Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well ...understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
Design patterns of biological cells Andrews, Steven S.; Wiley, H. Steven; Sauro, Herbert M.
BioEssays,
March 2024, Letnik:
46, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of ion for their designs. ...Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.
The chemical reaction networks that animate cell biology can be ed into a set of design patterns, each of which is a generalized solution to a frequently recurring problem. We present a catalog of 21 such patterns that describe cellular biosynthesis, reaction network structure, and reaction network function.
Motivation: Modern transcriptomics and proteomics enable us to survey the expression of RNAs and proteins at large scales. While these data are usually generated and analyzed separately, there is an ...increasing interest in comparing and co-analyzing transcriptome and proteome expression data. A major open question is whether transcriptome and proteome expression is linked and how it is coordinated. Results: Here we have developed a probabilistic clustering model that permits analysis of the links between transcriptomic and proteomic profiles in a sensible and flexible manner. Our coupled mixture model defines a prior probability distribution over the component to which a protein profile should be assigned conditioned on which component the associated mRNA profile belongs to. We apply this approach to a large dataset of quantitative transcriptomic and proteomic expression data obtained from a human breast epithelial cell line (HMEC). The results reveal a complex relationship between transcriptome and proteome with most mRNA clusters linked to at least two protein clusters, and vice versa. A more detailed analysis incorporating information on gene function from the Gene Ontology database shows that a high correlation of mRNA and protein expression is limited to the components of some molecular machines, such as the ribosome, cell adhesion complexes and the TCP-1 chaperonin involved in protein folding. Availability: Matlab code is available from the authors on request. Contact: srogers@dcs.gla.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.
We used deep sequencing technology to identify transcriptional adaptation of the euryhaline unicellular cyanobacterium Synechococcus sp. PCC 7002 and the marine facultative aerobe Shewanella ...putrefaciens W3-18-1 to growth in a co-culture and infer the effect of carbon flux distributions on photoautotroph-heterotroph interactions. The overall transcriptome response of both organisms to co-cultivation was shaped by their respective physiologies and growth constraints. Carbon limitation resulted in the expansion of metabolic capacities, which was manifested through the transcriptional upregulation of transport and catabolic pathways. Although growth coupling occurred via lactate oxidation or secretion of photosynthetically fixed carbon, there was evidence of specific metabolic interactions between the two organisms. These hypothesized interactions were inferred from the excretion of specific amino acids (for example, alanine and methionine) by the cyanobacterium, which correlated with the downregulation of the corresponding biosynthetic machinery in Shewanella W3-18-1. In addition, the broad and consistent decrease of mRNA levels for many Fe-regulated Synechococcus 7002 genes during co-cultivation may indicate increased Fe availability as well as more facile and energy-efficient mechanisms for Fe acquisition by the cyanobacterium. Furthermore, evidence pointed at potentially novel interactions between oxygenic photoautotrophs and heterotrophs related to the oxidative stress response as transcriptional patterns suggested that Synechococcus 7002 rather than Shewanella W3-18-1 provided scavenging functions for reactive oxygen species under co-culture conditions. This study provides an initial insight into the complexity of photoautotrophic-heterotrophic interactions and brings new perspectives of their role in the robustness and stability of the association.
Although members of the ErbB receptor family are found predominantly at the cell surface, these receptors undergo constant cycling between the plasma membrane and the endosomal compartment. In the ...absence of an activating ligand, these receptors are slowly internalized (
t
1/2 ∼ 30 min) but are quickly recycled. The constitutive degradation rate of the epidermal growth factor (EGF) receptor (EGFR) is slower than other ErbB family members and only the EGFR appears to alter its trafficking pattern in response to ligand binding. This altered pattern is characterized by accelerated internalization and enhanced lysosomal targeting. Ligand-regulated trafficking of the EGFR is mediated by a series of motifs distributed through the cytoplasmic domain of the receptor that are exposed by a combination of activation-mediated conformation changes and the binding of proteins such as Grb2. As a consequence of induced internalization, most EGFR signaling occurs within endosomes whereas signaling by the other members of the ErbB family appear to be generated predominantly from the cell surface. Overexpression of ErbB family members can disrupt normal receptor trafficking by driving heterodimerization of receptors with disparate trafficking patterns. Because different ErbB receptor substrates are localized in different cellular compartments, disrupted trafficking could be an important factor in the altered signaling patterns observed as a consequence of receptor overexpression.
Motivation: Measurement precision determines the power of any analysis to reliably identify significant signals, such as in screens for differential expression, independent of whether the ...experimental design incorporates replicates or not. With the compilation of large-scale RNA-Seq datasets with technical replicate samples, however, we can now, for the first time, perform a systematic analysis of the precision of expression level estimates from massively parallel sequencing technology. This then allows considerations for its improvement by computational or experimental means.
Results: We report on a comprehensive study of target identification and measurement precision, including their dependence on transcript expression levels, read depth and other parameters. In particular, an impressive recall of 84% of the estimated true transcript population could be achieved with 331 million 50 bp reads, with diminishing returns from longer read lengths and even less gains from increased sequencing depths. Most of the measurement power (75%) is spent on only 7% of the known transcriptome, however, making less strongly expressed transcripts harder to measure. Consequently, <30% of all transcripts could be quantified reliably with a relative error <20%. Based on established tools, we then introduce a new approach for mapping and analysing sequencing reads that yields substantially improved performance in gene expression profiling, increasing the number of transcripts that can reliably be quantified to over 40%. Extrapolations to higher sequencing depths highlight the need for efficient complementary steps. In discussion we outline possible experimental and computational strategies for further improvements in quantification precision.
Contact:
rnaseq10@boku.ac.at
Supplementary information:
Supplementary data are available at Bioinformatics online.
Although the ERK pathway has a central role in the response of cells to growth factors, its regulatory structure and dynamics are incompletely understood. To investigate ERK activation in real time, ...we expressed an ERK–GFP fusion protein in human mammary epithelial cells. On EGF stimulation, we observed sustained oscillations of the ERK–GFP fusion protein between the nucleus and cytoplasm with a periodicity of ∼15 min. The oscillations were persistent (>45 cycles), independent of cell cycle phase, and were highly dependent on cell density, essentially disappearing at confluency. Oscillations occurred even at ligand doses that elicited very low levels of ERK phosphorylation, and could be detected biochemically in both transfected and nontransfected cells. Mathematical modeling revealed that negative feedback from phosphorylated ERK to the cascade input was necessary to match the robustness of the oscillation characteristics observed over a broad range of ligand concentrations. Our characterization of single‐cell ERK dynamics provides a quantitative foundation for understanding the regulatory structure of this signaling cascade.
Synopsis
Our increasingly detailed knowledge of cell signaling dynamics is enabling us to construct well‐constrained mathematical models that can illuminate regulatory mechanisms and lead to the in silico prediction of cellular responses (Wiley et al, 2003; Di Ventura et al, 2006). The wealth of quantitative data on the ERK activation pathway, its central role in eukaryotic cell decision processes and the complexity of its regulatory network structure have led to several mathematical models for this pathway (for review, see Orton et al (2005)). Some of these models have predicted the existence of oscillations in the pathway. However, despite numerous biochemical and imaging‐based investigations into its dynamics, oscillatory behavior of the ERK pathway has never been experimentally observed. Potential oscillatory behavior of the ERK pathway is intriguing because it was recently demonstrated that the NF‐kB and p53–MDM2 signaling pathways can display oscillations under certain conditions (Lahav et al, 2004; Nelson et al, 2004).
As the localization of ERK has been reported to reflect its state of activation (Lenormand et al, 1993), we used a fusion protein of ERK and green fluorescent protein (ERK–GFP) to follow its activation in individual cells. To simplify the analysis of ERK translocation, we used monomeric red fluorescent protein fused to a nuclear‐localization signal (mRFPnuc) to selectively visualize the nucleus and to allow us to track cells during long‐term live‐cell experiments.
When we stimulated cells with epidermal growth factor (EGF), we observed a rapid translocation of the ERK–GFP fusion protein into the nucleus. Significantly, in many cells the ERK–GFP fusion protein oscillated between the nucleus and the cytoplasm with a periodicity of ∼15 min (Figure 2C). The oscillations were asynchronous between neighboring cells and the mRFPnuc marker did not display any periodic oscillation. Interestingly, the frequency of the oscillations was essentially invariant over a wide range of conditions and EGF concentration. Oscillations required the continuous presence of EGF (Figure 2A) and were very sensitive to cell density, essentially disappearing at confluency.
To ensure that the oscillations were not an artifact of high expression levels of ERK–GFP fusion protein in our cells, we used flow cytometry to sort cells into different expression populations. We found that oscillation frequency was independent of the level of ERK–GFP fusion protein. By using ELISA and western blot analysis of phospho‐ERK levels in both parental and ERK–GFP‐expressing cells, we were also able to demonstrate oscillations in ERK phosphorylation that corresponded to the oscillations in ERK–GFP nucleo–cytoplasmic localization. Interestingly, overexpression of ERK–GFP suppressed the phosphorylation of the endogenous cellular ERK such that the net level of ERK phosphorylation (endogenous+transfected) remained constant, suggesting that the levels of ERK are not rate limiting for its activation in cells.
To understand the mechanistic basis of the oscillations, we constructed a mathematical model of the ERK pathway that included both the details of the biochemical reactions and transport processes between the cytoplasm and nucleus (Figure 5). Our initial parameters were based on literature values, but were adjusted to yield the observed oscillation characteristics. We found that a negative feedback loop between ERK and the input to the ERK cascade was essential to reproduce the waveform and invariant frequency aspects of the oscillations. Our model exhibited two Hopf bifurcations, and predicted that oscillations would occur over a range of two orders of magnitude of input strengths. Above and below a critical level of stimulation, however, the model predicted that oscillations would cease. These characteristics matched our experimental observations very closely.
Our initial model was based on the average oscillation properties of the cell population. To test its ability to predict the oscillation characteristics in a population of cells with cell‐to‐cell parameter variability, we assumed a log‐normal distribution of cellular parameters with a coefficient of variation 0.2 to be consistent with experimental measurements of the variability in protein expression between individual cells in a population (Spencer et al, 2009). We observed that model predictions for the population response to different input strengths were very similar to our experimental results and the model was able to quantitatively reproduce the robustness of the oscillations and the degree of cell‐to‐cell variability seen in our experiments. The model was also able to successfully predict the effect of inhibiting phosphatase activities on the fraction of oscillating cells as a function of EGF concentration.
Our study is, to the best of our knowledge, the first to experimentally demonstrate that ERK can oscillate between the nucleus and cytoplasm after cell activation. As illustrated by our analysis of ERK‐mediated negative feedback, ERK oscillatory dynamics can provide extremely useful information for constraining models of this important signaling pathway. We predict that oscillations could occur in other cell types depending on the inherent properties of their ERK cascades and on the existence of a negative feedback loop. We compared the parameters of our ERK cascade model with the parameters in other published models and found that our kinase and phosphatase abundances are within the range reported by others. However, in our model, the ratios of the enzymes’ Km values to their substrate concentrations are smaller compared with other published models.
Our investigation of the characteristics of the oscillatory behavior of the ERK pathway was greatly facilitated by using automated image analysis because of its ability to generate a very detailed ERK waveform. It could also follow hundreds of cells simultaneously at a time resolution of <1 min and provide data on associated behaviors, such as gene expression, cell migration and cell division. Live‐cell imaging of ERK dynamics should greatly facilitate the productive coupling of experiments to mathematical theory and help delineate the full regulatory structure of the MAPK cascade.
Activating the ERK cascade of human mammary epithelial cells with EGF resulted in a rapid and sustained oscillation of an ERK‐GFP fusion protein between the nucleus and cytoplasm.
Oscillations occurred even at ligand doses that elicited very low levels of ERK phosphorylation, were continuous throughout the cell cycle and were correlated with cycles of ERK phosphorylation detected biochemically in both transfected and non‐transfected cells.
Mathematical modeling revealed that negative feedback from phosphorylated ERK to the cascade input was necessary to match the robustness of the oscillation characteristics observed over a broad range of ligand concentrations.
When cell‐cell variations in levels of the different components of the ERK cascade was included in the mathematical model, we were able to accurately predict the population response to different levels of EGF stimulation and the effect of treating cells with phosphatase inhibitors.
Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in ...regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)-also known as multiple reaction monitoring (MRM)-and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.
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