Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.     

An RNA Phage Lab: MS2 in Walter Fiers’ Laboratory of Molecular Biology in Ghent, from Genetic Code to Gene and Genome, 1963–1976

The importance of viruses as model organisms is well-established in molecular biology and Max Delbrück’s phage group set standards in the DNA phage field. In this paper, I argue that RNA phages, discovered in the 1960s, were also instrumental in the making of molecular biology. As part of experimental systems, RNA phages stood for messenger RNA (mRNA), genes and genome. RNA was thought to mediate information transfers between DNA and proteins. Furthermore, RNA was more manageable at the bench than DNA due to the availability of specific RNases, enzymes used as chemical tools to analyse RNA. Finally, RNA phages provided scientists with a pure source of mRNA to investigate the genetic code, genes and even a genome sequence. This paper focuses on Walter Fiers’ laboratory at Ghent University (Belgium) and their work on the RNA phage MS2. When setting up his Laboratory of Molecular Biology, Fiers planned a comprehensive study of the virus with a strong emphasis on the issue of structure. In his lab, RNA sequencing, now a little-known technique, evolved gradually from a means to solve the genetic code, to a tool for completing the first genome sequence. Thus, I follow the research pathway of Fiers and his ‘RNA phage lab’ with their evolving experimental system from 1960 to the late 1970s. This study illuminates two decisive shifts in post-war biology: the emergence of molecular biology as a discipline in the 1960s in Europe and of genomics in the 1990s.     

Human genomics and microarrays: implications for the plastic surgeon

The Human Genome Project was launched in 1989 in an effort to sequence the entire span of human DNA. Although coding sequences are important in identifying mutations, the static order of DNA does not explain how a cell or organism may respond to normal and abnormal biological processes. By examining the mRNA content of a cell, researchers can determine which genes are being activated in response to a stimulus.Traditional methods in molecular biology generally work on a "one gene: one experiment" basis, which means that the throughput is very limited and the "whole picture" of gene function is hard to obtain. To study each of the 60,000 to 80,000 genes in the human genome under each biological circumstance is not practical. Recently, microarrays (also known as gene or DNA chips) have emerged; these allow for the simultaneous determination of expression for thousands of genes and analysis of genome-wide mRNA expression.The purpose of this article is twofold: first, to provide the clinical plastic surgeon with a working knowledge and understanding of the fields of genomics, microarrays, and bioinformatics and second, to present a case to illustrate how these technologies can be applied in the study of wound healing.     

人工转录因子研究进展

转录因子是真核表达调控中非常重要的一类反式作用因子,通常由DNA结合结构域与效应结构域两部分组成,研究发现这两个结构域可以各自独立发生作用。基于转录因子的这种结构特点,可以人为地选择针对特定序列的DNA结合结构域与具有特定作用的效应结构域构建人工转录因子。目前人工转录因子的DNA结合结构域多为C₂H₂ 型锌指结构,每一个锌指单元由大约30个氨基酸组成,识别DNA双螺旋大沟中相连的3bp序列,并可通过氢键作用与相应的碱基结合;多个锌指可以串联成簇,从而识别并结合较长的DNA序列区域。常见的人工转录因子的效应结构域有激活结构域以及抑制结构域,不同的效应结构域赋予人工转录因子不同的功能。目前人工转录因子已经在基础研究、药物设计以及基因治疗等领域得到了广泛的应用。     

Nonlinear systems in medicine

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.     

High-level expression and molecular cloning of genes encoding Candida tropicalis peroxisomal proteins.

The development of peroxisomes in the cells of Candida tropicalis grown on oleic acid was accompanied by a markedly high expression of peroxisomal proteins. On the basis of this finding, the nuclear DNA library of this yeast was screened by differential hybridization, and 102 clones of oleic acid-inducible sequences were isolated. Seven coding regions were found to form clusters in three stretches of the genomic DNA. Five of the regions were identified as genes for peroxisomal polypeptides (PXPs). The coding sequence for PXP-2 hybrid selected an additional mRNA for PXP-4, the subunit of long-chain acyl coenzyme A oxidase, which was the most abundant PXP. PXP-2 and PXP-4 were close in apparent molecular weight and generated similar peptides when digested with a protease. The gene for PXP-4 was adjacent to that for PXP-2 on the genome and also hybridized to the mRNA coding for PXP-5. These and other similar results suggest that the genes for the peroxisomal proteins of this organism arose by duplication of a few ancestral genes.     

From the genome sequence to the proteome and back: evaluation of E. coli genome annotation with a 2-D gel-based proteomics approach

The ambition of systems biology to understand complex biological systems at the molecular level implies that we need to have a concrete and correct understanding of each molecular entity and its function. However, even for the best-studied organism, Escherichia coli, a large number of proteins have never been identified and characterised from wild-type cells, and/or await unravelling of their biological role. Instead, the ORF models for these proteins have been predicted by suitable algorithms and/or through comparison with known, homologous proteins from other organisms, approaches which may be prone to error. In the present study, we used a combination of 2-DE, MALDI-TOF-MS and PMF to identify 1151 different proteins in E. coli K12 JM109. Comparison of the experimental with the theoretical Mr and pI values (4000 experimental values each) allowed the identification of numerous proteins with incorrect or incomplete ORF annotations in the current E. coli genome databases. Several inconsistencies in genome annotation were verified experimentally, and up to 55 candidates await further investigation. Our findings demonstrate how an up-to-date 2-D gel-based proteomics approach can be used for improving the annotation of prokaryotic genomes. They also highlight the need for harmonization among the different E. coli genome databases.     

A high-quality catalog of the Drosophila melanogaster proteome

Understanding how proteins and their complex interaction networks convert the genomic information into a dynamic living organism is a fundamental challenge in biological sciences. As an important step towards understanding the systems biology of a complex eukaryote, we cataloged 63% of the predicted Drosophila melanogaster proteome by detecting 9,124 proteins from 498,000 redundant and 72,281 distinct peptide identifications. This unprecedented high proteome coverage for a complex eukaryote was achieved by combining sample diversity, multidimensional biochemical fractionation and analysis-driven experimentation feedback loops, whereby data collection is guided by statistical analysis of prior data. We show that high-quality proteomics data provide crucial information to amend genome annotation and to confirm many predicted gene models. We also present experimentally identified proteotypic peptides matching approximately 50% of D. melanogaster gene models. This library of proteotypic peptides should enable fast, targeted and quantitative proteomic studies to elucidate the systems biology of this model organism.