Estimation of Photorespiration Based on the Initial Rate of Postillumination CO(2) Release: I. A Nonsteady State Model for Measurement of CO(2) Exchange Transients

Although open systems have been used for the study of transients in leaf CO₂ exchange such as the postillumination burst, these systems frequently do not permit reliable estimates of transient rates due to their nonsteady state nature. A nonsteady state mathematical approach is described which predicts changes in CO₂ concentration in the leaf chamber and infrared gas analyzer measuring cell as a function of leaf CO₂ exchange rate in Nicotiana tabacum vars John Williams Broadleaf and Havana Seed. With the aid of a computer, a numerical formula simulates the mixing and dilution which occurs as CO₂ passes through the finite volume of the measuring cell of the analyzer. The method is presented with special relevance to photorespiration as manifested by the postillumination burst of CO₂. The latter is suggested to decline with the first order kinetics following darkening of a C₃ leaf. This approach provides a basis for reliable estimation of the initial and, hence, maximal rate of CO₂ evolution during the postillumination burst under a variety of environmental conditions.     

Metabolic network sensitivity analysis

A linear sensitivity analysis of metabolic regulation in nonsteady states is described. This treatment considers the effects of enzymatic and nonenzymatic reactions and spontaneous rapid equilibria. Sensitivity coefficients summarizing the influence of metabolite concentrations on reaction rates and pathway net flux are defined, as are sensitivity coefficients summarizing the effects of enzymes on metabolite concentrations and net flux. The sensitivity analysis is implemented in an easily used set of computer programs. A four-enzyme test model was shown to be resistant to intuitive interpretation. Sensitivity analysis showed a shift of control from the end of the enzymic sequence to the beginning of the sequence with changing metabolic state. The homeostatic behavior of the test system was shown to depend on the nonenzymatic reactions as well as on the enzymes. Under certain conditions metabolic regulation is shared so intimately among enzymes and spontaneous reactions that separation of their effects is impossible.     

The use of computers to study rates of lipid metabolism

Many complex problems of lipid metabolism are especially suited for multicompartmental analysis with computers. Examples are presented. The use of a model as a means of communicating one's working hypothesis and the model as it relates to experimental design are discussed. A number of principles relating to experimental design and to the interpretation and presentation of data are illustrated by 12 studies selected from the literature. These include evaluations of turnover and transport rates of liver and plasma triglycerides, triglyceride synthesis, phospholipid synthesis, and lipid oxidation to CO2. A discussion of computer-oriented vs. noncomputer-oriented techniques is included. Some of the practical problems involved in computer analysis are also considered. Among these are the choice of computer, computer applications, stepwise vs. multicompartmental analysis, validity of single-injection type experiments, avoidance of multicompartmental analysis, nonsteady state systems, and nomenclature.     

Effect of mixing on the washout and steady-state performance of continuous cultures

The effects of mixing on the critical mean holding time for washout and the steady state performance of growth processes in continuous flow reactors are investigated. Macromixing, micromixing, and cell recycle arc considered. The tanks-in-series model composed of N completely mixed flow reactors, the dispersion model, the plug flow model, and a combined model composed of a plug flow reactor and a continuous stirred tank flow reactor connected in series arc used to represent the macro-mixing or residence time distribution. The extreme cases of micromixing, namely, complete segregation and maximum mixedness, as well as intermediate states of micromixing are investigated to determine their effects on washout and the occurence of multiple steady states. A technique for predicting the maximum mixedness washout condition from a knowledge of the residence time distribution is presented and used to determine the washout condition for the dispersion model under maximum mixedness conditions.     

A mechanism for multiphasic uptake of solutes in plants

A molecular mechanism is proposed for unitary multiphasic uptake in which the carrier has two binding sites for the substrate. The first site binds n-1 molecules of substrate, and then one additional substrate molecule can become bound at the second binding site. Only this last molecule is transported in the operation of the carrier molecule. In the free state, the carrier can be activated to successive states with increasing affinities for the substrate in the two binding sites. The mechanism is resolved for the steady state conditions, obtaining a simple uptake rate equation, which fits the experimental data. Methods for determining the parameters of the equation are presented. Evidence other than kinetics is discussed for the mechanism. The mechanism also provides a physiological interpretation for multiphasic uptake: the active transport mechanisms (energy-requiring mechanisms) are prevented from operating at high substrate concentrations, thus preventing a waste of energy by the cells.     

A numerical study of flow in curved tubes simulating coronary arteries

Numerical simulations of pulsatile flow in coronary arteries which take into account the curvature associated with the bending of arteries over the surface of the heart are presented for resting, excited and drug induced states. The study was motivated by reported observations of atherosclerotic plaque localization on the inner curvature of coronary arteries. The simulated flow field appears quasi-steady under resting conditions with wall shear stress always highest on the outside wall and only a single secondary flow vortex in the half tube. However, reversal of wall shear stress direction at the inside wall does occur under resting flow conditions and this is not a quasi-steady characteristic. The flow field is markedly unsteady under excited conditions with wall shear stress sometimes peaking on the inside wall and an increase in the magnitude of wall shear stress reversal on the inside wall. However, only a single secondary flow vortex in the half tube is observed. Implications of the simulations for the role of fluid mechanics in coronary artery atherosclerosis are also discussed.     

Stability of steady states in nucleic acid poly (A-T) synthesis and the stirred flow reactor.

The template directed synthesis of poly[d(A-T)] from the nucleoside triphosphates in the presence of DNA polymerase I is carried out continuously in a stirred flow reactor for the first time. The initial objective is to test the kinetic stability of the established steady states at various flow rates. Graphical analysis predicts instable steady states for certain high flow rates. As a consequence of instabilities multiple steady states and steady-state hysteresis may occur. Steady-state hysteresis has now been found experimentally. For a different enzyme fraction of low exonuclease activity we found the steady-state absorbance at 260 nm to be almost invariant with flow rate at high enzyme concentrations even if the flow rate was increased by a large factor. We call this phenomenon kinetic buffering. Relaxation of a large flow perturbation approaches the steady state in a sigmoidal fashion. Concentration oscillations at 260 nm occurred in one experiment using an enzyme fraction of low exonuclease activity after perturbing the steady state by monomer (dATP). Advantages of the stirred flow reactor method over serial transfer are discussed.     

Kinetic hysteresis for fructose bisphosphatase: a change in substrate configuration specificity.

Kinetic hysteresis for rabbit liver fructose bisphosphatase in the presence of Mg²⁺ (pH 7.6) is exhibited by the varied rates at which product formation is reduced on the addition of different inhibitors under cycling conditions. Two different states of the enzyme are detected: the initial resting state which binds α-, β- and keto analogs of fructose 1,6-bisphosphate; and the active cycling state which binds, and is inhibited by, only the α-analog. Both enzyme states, however, bind the allosteric modifier, AMP, and a product analog, (α+β)methyl-D-fructofuranoside 6-phosphate to the same extent so that the resulting inhibition is state independent. A relatively slow first-order transition (0.13 min^?1) characterizes the reversion of the active enzyme to its resting state. The implications of this phenomenon for regulating fructose bisphosphatase activity $\text{in vivo}$ are discussed.     

Pigment production in chemostat cultures of Streptococcus bovis

Summary Streptococcus bovis 2B formed bright red cell clumps in glucose-limited defined medium under certain nonsteady state growth conditions. Scanning electron micrographs showed that clumped cells were more rounded than those from complex medium. Clumped cells appeared to be bound to one another at the cell surface and there was no sign of a polysaccharide matrix. Freeze fractured cells showed that the inner membrane particle distribution was different in the clumped cells from fast growing cells in complex or defined medium. Clumping is potentially a mechanism to decrease transport by reducing the cell surface area. It appears to be a nonsteady state phenomenon, occurring in situations leading to unbalanced growth.     

Insights into conformation and dynamics of protein GB1 during folding and unfolding by NMR

Understanding protein stability requires characterization of structural determinants of the folded and unfolded states. Many proteins are capable of populating partially folded states under specific solution conditions. Occasionally, coexistence of the folded and an unfolded state under non- or mildly denaturing conditions can be observed by NMR, allowing us to structurally probe these states under identical conditions. Here we report on a destabilized mutant of the B1 domain of protein G (GB1) whose equilibrium unfolding was systematically investigated. Backbone amide residual dipolar couplings (RDCs), the tryptophan Nepsilon-H resonance and the amide nitrogen transverse relaxation rates (R2s) for varying pH values and different temperatures were measured. The backbone amide RDCs indicate that prior to complete unfolding, two melting hot spots are formed at the turn around T11, L12 and K13 and the N terminus of the helix at A24 and T25. The RDCs for the low pH, thermally unfolded state of GB1 are very small and do not indicate the presence of any native-like structure. Amide nitrogen transverse relaxation rates for GB1 in the folded state at different temperatures exhibit large contributions from exchange processes and the associated dynamics display considerable heterogeneity. Our data provide clear evidence for intermediate conformations and multi-state equilibrium un/folding for this GB1 variant.     

Toward a self-similar theory of microbial populations

A fresh quest is made of segregated cell models of microbial populations with a view to determine whether the multivarite distribution of physiological states, during transient growth, can attain self-similar forms (i.e., become time invariant) when each physiological state variable is scaled with respect to its population average. Such self-similar growth situations are believed to be more general than those of balanced growth. The conditions under which self-similarity is possible are investigated. Thus conditions are stipulated on the synthesis rates of different physiological entities, cell division rate, and the partitioning of the parent cell's components among the daughter cells (assuming binary division) in order for self-similar growth to be attained. Subject to the attainment of self-similar growth, it is shown that cytometric data can be analyzed systematically to determine how the rates of syntheses of various biochemical entities and cell division rates vary with the physiological entities that are measured. Inverse problems, represented by algebraic systems, are identified which will potentially allow flow cytometric data to be inverted to yield quantitative information on the absolute rates of cellular growth and reproductory processes as a function of the cell states chosen for measurement. It is suggested that the methods become more effective when cytometry can be used to make direct observations on dividing cells so that the number of unknowns in the inverse problem can be reduced, thus facilitating its more complete solution. Preliminary analysis of cytometric data obtained in the literature show promise of self-similarity and thus the possibility of application of the methods discussed here. (c) 1994 John Wiley & Sons, Inc.     

The steady state kinetics of some biological systems: III. Thermodynamic aspects

Some thermodynamic aspects of steady systems are considered. The time rates of changes, “flux”, of various thermodynamic quantities are formulated. In particular the free energy flux in the steady state, the difference between the free energy flux in the steady and time dependent states and the change in free energy flux upon transition between steady states are discussed. Equations are derived which exhibit the formal similarities and differences between the free energy flux and the conventional free energy change. The temperature dependence of the steady state rate is examined and conditions for “mastery” by a single step discussed. A brief discussion of the role ofrate in the coupling of exergonic and endergonic reactions is given.     

Growth of a Catharanthus roseus cell suspension culture in a modified chemostat under glucose-limiting conditions

Summary A system for the continuous cultivation of plant cells has been developed, based on a commercially available 3–1 turbine-stirred fermentor. A special device was constructed to provide for homogeneous effluent from the culture at low dilution rates. Two steady states with Catharanthus roseus cells growing under glucose limitation are described with respect to biomass yield on the carbon and energy source glucose, specific oxygen consumption, specific carbon dioxide production and (by)product formation. From a carbon balance for each steady state it is shown that the flow of carbon to the culture (as glucose) practically equalled the flow of carbon from the culture (as biomass, carbon dioxide and (by)product). Biomass yields on glucose were 0.31 g/g and 0.35 g/g at dilution rates of 0.0060 l/h and 0.0081 l/h respectively. The striking difference between the obtained yield coefficients and biomass yield commonly found for batch-cultured plant cells is discussed.     

Hydrogen exchange in native and denatured states of hen egg-white lysozyme.

The hydrogen exchange kinetics of 68 individual amide protons in the native state of hen lysozyme have been measured at pH 7.5 and 30 degrees C by 2D NMR methods. These constitute the most protected subset of amides, with exchange half lives some 10(5)-10(7) times longer than anticipated from studies of small model peptides. The observed distribution of rates under these conditions can be rationalized to a large extent in terms of the hydrogen bonding of individual amides and their burial from bulk solvent. Exchange rates have also been measured in a reversibly denatured state of lysozyme; this was made possible under very mild conditions, pH 2.0 35 degrees C, by lowering the stability of the native state through selective cleavage of the Cys-6-Cys-127 disulfide cross-link (CM6-127 lysozyme). In this state the exchange rates for the majority of amides approach, within a factor of 5, the values anticipated from small model peptides. For a few amides, however, there is evidence for significant retardation (up to nearly 20-fold) relative to the predicted rates. The pattern of protection observed under these conditions does not reflect the behavior of the protein under strongly native conditions, suggesting that regions of native-like structure do not persist significantly in the denatured state of CM6-127 lysozyme. The pattern of exchange rates from the native protein at high temperature, pH 3.8 69 degrees C, resembles that of the acid-denatured state, suggesting that under these conditions the exchange kinetics are dominated by transient global unfolding. The rates of folding and unfolding under these conditions were determined independently by magnetization transfer NMR methods, enabling the intrinsic exchange rates from the denatured state to be deduced on the basis of this model, under conditions where the predominant equilibrium species is the native state. Again, in the case of most amides these rates showed only limited deviation from those predicted by a simple random coil model. This reinforces the view that these denatured states of lysozyme have little persistent residual order and contrasts with the behavior found for compact partially folded states of proteins, including an intermediate detected transiently during the refolding of hen lysozyme.     

A biochemically structured model for Saccharomyces cerevisiae.

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.     

Hydrolysis of nucleoside triphosphates other than ATP by nitrogenase

The hydrolysis of ATP to ADP and P(i) is an integral part of all substrate reduction reactions catalyzed by nitrogenase. In this work, evidence is presented that nitrogenases isolated from Azotobacter vinelandii and Clostridium pasteurianum can hydrolyze MgGTP, MgITP, and MgUTP to their respective nucleoside diphosphates at rates comparable to those measured for MgATP hydrolysis. The reactions were dependent on the presence of both the iron (Fe) protein and the molybdenum-iron (MoFe) protein. The oxidation state of nitrogenase was found to greatly influence the nucleotide hydrolysis rates. MgATP hydrolysis rates were 20 times higher under dithionite reducing conditions (approximately 4,000 nmol of MgADP formed per min/mg of Fe protein) as compared with indigo disulfonate oxidizing conditions (200 nmol of MgADP formed per min/mg of Fe protein). In contrast, MgGTP, MgITP, and MgUTP hydrolysis rates were significantly higher under oxidizing conditions (1,400-2,000 nmol of MgNDP formed per min/mg of Fe protein) as compared with reducing conditions (80-230 nmol of MgNDP formed per min/mg of Fe protein). The K(m) values for MgATP, MgGTP, MgUTP, and MgITP hydrolysis were found to be similar (330-540 microM) for both the reduced and oxidized states of nitrogenase. Incubation of Fe and MoFe proteins with each of the MgNTP molecules and AlF(4)(-) resulted in the formation of non-dissociating protein-protein complexes, presumably with trapped AlF(4)(-) x MgNDP. The implications of these results in understanding how nucleotide hydrolysis is coupled to substrate reduction in nitrogenase are discussed.     

Computer simulation of firefly flash sequences.

A new method is proposed for measuring nonsteady flow rates when this flow is pulsatile in nature. This method involves the use of indicators and does not require direct access to the vessel carrying the fluid. No knowledge of the associated mathematics is required for its application. The investigator infuses indator into the vessel leading into a capillary or similar labyrinth at a time-varying rate such that the indicator concentration at the outflow from the labyrinth remains constant in time. When this condition at the outflow has been achieved, the pulsatile flow rate at the inflow is given simply as the ratio of the varying infusion rate to the constant outflow indicator concentration.     

Kinetics of poly-enzyme system reactions. II. Nonsteady-state kinetics. Presteady-state and relation modes in a bi-enzyme system and linear sequences

Kinetic aspects of reactions in homogeneous multienzyme systems under nonsteady state conditions were investigated. An analysis of formal-kinetic relationships, describing the time course of system was conducted with a bienzyme system. Presteady state kinetics of processes in lineal multienzyme systems was investigated. Relax-kinetics methods were applied for the analysis of processes in lineal sequences. Methods of determination of number of stages initial substrate transformations and of number of enzymes were developed as well as methods for the analysis of sequences of intermediates in reaction pathway. Methods of determination of Vmax and Kmax for each individual enzyme are considered.