A rapid genome-scale response of the transcriptional oscillator to perturbation reveals a period-doubling path to phenotypic change

State-transition modeling of blood transcriptome predicts disease evolution and treatment response in chronic myeloid leukemia

Chronic myeloid leukemia (CML) is initiated and maintained by BCR::ABL which is clinically targeted using tyrosine kinase inhibitors (TKIs). TKIs can induce long-term remission but are also not curative. Thus, CML is an ideal system to test our hypothesis that transcriptome-based state-transition models accurately predict cancer evolution and treatment response. We collected time-sequential blood samples from tetracycline-off (Tet-Off) BCR::ABL-inducible transgenic mice and wild-type controls. From the transcriptome, we constructed a CML state-space and a three-well leukemogenic potential landscape. The potential's stable critical points defined observable disease states. Early states were characterized by anti-CML genes opposing leukemia; late states were characterized by pro-CML genes. Genes with expression patterns shaped similarly to the potential landscape were identified as drivers of disease transition. Re-introduction of tetracycline to silence the BCR::ABL gene returned diseased mice transcriptomes to a near healthy state, without reaching it, suggesting parts of the transition are irreversible. TKI only reverted the transcriptome to an intermediate disease state, without approaching a state of health; disease relapse occurred soon after treatment. Using only the earliest time-point as initial conditions, our state-transition models accurately predicted both disease progression and treatment response, supporting this as a potentially valuable approach to time clinical intervention, before phenotypic changes become detectable.

Electromagnetic Fields, Genomic Instability and Cancer: A Systems Biological View

This review discusses the use of systems biology in understanding the biological effects of electromagnetic fields, with particular focus on induction of genomic instability and cancer. We introduce basic concepts of the dynamical systems theory such as the state space and attractors and the use of these concepts in understanding the behavior of complex biological systems. We then discuss genomic instability in the framework of the dynamical systems theory, and describe the hypothesis that environmentally induced genomic instability corresponds to abnormal attractor states; large enough environmental perturbations can force the biological system to leave normal evolutionarily optimized attractors (corresponding to normal cell phenotypes) and migrate to less stable variant attractors. We discuss experimental approaches that can be coupled with theoretical systems biology such as testable predictions, derived from the theory and experimental methods, that can be used for measuring the state of the complex biological system. We also review potentially informative studies and make recommendations for further studies.

Temporal metabolic partitioning of the yeast and protist cellular networks: the cell is a global scale-invariant (fractal or self-similar) multioscillator

Britton Chance, electronics expert when a teenager, became an enthusiastic student of biological oscillations, passing on this enthusiasm to many students and colleagues, including one of us (DL). This historical essay traces BC's influence through the accumulated work of DL to DL's many collaborators. The overall temporal organization of mass-energy, information, and signaling networks in yeast in self-synchronized continuous cultures represents, until now, the most characterized example of in vivo elucidation of time structure. Continuous online monitoring of dissolved gases by direct measurement (membrane-inlet mass spectrometry, together with NAD(P)H and flavin fluorescence) gives strain-specific dynamic information from timescales of minutes to hours as does two-photon imaging. The predominantly oscillatory behavior of network components becomes evident, with spontaneously synchronized cellular respiration cycles between discrete periods of increased oxygen consumption (oxidative phase) and decreased oxygen consumption (reductive phase). This temperature-compensated ultradian clock provides coordination, linking temporally partitioned functions by direct feedback loops between the energetic and redox state of the cell and its growing ultrastructure. Multioscillatory outputs in dissolved gases with 13 h, 40 min, and 4 min periods gave statistical self-similarity in power spectral and relative dispersional analyses: i.e., complex nonlinear (chaotic) behavior and a functional scale-free (fractal) network operating simultaneously over several timescales.

The molecular basis of metabolic cycles and their relationship to circadian rhythms

Metabolic cycles result from the partitioning of oxidative and reductive metabolism into rhythmic phases of gene expression and oscillating post-translational protein modifications. Relatively little is known about how these switches in gene expression are controlled, although recent studies have suggested that transcription itself may play a central role. This review explores the molecular basis of the metabolic and gene-expression oscillations in the yeast Saccharomyces cerevisiae, as well as how they relate to other biological time-keeping mechanisms, such as circadian rhythms.

Nonlinear response theory in chemical kinetics

A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.

The dynamics of cellular energetics during continuous yeast culture

A plethora of data is accumulating from high throughput methods on metabolites, coenzymes, proteins, and nucleic acids and their interactions as well as the signalling and regulatory functions and pathways of the cellular network. The frozen moment viewed in a single discrete time sample requires frequent repetition and updating before any appreciation of the dynamics of component interaction becomes possible. Even then in a sample derived from a cell population, time-averaging of processes and events that occur in out-of-phase individuals blur the detailed complexity of single cell organization. Continuously-grown cultures of yeast can become spontaneously self-synchronized, thereby enabling resolution of far more detailed temporal structure. Continuous on-line monitoring by rapidly responding sensors (O2 electrode and membrane-inlet mass spectrometry for O2, CO2 and H2S; direct fluorimetry for NAD(P)H and flavins) gives dynamic information from time-scales of minutes to hours. Supplemented with capillary electophoresis and gas chromatography mass spectrometry and transcriptomics the predominantly oscillatory behaviour of network components becomes evident, with a 40 min cycle between a phase of increased respiration (oxidative phase) and decreased respiration (reductive phase). Highly pervasive, this ultradian clock provides a coordinating function that links mitochondrial energetics and redox balance to transcriptional regulation, mitochondrial structure and organelle remodelling, DNA duplication and cell division events. Ultimately, this leads to a global partitioning of anabolism and catabolism and the enzymes involved, mediated by a relatively simple ATP feedback loop on chromatin architecture.

Period doubling induced by thermal noise amplification in genetic circuits

Rhythms of life are dictated by oscillations, which take place in a wide rage of biological scales. In bacteria, for example, oscillations have been proven to control many fundamental processes, ranging from gene expression to cell divisions. In genetic circuits, oscillations originate from elemental block such as autorepressors and toggle switches, which produce robust and noise-free cycles with well defined frequency. In some circumstances, the oscillation period of biological functions may double, thus generating bistable behaviors whose ultimate origin is at the basis of intense investigations. Motivated by brain studies, we here study an “elemental” genetic circuit, where a simple nonlinear process interacts with a noisy environment. In the proposed system, nonlinearity naturally arises from the mechanism of cooperative stability, which regulates the concentration of a protein produced during a transcription process. In this elemental model, bistability results from the coherent amplification of environmental fluctuations due to a stochastic resonance of nonlinear origin. This suggests that the period doubling observed in many biological functions might result from the intrinsic interplay between nonlinearity and thermal noise.

Time resolved DNA occupancy dynamics during the respiratory oscillation uncover a global reset point in the yeast growth program

The structural dynamics of chromatin have been implicated in the regulation of fundamental eukaryotic processes, such as DNA transcription, replication and repair. Although previous studies have revealed that the chromatin landscape, nucleosome remodeling and histone modification events are intimately tied into cellular energetics and redox state, few studies undertake defined time-resolved measurements of these state variables. Here, we use metabolically synchronous, continuously-grown yeast cultures to measure DNA occupancy and track global patterns with respect to the metabolic state of the culture. Combined with transcriptome analyses and ChIP-qPCR experiments, these paint an intriguing picture where genome-wide nucleosome focusing occurs during the recovery of energy charge, followed by clearance of the promoter regions and global transcriptional slow-down, thus indicating a nucleosome-mediated “reset point” for the cycle. The reset begins at the end of the catabolic and stress-response transcriptional programs and ends prior to the start of the anabolic and cell-growth transcriptional program, and the histones on genes from both the catabolic and anabolic superclusters are deacetylated.

Quantifying periodicity in omics data

Oscillations play a significant role in biological systems, with many examples in the fast, ultradian, circadian, circalunar, and yearly time domains. However, determining periodicity in such data can be problematic. There are a number of computational methods to identify the periodic components in large datasets, such as signal-to-noise based Fourier decomposition, Fisher's g-test and autocorrelation. However, the available methods assume a sinusoidal model and do not attempt to quantify the waveform shape and the presence of multiple periodicities, which provide vital clues in determining the underlying dynamics. Here, we developed a Fourier based measure that generates a de-noised waveform from multiple significant frequencies. This waveform is then correlated with the raw data from the respiratory oscillation found in yeast, to provide oscillation statistics including waveform metrics and multi-periods. The method is compared and contrasted to commonly used statistics. Moreover, we show the utility of the program in the analysis of noisy datasets and other high-throughput analyses, such as metabolomics and flow cytometry, respectively.

Coordinated metabolic transitions during Drosophila embryogenesis and the onset of aerobic glycolysis

Rapidly proliferating cells such as cancer cells and embryonic stem cells rely on a specialized metabolic program known as aerobic glycolysis, which supports biomass production from carbohydrates. The fruit fly Drosophila melanogaster also utilizes aerobic glycolysis to support the rapid growth that occurs during larval development. Here we use singular value decomposition analysis of modENCODE RNA-seq data combined with GC-MS-based metabolomic analysis to analyze the changes in gene expression and metabolism that occur during Drosophila embryogenesis, spanning the onset of aerobic glycolysis. Unexpectedly, we find that the most common pattern of co-expressed genes in embryos includes the global switch to glycolytic gene expression that occurs midway through embryogenesis. In contrast to the canonical aerobic glycolytic pathway, however, which is accompanied by reduced mitochondrial oxidative metabolism, the expression of genes involved in the tricarboxylic cycle (TCA cycle) and the electron transport chain are also upregulated at this time. Mitochondrial activity, however, appears to be attenuated, as embryos exhibit a block in the TCA cycle that results in elevated levels of citrate, isocitrate, and α-ketoglutarate. We also find that genes involved in lipid breakdown and β-oxidation are upregulated prior to the transcriptional initiation of glycolysis, but are downregulated before the onset of larval development, revealing coordinated use of lipids and carbohydrates during development. These observations demonstrate the efficient use of nutrient stores to support embryonic development, define sequential metabolic transitions during this stage, and demonstrate striking similarities between the metabolic state of late-stage fly embryos and tumor cells.

Free energy rhythms in Saccharomyces cerevisiae: a dynamic perspective with implications for ribosomal biogenesis

To describe the time course of cellular systems, we integrate ideas from thermodynamics and information theory to discuss the work needed to change the state of the cell. The biological example analyzed is experimental microarray transcription level oscillations of yeast in the different phases as characterized by oxygen consumption. Surprisal analysis was applied to identify groups of transcripts that oscillate in concert and thereby to compute changes in free energy with time. Three dominant transcript groups were identified by surprisal analysis. The groups correspond to the respiratory, early, and late reductive phases. Genes involved in ribosome biogenesis peaked at the respiratory phase. The work to prepare the state is shown to be the sum of the contributions of these groups. We paid particular attention to work requirements during ribosomal building, and the correlation with ATP levels and dissolved oxygen. The suggestion that cells in the respiratory phase likely build ribosomes, an energy intensive process, in preparation for protein production during the S phase of the cell cycle is validated by an experiment. Surprisal analysis thereby provided a useful tool for determining the synchronization of transcription events and energetics in a cell in real time.

The yin and yang of yeast transcription: elements of a global feedback system between metabolism and chromatin

When grown in continuous culture, budding yeast cells tend to synchronize their respiratory activity to form a stable oscillation that percolates throughout cellular physiology and involves the majority of the protein-coding transcriptome. Oscillations in batch culture and at single cell level support the idea that these dynamics constitute a general growth principle. The precise molecular mechanisms and biological functions of the oscillation remain elusive. Fourier analysis of transcriptome time series datasets from two different oscillation periods (0.7 h and 5 h) reveals seven distinct co-expression clusters common to both systems (34% of all yeast ORF), which consolidate into two superclusters when correlated with a compilation of 1,327 unrelated transcriptome datasets. These superclusters encode for cell growth and anabolism during the phase of high, and mitochondrial growth, catabolism and stress response during the phase of low oxygen uptake. The promoters of each cluster are characterized by different nucleotide contents, promoter nucleosome configurations, and dependence on ATP-dependent nucleosome remodeling complexes. We show that the ATP:ADP ratio oscillates, compatible with alternating metabolic activity of the two superclusters and differential feedback on their transcription via activating (RSC) and repressive (Isw2) types of promoter structure remodeling. We propose a novel feedback mechanism, where the energetic state of the cell, reflected in the ATP:ADP ratio, gates the transcription of large, but functionally coherent groups of genes via differential effects of ATP-dependent nucleosome remodeling machineries. Besides providing a mechanistic hypothesis for the delayed negative feedback that results in the oscillatory phenotype, this mechanism may underpin the continuous adaptation of growth to environmental conditions.

On a fundamental structure of gene networks in living cells

Computers are organized into hardware and software. Using a theoretical approach to identify patterns in gene expression in a variety of species, organs, and cell types, we found that biological systems similarly are comprised of a relatively unchanging hardware-like gene pattern. Orthogonal patterns of software-like transcripts vary greatly, even among tumors of the same type from different individuals. Two distinguishable classes could be identified within the hardware-like component: those transcripts that are highly expressed and stable and an adaptable subset with lower expression that respond to external stimuli. Importantly, we demonstrate that this structure is conserved across organisms. Deletions of transcripts from the highly stable core are predicted to result in cell mortality. The approach provides a conceptual thermodynamic-like framework for the analysis of gene-expression levels and networks and their variations in diseased cells.

Dynamics of oscillatory phenotypes in Saccharomyces cerevisiae reveal a network of genome-wide transcriptional oscillators

Genetic and environmental factors are well-studied influences on phenotype; however, time is a variable that is rarely considered when studying changes in cellular phenotype. Time-resolved microarray data revealed genome-wide transcriptional oscillation in a yeast continuous culture system with ∼ 2 and ∼ 4 h periods. We mapped the global patterns of transcriptional oscillations into a 3D map to represent different cellular phenotypes of redox cycles. This map shows the dynamic nature of gene expression in that transcripts are ordered and coupled to each other through time and concentration space. Although cells differed in oscillation periods, transcripts involved in certain processes were conserved in a deterministic way. When oscillation period lengthened, the peak to trough ratio of transcripts increased and the fraction of cells in the unbudded (G0/G1) phase of the cell division cycle increased. Decreasing the glucose level in the culture medium was one way to increase the redox cycle, possibly from changes in metabolic flux. The period may be responding to lower glucose levels by increasing the fraction of cells in G1 and reducing S-phase gating so that cells can spend more time in catabolic processes. Our results support that gene transcripts are coordinated with metabolic functions and the cell division cycle.

Time-structure of the yeast metabolism in vivo

All previous studies on the yeast metabolome have yielded a plethora of information on the components, function and organisation of low molecular mass and macromolecular components involved in the cellular metabolic network. Here we emphasise that an understanding of the global dynamics of the metabolome in vivo requires elucidation of the temporal dynamics of metabolic processes on many time-scales. We illustrate this using the 40 min oscillation in respiratory activity displayed in auto-synchronous continuously grown cultures of Saccharomyces cerevisiae, where respiration cycles between a phase of increased respiration (oxidative phase) and decreased respiration (reductive phase). Thereby an ultradian clock, i.e. a timekeeping device that runs through many cycles during one day, is involved in the co-ordination of the vast majority of events and processes in yeast. Through continuous online measurements, we first show that mitochondrial and redox physiology are intertwined to produce the temporal landscape on which cellular events occur. Next we look at the higher order processes of DNA duplication and mitochondrial structure to reveal that both events are choreographed during the respiratory cycles. Furthermore, spectral analysis using the discrete Fourier transformation of high-resolution (10 Hz) time-series of NAD(P)H confirms the existence of higher frequency components of biological origin and that these follow a scale-free architecture even in stable oscillating modes. A different signal-processing approach using discrete wavelet transformations (DWT) indicates that there is a significant contribution to the overall signal from ` ~5, ~ 10 and ~ 20-minutes cycles and the amplitudes of these cycles are phase-dependent. Further investigation (derivative of Gaussian continuous wavelet transformation) reveals that the observed 20-minutes cycles are actually confined to the reductive phase and consist of two ~15-minutes cycles. Moreover, the 5 and 10-minutes cycles are restricted to the oxidative phase of the cycle. The mitochondrial origin of these signals was confirmed by pulse-injection of the cytochrome c oxidase inhibitor H(2)S. We next discuss how these multi-oscillatory states can impinge on the apparently complex reactome (represented as a phase diagram of 1,650 chemical species that show oscillatory behaviour). We conclude that biological processes can be considerably more comprehensible when dynamic in vivo time-structure is taken into account.

Adaptation of organisms by resonance of RNA transcription with the cellular redox cycle

Sequence variation in organisms differs across the genome and the majority of mutations are caused by oxidation, yet its origin is not fully understood. It has also been shown that the reduction-oxidation reaction cycle is the fundamental biochemical cycle that coordinates the timing of all biochemical processes in the cell, including energy production, DNA replication, and RNA transcription. We show that the temporal resonance of transcriptome biosynthesis with the oscillating binary state of the reduction-oxidation reaction cycle serves as a basis for non-random sequence variation at specific genome-wide coordinates that change faster than by accumulation of chance mutations. This work demonstrates evidence for a universal, persistent and iterative feedback mechanism between the environment and heredity, whereby acquired variation between cell divisions can outweigh inherited variation.

Global effects of DNA replication and DNA replication origin activity on eukaryotic gene expression

This report provides a global view of how gene expression is affected by DNA replication. We analyzed synchronized cultures of Saccharomyces cerevisiae under conditions that prevent DNA replication initiation without delaying cell cycle progression. We use a higher-order singular value decomposition to integrate the global mRNA expression measured in the multiple time courses, detect and remove experimental artifacts and identify significant combinations of patterns of expression variation across the genes, time points and conditions. We find that, first, approximately 88% of the global mRNA expression is independent of DNA replication. Second, the requirement of DNA replication for efficient histone gene expression is independent of conditions that elicit DNA damage checkpoint responses. Third, origin licensing decreases the expression of genes with origins near their 3' ends, revealing that downstream origins can regulate the expression of upstream genes. This confirms previous predictions from mathematical modeling of a global causal coordination between DNA replication origin activity and mRNA expression, and shows that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown biological modes of regulation.

Calibration of microarray gene-expression data

Calibration of microarray measurements aims at removing systematic biases from the probe-level data to get expression estimates that linearly correlate with the transcript abundance in the studied samples. The improvement of calibration methods is an essential prerequisite for estimating absolute expression levels, which, in turn, are required for quantitative analyses of transcriptional regulation, for example, in the context of gene profiling of diseases. We address hybridization on microarrays as a reaction process in a complex environment and express the measured intensities as a function of the input quantities of the experiment. Popular calibration methods such as MAS5, dChip, RMA, gcRMA, vsn, and PLIER are briefly reviewed and assessed in light of the hybridization model and of previous benchmark studies. We present our hook method, a new calibration approach that is based on a graphical summary of the actual hybridization characteristics of a particular microarray. Although single-chip related, hook performs as well as the multi-chip-related gcRMA, presently one of the best state-of-the-art methods for estimating expression values. The hook method, in addition, provides a set of chip summary characteristics that evaluate the performance of a given hybridization. The algorithm of the method is briefly described and its performance is exemplified.

Chemostat-based micro-array analysis in baker's yeast

Chemostat cultivation of micro-organisms offers unique opportunities for experimental manipulation of individual environmental parameters at a fixed, controllable specific growth rate. Chemostat cultivation was originally developed as a tool to study quantitative aspects of microbial growth and metabolism. Renewed interest in this cultivation method is stimulated by the availability of high-information-density techniques for systemic analysis of microbial cultures, which require high reproducibility and careful experimental design. Genome-wide analysis of transcript levels with DNA micro-arrays is currently the most commonly applied of these high-information-density analysis tools for microbial gene expression. Based on published studies on the yeast Saccharomyces cerevisiae, a critical overview is presented of the possibilities and pitfalls associated with the combination of chemostat cultivation and transcriptome analysis with DNA micro-arrays. After a brief introduction to chemostat cultivation and micro-array analysis, key aspects of experimental design of chemostat-based micro-array experiments are discussed. The main focus of this review is on key biological concepts that can be accessed by chemostat-based micro-array analysis. These include effects of specific growth rate on transcriptional regulation, context-dependency of transcriptional responses, correlations between transcript profiles and contribution of the corresponding proteins to cellular function and fitness, and the analysis and application of evolutionary adaptation during prolonged chemostat cultivation. It is concluded that, notwithstanding the incompatibility of chemostat cultivation with high-throughput analysis, integration of chemostat cultivation with micro-array analysis and other high-information-density analytical approaches (e.g. proteomics and metabolomics techniques) offers unique advantages in terms of reproducibility and experimental design in comparison with standard batch cultivation systems. Therefore, chemostat cultivation and derived methods for controlled cultivation of micro-organisms are anticipated to become increasingly important in microbial physiology and systems biology.

Activating and inhibiting connections in biological network dynamics

Background

Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior – for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results

Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion

The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers

Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

The scale-free dynamics of eukaryotic cells

Temporal organization of biological processes requires massively parallel processing on a synchronized time-base. We analyzed time-series data obtained from the bioenergetic oscillatory outputs of Saccharomyces cerevisiae and isolated cardiomyocytes utilizing Relative Dispersional (RDA) and Power Spectral (PSA) analyses. These analyses revealed broad frequency distributions and evidence for long-term memory in the observed dynamics. Moreover RDA and PSA showed that the bioenergetic dynamics in both systems show fractal scaling over at least 3 orders of magnitude, and that this scaling obeys an inverse power law. Therefore we conclude that in S. cerevisiae and cardiomyocytes the dynamics are scale-free in vivo. Applying RDA and PSA to data generated from an in silico model of mitochondrial function indicated that in yeast and cardiomyocytes the underlying mechanisms regulating the scale-free behavior are similar. We validated this finding in vivo using single cells, and attenuating the activity of the mitochondrial inner membrane anion channel with 4-chlorodiazepam to show that the oscillation of NAD(P)H and reactive oxygen species (ROS) can be abated in these two evolutionarily distant species. Taken together these data strongly support our hypothesis that the generation of ROS, coupled to redox cycling, driven by cytoplasmic and mitochondrial processes, are at the core of the observed rhythmicity and scale-free dynamics. We argue that the operation of scale-free bioenergetic dynamics plays a fundamental role to integrate cellular function, while providing a framework for robust, yet flexible, responses to the environment.

"Hook"-calibration of GeneChip-microarrays: chip characteristics and expression measures

Background

Microarray experiments rely on several critical steps that may introduce biases and uncertainty in downstream analyses. These steps include mRNA sample extraction, amplification and labelling, hybridization, and scanning causing chip-specific systematic variations on the raw intensity level. Also the chosen array-type and the up-to-dateness of the genomic information probed on the chip affect the quality of the expression measures. In the accompanying publication we presented theory and algorithm of the so-called hook method which aims at correcting expression data for systematic biases using a series of new chip characteristics.

Results

In this publication we summarize the essential chip characteristics provided by this method, analyze special benchmark experiments to estimate transcript related expression measures and illustrate the potency of the method to detect and to quantify the quality of a particular hybridization. It is shown that our single-chip approach provides expression measures responding linearly on changes of the transcript concentration over three orders of magnitude. In addition, the method calculates a detection call judging the relation between the signal and the detection limit of the particular measurement. The performance of the method in the context of different chip generations and probe set assignments is illustrated. The hook method characterizes the RNA-quality in terms of the 3'/5'-amplification bias and the sample-specific calling rate. We show that the proper judgement of these effects requires the disentanglement of non-specific and specific hybridization which, otherwise, can lead to misinterpretations of expression changes. The consequences of modifying probe/target interactions by either changing the labelling protocol or by substituting RNA by DNA targets are demonstrated.

Conclusion

The single-chip based hook-method provides accurate expression estimates and chip-summary characteristics using the natural metrics given by the hybridization reaction with the potency to develop new standards for microarray quality control and calibration.

Evolution of the clock from yeast to man by period-doubling folds in the cellular oscillator

Analysis of genome-wide oscillations in transcription reveals that the cell is an oscillator and an attractor and that the maintenance of a stable phenotype requires that maximums in expression in clusters of transcripts must be poised at antipodal phases around the steady state-this is the dynamic architecture of phenotype. Plots of the path through concentration phase space taken by all of the transcripts of Saccharomyces cerevisiae yield a simple three-dimensional surface. How this surface might change as period lengthens or as a cell differentiates is at the center of current work. We have shown that changes in gene expression in response to mutation or perturbation by drugs occur through a folding or unfolding of the surface described by this circle of transcripts and we suggest that the path from this 40-minute oscillation to the cell cycle and circadian rhythms takes place through a series of period-two or period-three bifurcations. These foldings in the surface of the putative attractor result in an increasingly dense set of nested trajectories in the concentrations of message and protein. Evolutionary advantage might accrue to an organism that could change period by changes in just one or a few genes as day length increased from 4 hours in the prebiotic Earth, through 8 hours during the expansion of photoautotrophs, to the present 24 hours.

Genome-scale cluster analysis of replicated microarrays using shrinkage correlation coefficient

Background

Currently, clustering with some form of correlation coefficient as the gene similarity metric has become a popular method for profiling genomic data. The Pearson correlation coefficient and the standard deviation (SD)-weighted correlation coefficient are the two most widely-used correlations as the similarity metrics in clustering microarray data. However, these two correlations are not optimal for analyzing replicated microarray data generated by most laboratories. An effective correlation coefficient is needed to provide statistically sufficient analysis of replicated microarray data.

Results

In this study, we describe a novel correlation coefficient, shrinkage correlation coefficient (SCC), that fully exploits the similarity between the replicated microarray experimental samples. The methodology considers both the number of replicates and the variance within each experimental group in clustering expression data, and provides a robust statistical estimation of the error of replicated microarray data. The value of SCC is revealed by its comparison with two other correlation coefficients that are currently the most widely-used (Pearson correlation coefficient and SD-weighted correlation coefficient) using statistical measures on both synthetic expression data as well as real gene expression data from Saccharomyces cerevisiae. Two leading clustering methods, hierarchical and k-means clustering were applied for the comparison. The comparison indicated that using SCC achieves better clustering performance. Applying SCC-based hierarchical clustering to the replicated microarray data obtained from germinating spores of the fern Ceratopteris richardii, we discovered two clusters of genes with shared expression patterns during spore germination. Functional analysis suggested that some of the genetic mechanisms that control germination in such diverse plant lineages as mosses and angiosperms are also conserved among ferns.

Conclusion

This study shows that SCC is an alternative to the Pearson correlation coefficient and the SD-weighted correlation coefficient, and is particularly useful for clustering replicated microarray data. This computational approach should be generally useful for proteomic data or other high-throughput analysis methodology.

Collective behavior in gene regulation: the cell is an oscillator, the cell cycle a developmental process

The finding of a genome-wide oscillation in transcription that gates cells into S phase and coordinates mitochondrial and metabolic functions has altered our understanding of how the cell cycle is timed and how stable cellular phenotypes are maintained. Here we present the evidence and arguments in support of the idea that everything oscillates, and the rationale for viewing the cell as an attractor from which deterministic noise can be tuned by appropriate coupling among the many feedback loops, or regulons, that make up the transcriptional-respiratory attractor cycle. The existence of this attractor also explains many of the dynamic macroscopic properties of the cell cycle and appears to be the timekeeping oscillator in both cell cycles and circadian rhythms. The path taken by this primordial oscillator in the course of differentiation or drug response may involve period-doubling behavior. Evidence for a relatively high-frequency timekeeping oscillator in yeast and mammalian cells comes from expression array analysis, and GC/MS in the case of yeast, and primarily from macroscopic measures of phase response to perturbation in the case of mammalian cells. Low-amplitude, genome-wide oscillations, a ubiquitous but often unrecognized attribute of phenotype, may be a source of seemingly intractable biological noise in microarray and proteomic studies. These oscillations in transcript and protein levels and the repeated cycles of synthesis and degradation they require, represent a high energy cost to the cell which must, from an evolutionary point of view, be recovered as essential information. We suggest that the information contained in this genome-wide oscillation is the dynamic code that organizes a stable phenotype from an otherwise passive genome.

Glutathione and Gts1p drive beneficial variability in the cadmium resistances of individual yeast cells

Phenotypic heterogeneity among individual cells within isogenic populations is widely documented, but its consequences are not well understood. Here, cell-to-cell variation in the stress resistance of Saccharomyces cerevisiae, particularly to cadmium, was revealed to depend on the antioxidant glutathione. Heterogeneity was decreased strikingly in gsh1 mutants. Furthermore, cells sorted according to differing reduced-glutathione (GSH) contents exhibited differing stress resistances. The vacuolar GSH-conjugate pathway of detoxification was implicated in heterogeneous Cd resistance. Metabolic oscillations (ultradian rhythms) in yeast are known to modulate single-cell redox and GSH status. Gts1p stabilizes these oscillations and was found to be required for heterogeneous Cd and hydrogen-peroxide resistance, through the same pathway as Gsh1p. Expression of GTS1 from a constitutive tet-regulated promoter suppressed oscillations and heterogeneity in GSH content, and resulted in decreased variation in stress resistance. This enabled manipulation of the degree of gene expression noise in cultures. It was shown that cells expressing Gts1p heterogeneously had a competitive advantage over more-homogeneous cell populations (with the same mean Gts1p expression), under continuous and fluctuating stress conditions. The results establish a novel molecular mechanism for single-cell heterogeneity, and demonstrate experimentally fitness advantages that depend on deterministic variation in gene expression within cell populations.

Redox rhythmicity: clocks at the core of temporal coherence

Ultradian rhythms are those that cycle many times in a day and are therefore measured in hours, minutes, seconds or even fractions of a second. In yeasts and protists, a temperature-compensated clock with a period of about an hour (30-90 minutes) provides the time base upon which all central processes are synchronized. A 40-minute clock in yeast times metabolic, respiratory and transcriptional processes, and controls cell division cycle progression. This system has at its core a redox cycle involving NAD(P)H and dithiol-disulfide interconversions. It provides an archetype for biological time keeping on longer time scales (e.g. the daily cycles driven by circadian clocks) and underpins these rhythms, which cannot be understood in isolation. Ultradian rhythms are the foundation upon which the coherent functioning of the organism depends.

Genomic signal processing: from matrix algebra to genetic networks

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.