Cooperative RNA Polymerase Molecules Behavior on a Stochastic Sequence-Dependent Model for Transcription Elongation

The transcription process is crucial to life and the enzyme RNA polymerase (RNAP) is the major component of the transcription machinery. The development of single-molecule techniques, such as magnetic and optical tweezers, atomic-force microscopy and single-molecule fluorescence, increased our understanding of the transcription process and complements traditional biochemical studies. Based on these studies, theoretical models have been proposed to explain and predict the kinetics of the RNAP during the polymerization, highlighting the results achieved by models based on the thermodynamic stability of the transcription elongation complex. However, experiments showed that if more than one RNAP initiates from the same promoter, the transcription behavior slightly changes and new phenomenona are observed. We proposed and implemented a theoretical model that considers collisions between RNAPs and predicts their cooperative behavior during multi-round transcription generalizing the Bai et al. stochastic sequence-dependent model. In our approach, collisions between elongating enzymes modify their transcription rate values. We performed the simulations in Mathematica® and compared the results of the single and the multiple-molecule transcription with experimental results and other theoretical models. Our multi-round approach can recover several expected behaviors, showing that the transcription process for the studied sequences can be accelerated up to 48% when collisions are allowed: the dwell times on pause sites are reduced as well as the distance that the RNAPs backtracked from backtracking sites. © 2013 Costa et al.

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

Cooperative effects of H+ and H- hydrido carbonyl ruthenium derivatives; role of homogeneous and heterogeneous protonic and lewis acids in catalytic hydrocarbonylation reactions

The role played by H+ hydrido iodocarbonyl and H- hydrido carbonyl ruthenium catalysts in the different catalytic steps of hydroformylation and hydroesterification of olefins, and in the homologation of alcohols has been investigated. The H- hydrido carbonyl species are mainly involved in the activation of olefins and in the hydrogenation of the acyl intermediates to aldehydes and alcohols, whereas the H+ hydrido iodocarbonyl derivatives are involved in the activation of alcohols and other oxygenated substrates, and in their carbonylation to esters. The cooperation between the two species, possible under particular reaction conditions, results in an improvement of the selectivity towards homologation (carbonylation plus hydrogenation) products. Heterogeneous Lewis acid promoters, easily recyclable from the reaction mixture, have also been successfully used in the hydrocarbonylation of alcohols, resulting in an increase of the carbonylation and homologation products. A reaction pathway in agreement with the experimental results is discussed. © 1989.