Hendrik J. Viljoen

Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis

It is generally accepted that the translation rate depends on the availability of cognate aa-tRNAs. In this study it is shown that the key factor that determines translation rate is the competition between near-cognate and cognate aa-tRNAs. The transport mechanism in the cytoplasm is diffusion, thus the competition between cognate, near-cognate and non-cognate aa-tRNAs to bind to the ribosome is a stochastic process. Two competition measures are introduced; C(i) and R(i) (i=1, 64) are quotients of the arrival frequencies of near-cognates vs. cognates and non-cognates vs. cognates, respectively. Furthermore, the reaction rates of bound cognates differ from those of bound near-cognates. If a near-cognate aa-tRNA binds to the A site of the ribosome, it may be rejected at the anti-codon recognition step or proofreading step or it may be accepted. Regardless of its fate, the near-cognates and non-cognates have caused delays of varying duration to the observed rate of translation. Rate constants have been measured at a temperature of 20 degrees C by (Gromadski, K.B., Rodnina, M.V., 2004. Kinetic determinants of high-fidelity tRNA discrimination on the ribosome. Mol. Cell 13, 191-200). These rate constants have been re-evaluated at 37 degrees C, using experimental data at 24.5 degrees C and 37 degrees C (Varenne, S., et al., 1984. Translation in a non-uniform process: effect of tRNA availability on the rate of elongation of nascent polypeptide chains. J. Mol. Biol. 180, 549-576). The key results of the study are: (i) the average time (at 37 degrees C) to add an amino acid, as defined by the ith codon, to the nascent peptide chain is: tau(i)=9.06+1.445x[10.48C(i)+0.5R(i)] (in ms); (ii) the misreading frequency is directly proportional to the near-cognate competition, E(i)=0.0009C(i); (iii) the competition from near-cognates, and not the availability of cognate aa-tRNAs, is the most important factor that determines the translation rate - the four codons with highest near-cognate competition (in the case of E. coli) are [GCC]>[CGG]>[AGG]>[GGA], which overlap only partially with the rarest codons: [AGG]<[CCA]<[GCC]<[CAC]; (iv) based on the kinetic rates at 37 degrees C, the average time to insert a cognate amino acid is 9.06ms and the average delay to process a near-cognate aa-tRNA is 10.45ms and (vii) the model also provides estimates of the vacancy times of the A site of the ribosome - an important factor in frameshifting.

Brief Communication: A fundamental study of the PCR amplification of GC-rich DNA templates

A theoretical analysis is presented with experimental confirmation to conclusively demonstrate the critical role that annealing plays in efficient PCR amplification of GC-rich templates. The analysis is focused on the annealing of primers at alternative binding sites (competitive annealing) and the main result is a quantitative expression of the efficiency (eta) of annealing as a function of temperature (T(A)), annealing period (t(A)), and template composition. The optimal efficiency lies in a narrow region of T(A) and t(A) for GC-rich templates and a much broader region for normal GC templates. To confirm the theoretical findings, the following genes have been PCR amplified from human cDNA template: ARX and HBB (with 78.72% and 52.99% GC, respectively). Theoretical results are in excellent agreement with the experimental findings. Optimum annealing times for GC-rich genes lie in the range of 3-6s and depend on annealing temperature. Annealing times greater than 10s yield smeared PCR amplified products. The non-GC-rich gene did not exhibit this sensitivity to annealing times. Theory and experimental results show that shorter annealing times are not only sufficient but can actually aid in more efficient PCR amplification of GC-rich templates.

Interaction between chemical reaction and natural convection in porous media

Abstract Natural convection in porous media has received much attention in the last decades. Most of the work, however, has been devoted to the case of a global driving force resulting from thermal or concentration gradients applied to the boundaries of the system. As changes in the density lead to natural convection, chemical reactions can provide a distributed driving force for secondary flows. The conditions for the onset of natural convection are represented by the critical value of the thermal Rayleigh number. The critical value is found by performing a linear stability analysis of the basic reaction regime. Results are reported for the onset of both oscillatory and monotonic instabilities. The stability of the convective modes is studied by using a variational approach and deriving a set of spectral equations by means of a truncated mode interaction. The initial-value problem is analyzed by continuation routines and bifurcation diagrams are drawn. These diagrams constitute a valuable tool in the design of heterogeneous reacting systems. The numerical solution of the full governing equations serves to corroborate the predictions of the simplified model as well as to illustrate the effects of natural-convection phenomena on systems with chemical reaction.

A quantitative model of error accumulation during PCR amplification

The amplification of target DNA by the polymerase chain reaction (PCR) produces copies which may contain errors. Two sources of errors are associated with the PCR process: (1) editing errors that occur during DNA polymerase-catalyzed enzymatic copying and (2) errors due to DNA thermal damage. In this study a quantitative model of error frequencies is proposed and the role of reaction conditions is investigated. The errors which are ascribed to the polymerase depend on the efficiency of its editing function as well as the reaction conditions; specifically the temperature and the dNTP pool composition. Thermally induced errors stem mostly from three sources: A+G depurination, oxidative damage of guanine to 8-oxoG and cytosine deamination to uracil. The post-PCR modifications of sequences are primarily due to exposure of nucleic acids to elevated temperatures, especially if the DNA is in a single-stranded form. The proposed quantitative model predicts the accumulation of errors over the course of a PCR cycle. Thermal damage contributes significantly to the total errors; therefore consideration must be given to thermal management of the PCR process.

Bifurcation analysis of chemically driven convection

Abstract The problem of the progress of an exothermic chemical reaction under conditions apt for the onset of natural convection is considered. The governing partial differential equations are reduced to a set of ordinary differential equations by using a variational approach and a simplified model is obtained. Bifurcation diagrams of the simplified model are presented for various values of the Rayleigh number. Substantial changes in the topology of the solutions space are predicted by the non-linear stability analysis. Qualitatively agreement between predictions and numerical results confirms the validity of the simplified model to represent the behavior of the original equations. Numerical solutions of the full governing equations serve to illustrate the effects of natural convection phenomena in systems with chemical reaction.

Mechanotransduction of Ultrasound is Frequency Dependent Below the Cavitation Threshold

This study provides evidence that low-intensity ultrasound directly affects nuclear processes, and the magnitude of the effect varies with frequency. In particular, we show that the transcriptional induction of first load-inducible genes, which is independent of new protein synthesis, is frequency dependent. Bovine chondrocytes were exposed to low-intensity (below the cavitational threshold) ultrasound at 2, 5 and 8 MHz. Ultrasound elevated the expression of early response genes c-Fos, c-Jun and c-Myc, maximized at 5 MHz. The phosphorylated ERK inhibitor PD98059 abrogated any increase in c-series gene expression, suggesting that signaling occurs via the MAPPK/ERK pathway. However, phosphorylated ERK levels did not change with ultrasound frequency, indicating that processes downstream of ERK phosphorylation (such as nuclear transport and chromatin reorganization) respond to ultrasound with frequency dependence. A quantitative, biphasic mathematical model based on Biot theory predicted that cytoplasmic and nuclear stress is maximized at 5.2 ± 0.8 MHz for a chondrocyte, confirming experimental measurements.

Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.

Stability analysis of chemical reaction and free convection in porous media

Abstract Stability analysis of an isothermal first order and nonisothermal zero order reaction in the presence of free convection is performed. Critical values of the Rayleigh number for both cases are analytically calculated. The calculated values compare favorably with the numerical simulation of the full governing equations.

Effective Thermal Conductivity Estimates Of Particulate Mixtures

Several theories have been advanced to estimate effective thermal conductivities of particulate mixtures, but most theories have focused on the dilute case. A method is proposed to estimate the effective thermal conductivity coefficient of mixtures of arbitrary concentration. Earlier the authors developed a theory to determine the expected contact area between different species. This theory is employed to determine the Kapitza resistance of the heterogeneous mixture and forms part of an overall theory to estimate the effective thermal conductivity. Results are compared with other theoretical estimates and with experiments.

Comparative study of analytical methods for Hugoniot curves of porous materials

This study compares five methods to compute Hugoniots for porous materials, with experimental data for porous copper. The methods compare well when porosities are low. Three methods model shock velocity versus particle velocity data over a range of porosities with reasonable accuracy. P–v data are much more discriminatory and only two methods reproduce experimental data at high porosities with some degree of accuracy. Comparisons are made by plotting analytical results on curves fitted through experimental data points. Above certain porosities Hugoniot curves display anomalous behavior where (dP/dv)>0. A new method is presented which contains only two parameters {KT, and [(∂KT/∂P)]T} and which models both normal and anomalous Hugoniots curves.