Special thanks to Kevin Leubke for more than a thoughtful discussion and for the role he played in making apartment 302 such a fun place to live. It was used to investigate different models of translational regulation of RNA polymerase (synthesis of 3 subunits.
A Theoretical Approach to Studying the Regulation
Introduction
Thus, a mathematical description of the entire cell is not required to describe the transient behavior of the subsystem. We faced this problem while studying the synthesis of the major RNA polymerase subunits in E.
Approach
This is a consequence of the fact that the error is highly dependent on the properties of the new steady state that would actually be reached by the surrounding system. The discrepancy between the two will depend on the size and nature of the disturbance.
Mathematical Description of Gene Expression
The emergence of the next r1 length class (which can be denoted To to t = !lt) is described by equation (3), where [r0] replaces [r1. The situation with the first term on the right-hand side of equation (3) is similar in that a product of means is assumed to be equivalent to the mean of the product.
Modeling the Perturbation
Since the actual rate is limited to integral values, the Poisson formula cannot be applied to populations large enough for the probability to resemble a continuous function. By specifying a value for P and applying equation (7), one can determine equally likely (or unlikely) outlier rates for each of the expected rates.
Model Application
Over the course of one generation, approximately 40% of cells will experience a shift of this magnitude. We operationally defined a key protein as a protein that, when significantly shifted in steady-state concentration, leads to a significant shift in steady-state growth configuration.
Discussion
The overall probability that the target regions will survive until transcription is complete is given by the product of the probabilities for each step:. As indicated by the bold arrows, these processes depend on properties of the black frame.
Translational Regulation of rpoB Expression
Equations Governing Expression
The responses indicated by dashed lines were calculated with the same parameter values, the only difference being that the protein product was hypothetically assumed to be unrelated to RNA polymerase (ie, the equations from the previous paper were used without modification). The conclusion to be drawn from these considerations is that, in the context of this approach, recovery of the initial steady state is a necessary but insufficient condition for balanced exponential growth to be realized.
Transcriptional Regulation
In vitro synthesis of the first dipeptide bond of (3 subunits of Escherichia coli RNA polymerase. Relative activities of translational regulatory sites in the rplKAJL rpoBC gene cluster of Escherichia coli. Since the assumptions leading to (2) above are consistent with the data (excluding the onset period), this appears to be a reasonable representation of the net response occurring in the cells in this experiment.
Binding of the solute molecule to the protein is likely to occur in the transport process. If the
Equations for the internal driving force of the latter two have been written (equations (3) and (4)). El indicates the position of the resonance of ethanol-Cl (not present in these spectra).
Assigning Values to Kinectic Parameters
Translational Regulation (case 1)
Equation (9) applies to all length classes. S.,.o is taken as zero), while equation (8) holds for all but the first. Physical limitations must be considered before attempting to optimize the values of k1 and r1 • A theoretical upper limit on the rate constant for RN binding A polymerase/promoter has been estimated assuming that the interaction will be controlled entirely by diffusion (von Hippel et al., 1984). Rate constants for cleavage of RN A polymerase from strong promoters can be as low as 10-5 sec-1 (Cech and McClure, 1980).
We estimate the nonbinding limit r1 to be on the order of 1010 s-1. • The value of r1 should be much lower than this to call the interaction "binding" in the usual sense. In addition to physical constraints, the values of k1 and :r1 are limited by the fast equilibrium condition. There are conflicting demands placed on :r1• Fast equilibrium requires :r1 to be large, while optimal response requires that it be small, but since "large" and "small" must be judged in terms of different numbers, we can try compromise.
Translational Regulation (case 2)
Comparing these equations shows that if µ, and 61 are non-negligible, they effectively reduce the value of K1. Therefore, the maximum possible value of 'Ill' is 'i, and the kinetic values determined above can be used to calculate the optimal response of the current model. The maximum fast equilibrium value of W for this model, 4, indicates that cooperative sequential binding has the potential to dramatically improve the control response.
The curves in Figure 9 were generated by selecting the largest physically reasonable rate constants (representing the closest physically reasonable approach. 53 - . to equilibrium) which yield the same set of equilibrium constants used to generate the curves in Figure 7. Most importantly , since the upper curves in Figure 9 fall well below the corresponding curves in Figure 7, we conclude that the optimal parameter set for the four-site model precludes equilibrium of the message complexes.
Discussion
With this in mind, we will use the results of Dennis et al. 1985) as an estimate of the stringency of translational regulation in E. The rate constant for dissociation of the pb complex, r,-, is inversely proportional to the half-life of this complex. This work was supported by the Energy Conversion and Utilization Technologies (ECUT) Program in the USA.
Direct evidence for rifampicin-promoted read-through of the partial terminator tL 7 in the rpoBC operon of Escherichia coli. Autogenous regulation of the RNA polymerase B subunit of Escherichia coli occurs at the translational level in vivo. About 75% of the transcripts initiated at the PLlo promoter are terminated at the attenuator (atn) located in the intergenic region upstream of rpoB.
Experimental Characterization of the Interaction
Materials and Methods
This fragment (Figure 1) was ligated with DNA from an EcoRI digest of plasmid pET5 (donated by Dr. F.W. Studier). Because our goal was to produce a transcript identical to part of the rplL-rpoB mRNA, only one of two possible insertion orientations was acceptable. Under the assumption that translational control by binding to mRNA would involve binding near the rpoB Shine-Dalgarno sequence, we limited our investigation to a region within approximately 500 bases of the SD sequence.
As a template for the synthesis of the control transcript, plasmid pET5 was digested with PstI (Figure 1) and gel purified. Inhibition of any residual RNase activity was allowed to proceed for 10 minutes at room temperature before adding T7 RNA polymerase (30 units). Low levels of each nucleic acid were added due to the possibility that RNA polymerase binding is NTP dependent.
Results and Discussion
Comparing equations (5) and (6) immediately leads to the conclusion that the values of the two step functions must be equal in equilibrium. We again consider the uptake of a metabolite with a uniform negative charge, x-,. the two transport reactions in the Rottenberg model are:. where i and o denote values relating to the interior and exterior of the cytoplasm, respectively. The chemical shift of the phosphate peak can therefore be used to measure pH (Gadian, 1982).
The comparison shows that the rate of acetate production about 25 minutes after the addition of glucose is about 20% of the average rate during the first ten minutes of glycolysis. The rate of lactate production after 25 minutes is only 11% of the average rate during the first ten minutes. The role of the transport system is supposed to improve the net rate of effi.ux.
Application of 31 P Nuclear Magnetic Resonance
The Ussing-Teorell Equation
If a membrane separates two solutions of A and is permeable to A, the net flux of A from side 1 to side 2 is simply the difference between the two. Knowledge of the unidirectional fluxes is of course of greater value from a kinetic point of view than knowledge of the net flux. This form of the Ussing-Teorell equation is valid when there is no net water flow through the membrane.
Because unidirectional fluxes through biological membranes can be easily measured, this relationship has proven useful in testing transport models (Stein, 1989; Ussing, 1952).
Flux Constraints for Protein-Mediated Transport
The movement of the molecule will then be very limited and a little like free diffusion. Furthermore, since the size of the maximum energy barrier is determined by the interaction between the solute molecule and the transportase, this factor is included in Due to the complex dependence on the architecture of the transportase, little can be said about the relationship between 4>i; and ~ W. We have treated the activities aA 1 and aA2 as if they apply to the entire solution volume on their respective sides of the membrane. If net transport occurs, there is usually a region in the immediate vicinity of the membrane (the Nernst diffusion layer; see Lakshminarayanaiah, 1969) where a significant concentration gradient exists. A schematic of the Rottenberg carrier model for transport of a singly charged anion is given in Figure 2. Equations (3) and (4) represent the intrinsic concentration dependence of the net transport rates for the one-proton and two-proton transport modes. The only addition is that the ratio of effective permeability of the two species is a function of pH. It was found that the transmembrane electrical potential, AW, was quite stable during the course of the experiment (Figure 7). After a short drop, it increases at a faster rate than before for the duration of the experiment. This was verified by comparing the peak areas in the 13 C NMR spectra of the lysate samples prepared at 24. Assuming that lactate transport is a passive process, protein-mediated transport in the first part of the experiment would occur either via the zero-proton mode (in which case simple diffusion is dominant) or via the half-proton mode (in which case protein-mediated transport is dominant). C Driver program for modeling the regulation of the synthesis of the C RNA polymerase beta subunit in Escherichia coli. ResultsDiscussion
Transport of Lactate and Acetate
