RESUMEN
Four inter-related measures of phase are described to study the phase synchronization of cellular oscillators, and computation of these measures is described and illustrated on single cell fluorescence data from the model filamentous fungus, Neurospora crassa. One of these four measures is the phase shift Ï in a sinusoid of the form x(t) = A(cos(ωt + Ï), where t is time. The other measures arise by creating a replica of the periodic process x(t) called the Hilbert transform xÌ(t), which is 90 degrees out of phase with the original process x(t). The second phase measure is the phase angle FH(t) between the replica xÌ(t) and x(t), taking values between -π and π. At extreme values the Hilbert Phase is discontinuous, and a continuous form FC(t) of the Hilbert Phase is used, measuring time on the nonnegative real axis (t). The continuous Hilbert Phase FC(t) is used to define the phase MC(t1,t0) for an experiment beginning at time t0 and ending at time t1. In that phase differences at time t0 are often of ancillary interest, the Hilbert Phase FC(t0) is subtracted from FC(t1). This difference is divided by 2π to obtain the phase MC(t1,t0) in cycles. Both the Hilbert Phase FC(t) and the phase MC(t1,t0) are functions of time and useful in studying when oscillators phase-synchronize in time in signal processing and circadian rhythms in particular. The phase of cellular clocks is fundamentally different from circadian clocks at the macroscopic scale because there is an hourly cycle superimposed on the circadian cycle.
Asunto(s)
Relojes Biológicos/fisiología , Relojes Circadianos/fisiología , Ritmo Circadiano/fisiología , Neurospora crassa/fisiología , Análisis de la Célula Individual/métodos , Algoritmos , Relojes Biológicos/genética , Proteínas Fúngicas/genética , Regulación Fúngica de la Expresión Génica , Mediciones Luminiscentes/métodos , Modelos Biológicos , Neurospora crassa/citología , Neurospora crassa/metabolismo , Procesos Estocásticos , Factores de TiempoRESUMEN
Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment. To this end the Maximally Informative Next Experiment (MINE) criterion for experimental design was developed. Here we explore this idea in a simplified context, the linear model. Four variations of the MINE method for the linear model were created: MINE-like, MINE, MINE with random orthonormal basis, and MINE with random rotation. Each method varies in how it maximizes the MINE criterion. Theorem 1 establishes sufficient conditions for the maximization of the MINE criterion under the linear model. Theorem 2 establishes when the MINE criterion is equivalent to the classic design criterion of D-optimality. By simulation under the linear model, we establish that the MINE with random orthonormal basis and MINE with random rotation are faster to discover the true linear relation with p regression coefficients and n observations when p>>n. We also establish in simulations with n<100, p=1000, σ=0.01 and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.
Asunto(s)
Genómica/métodos , Modelos GenéticosRESUMEN
An ensemble of genetic networks that describe how the model fungal system, Neurospora crassa, utilizes quinic acid (QA) as a sole carbon source has been identified previously. A genetic network for QA metabolism involves the genes, qa-1F and qa-1S, that encode a transcriptional activator and repressor, respectively and structural genes, qa-2, qa-3, qa-4, qa-x, and qa-y. By a series of 4 separate and independent, model-guided, microarray experiments a total of 50 genes are identified as QA-responsive and hypothesized to be under QA-1F control and/or the control of a second QA-responsive transcription factor (NCU03643) both in the fungal binuclear Zn(II)2Cys6 cluster family. QA-1F regulation is not sufficient to explain the quantitative variation in expression profiles of the 50 QA-responsive genes. QA-responsive genes include genes with products in 8 mutually connected metabolic pathways with 7 of them one step removed from the tricarboxylic (TCA) Cycle and with 7 of them one step removed from glycolysis: (1) starch and sucrose metabolism; (2) glycolysis/glucanogenesis; (3) TCA Cycle; (4) butanoate metabolism; (5) pyruvate metabolism; (6) aromatic amino acid and QA metabolism; (7) valine, leucine, and isoleucine degradation; and (8) transport of sugars and amino acids. Gene products both in aromatic amino acid and QA metabolism and transport show an immediate response to shift to QA, while genes with products in the remaining 7 metabolic modules generally show a delayed response to shift to QA. The additional QA-responsive cutinase transcription factor-1ß (NCU03643) is found to have a delayed response to shift to QA. The series of microarray experiments are used to expand the previously identified genetic network describing the qa gene cluster to include all 50 QA-responsive genes including the second transcription factor (NCU03643). These studies illustrate new methodologies from systems biology to guide model-driven discoveries about a core metabolic network involving carbon and amino acid metabolism in N. crassa.
Asunto(s)
Genes Fúngicos/genética , Familia de Multigenes/genética , Neurospora crassa/genética , Ácido Quínico/metabolismo , Biología de Sistemas , Sitios de Unión , Biología Computacional , Perfilación de la Expresión Génica , Regulación Fúngica de la Expresión Génica/efectos de los fármacos , Redes Reguladoras de Genes/genética , Cinética , Análisis de los Mínimos Cuadrados , Modelos Genéticos , Neurospora crassa/efectos de los fármacos , Análisis de Secuencia por Matrices de Oligonucleótidos , Ácido Quínico/farmacología , ARN Mensajero/genética , ARN Mensajero/metabolismoRESUMEN
A model-driven discovery process, Computing Life, is used to identify an ensemble of genetic networks that describe the biological clock. A clock mechanism involving the genes white-collar-1 and white-collar-2 (wc-1 and wc-2) that encode a transcriptional activator (as well as a blue-light receptor) and an oscillator frequency (frq) that encodes a cyclin that deactivates the activator is used to guide this discovery process through three cycles of microarray experiments. Central to this discovery process is a new methodology for the rational design of a Maximally Informative Next Experiment (MINE), based on the genetic network ensemble. In each experimentation cycle, the MINE approach is used to select the most informative new experiment in order to mine for clock-controlled genes, the outputs of the clock. As much as 25% of the N. crassa transcriptome appears to be under clock-control. Clock outputs include genes with products in DNA metabolism, ribosome biogenesis in RNA metabolism, cell cycle, protein metabolism, transport, carbon metabolism, isoprenoid (including carotenoid) biosynthesis, development, and varied signaling processes. Genes under the transcription factor complex WCC ( = WC-1/WC-2) control were resolved into four classes, circadian only (612 genes), light-responsive only (396), both circadian and light-responsive (328), and neither circadian nor light-responsive (987). In each of three cycles of microarray experiments data support that wc-1 and wc-2 are auto-regulated by WCC. Among 11,000 N. crassa genes a total of 295 genes, including a large fraction of phosphatases/kinases, appear to be under the immediate control of the FRQ oscillator as validated by 4 independent microarray experiments. Ribosomal RNA processing and assembly rather than its transcription appears to be under clock control, suggesting a new mechanism for the post-transcriptional control of clock-controlled genes.