual acuity increased from 0.23+/-0.10 at the 3-month evaluation to 0.54+/-0.19 after suture removal. After suture removal, there was a statistically significant inverse correlation between VA and tilt (P = 0.02 in patients with keratoconus and P = 0.05 in those with Fuchs' dystrophy). CONCLUSIONS: Zernike representation of corneal topography height data renders a reconstruction of clinically relevant corneal topography parameters with a marked reduction of redundance and a small error. Correlation of amount/axis of refractive cylinder with respective Zernike parameters is more accurate than with keratometry or respective SimK values of corneal topography analysis. (+info)
Adaptation of bulk constitutive equations to insoluble monolayer collapse at the air-water interface.
(23/9350)
A constitutive equation based on stress-strain models of bulk solids was adapted to relate the surface pressure, compression rate, and temperature of an insoluble monolayer of monodendrons during collapse at the air-water interface. A power law relation between compression rate and surface pressure and an Arrhenius temperature dependence of the steady-state creep rate were observed in data from compression rate and creep experiments in the collapse region. These relations were combined into a single constitutive equation to calculate the temperature dependence of the collapse pressure with a maximum error of 5 percent for temperatures ranging from 10 degrees to 25 degrees C. (+info)
Comparison of indirect calorimetry, the Fick method, and prediction equations in estimating the energy requirements of critically ill patients.
(24/9350)
BACKGROUND: Accurate measurement of resting energy expenditure (REE) is helpful in determining the energy needs of critically ill patients requiring nutritional support. Currently, the most accurate clinical tool used to measure REE is indirect calorimetry, which is expensive, requires trained personnel, and has significant error at higher inspired oxygen concentrations. OBJECTIVE: The purpose of this study was to compare REE measured by indirect calorimetry with REE calculated by using the Fick method and prediction equations by Harris-Benedict, Ireton-Jones, Fusco, and Frankenfield. DESIGN: REEs of 36 patients [12 men and 24 women, mean age 58+/-22 y and mean Acute Physiology and Chronic Health Evaluation II score 22+/-8] in a hospital intensive care unit and receiving mechanical ventilation and total parenteral nutrition (TPN) were measured for > or = 15 min by using indirect calorimetry and compared with REEs calculated from a mean of 2 sets of hemodynamic measurements taken during the metabolic testing period with an oximetric pulmonary artery catheter. RESULTS: Mean REE by indirect calorimetry was 8381+/-1940 kJ/d and correlated poorly with the other methods tested (r = 0.057-0.154). This correlation did not improve after adjusting for changes in respiratory quotient (r2 = 0.28). CONCLUSIONS: These data do not support previous findings showing a strong correlation between REE determined by the Fick method and other prediction equations and indirect calorimetry. In critically ill patients receiving TPN, indirect calorimetry, if available, remains the most appropriate clinical tool for accurate measurement of REE. (+info)