Showing papers on "Crossover published in 1974"

A linear steady-state treatment of enzymatic chains. Critique of the crossover theorem and a general procedure to identify interaction sites with an effector.

Abstract: A theoretical analysis of the crossover theorem is presented based on a linear approximation. Cases are considered in which the simple crossover theorem may lead to erroneus conclusions. Among them are the following : more than one interaction site of an effector with the enzymatic chain; influx and efflux of metabolites regulated by outer metabolic processes ; existence of inner effectors ; conservation equations for metabolite concentrations ; and changes of the state of complexes with the metabolites. It is shown that the action of an effector does not always produce a crossover at the affected enzyme. On the other hand, examples are given where “pseudo-crossovers’’ occur at unaffected enzymes. It is concluded that for real systems the identification of the interaction sites of an effector with an enzymatic chain cannot be achieved by the simple crossover theorem. Furthermore, even the identification of “rate controlling” or “regulatory important” enzymes by means of crossovers must be done with great caution. A simple and general procedure for the identification of interaction sites of an outer effector with an enzymatic chain is proposed. It requires the determination of the flux through the chain, the concentrations of the substrates and products of the enzymatic step under consideration and the rate law by which an inner effector, if present, influences the reaction rate of this step. The crossover theorem was first formulated by Chance et al. [l-41. It deals with the influence of outer effectors on the levels of the metabolites in an enzymatic chain. In its simplest form, the “classical” crossover theorem can be stated in the following way: the variations of the concentrations of the metabolites before and beyond an enzyme which is influenced by an effector have different signs. It has been widely used to identify the interaction sites of effectors within the chain. Chance et al. [l--51 have applied the crossover theorem for the investigation of the changes in the steady-state oxidation-reduction levels of the components of the respiratory chain. With the help of this theorem they were able to identify the sites of phosphorylation. An inspection of the literature on metabolic regulation shows that subsequently the crossover theorem has been applied to a variety of systems including very complicated ones. It was tacitly assumed that in all these cases the crossover theorem is valid in its simple form (e.g. [6-8)). Only few theoretical considerations of the crossover theorem have been published so far. Chance et al. [7] have studied the crossover behaviour of the respiratory chain by means of analogue computers. In a more general manner, Holmes [9] considered several types of sequences of chemical reactions and proved the theorem for some simple cases. For the characterization of a crossover he used pairs of neighbouring metabolites where the signs (-, +) and (+, -) indicate the direction of the variation of the concentrations produced by the effector. For the condition that the effector increases the flux the pairs were called “forward)’ and “backward” crossovers, respectively, by Williamson [lo]. The present paper deals with the limitations of the simple crossover theorem in its application to real systema. We shall consider five situations where the crossover theorem is not valid. It will be shown that the uncritical application of the crossover theorem may lead to serious misinterpretations. On the other hand, the procedure proposed in this paper for the identification of the interaction sites of an effector with an enzymatic chain will give correct results if the linear approximation holds. Parts of the results have been presented at the FEBS Advanced Course on “Mathematical Models of Metabolic Regulation”, Oberhof, November 1972.

Zero crossover detector with variable hysteresis

Abstract: A zero crossover detector having a switching circuit for developing a digital output signal with transitions therein corresponding to, and occurring simultaneously with, the zero crossover points of an input AC signal, is provided with a control circuit for establishing a substantial zero hysteresis voltage level or switching level for the switching circuit immediately prior to each zero crossover of the input signal to eliminate phase delay in the output signal which would otherwise occur and for establishing a nonzero hysteresis level for the amplifier immediately after the output transition to maximize noise immunity.

Crossover frequencies in a multicomponent plasma

Abstract: An attempt has been made to generalise a method developed earlier for the qualitative assessment of crossover frequencies (existence and behaviour) in multicomponent plasmas with one negative ion species to plasmas with any number of positive and negative ion species. It is shown that a great deal of qualitative information can be obtained regarding the crossover frequencies for any given plasma model without recourse to cumbersome numerical study. Possible applications of the study in the interpretation of frequency time spectrograms for the detection of negative ion whistlers and in the measurement of concentrations and masses of negative ions are noted.

Synaptic initiation and extension as prerequisites for crossing over

Abstract: The effect on crossover frequency in maize of three hour heat treatment was studied when treatment was applied at zygotene (substantially later than the major DNA synthetic period) and at pachytene. Crossover frequency assay was based upon bridge and fragment frequency at anaphase I in heterozygotes for a short paracentric inversion. Effect of treatment was studied in three distinguishable synaptic classes: (1) overall crossover frequency within the inversion, (2) double crossover frequency where two separate events of pairing initiation are required (coincident crossovers within and proximal to the inversion) and (3) double crossover frequency within the inversion, where spreading of synapsis over a short distance from a single event of pairing initiation can provide the requisite pairing. Evidence is reported: (1) that overall crossover frequency within the inversion was very significantly increased by treatment at zygotene but not detectably affected by treatment at pachytene; (2) that double crossover frequency within the inversion was very significantly increased by treatment at pachytene and may have been somewhat increased by treatment at zygotene. Results are consistent with the model that most crossover sites may be established at, or approximately at, events of synaptic initiation but that establishment of infrequent second crossover sites near those formed first can follow or accompany the spreading of synapsis to adjoining regions.