Johan Paulsson

Summing up the noise in gene networks

Random fluctuations in genetic networks are inevitable as chemical reactions are probabilistic and many genes, RNAs and proteins are present in low numbers per cell. Such ‘noise’ affects all life processes and has recently been measured using green fluorescent protein (GFP). Two studies show that negative feedback suppresses noise, and three others identify the sources of noise in gene expression. Here I critically analyse these studies and present a simple equation that unifies and extends both the mathematical and biological perspectives.

Real-Time Kinetics of Gene Activity in Individual Bacteria

Protein levels have been shown to vary substantially between individual cells in clonal populations. In prokaryotes, the contribution to such fluctuations from the inherent randomness of gene expression has largely been attributed to having just a few transcripts of the corresponding mRNAs. By contrast, eukaryotic studies tend to emphasize chromatin remodeling and burst-like transcription. Here, we study single-cell transcription in Escherichia coli by measuring mRNA levels in individual living cells. The results directly demonstrate transcriptional bursting, similar to that indirectly inferred for eukaryotes. We also measure mRNA partitioning at cell division and correlate mRNA and protein levels in single cells. Partitioning is approximately binomial, and mRNA-protein correlations are weaker earlier in the cell cycle, where cell division has recently randomized the relative concentrations. Our methods further extend protein-based approaches by counting the integer-valued number of transcript with single-molecule resolution. This greatly facilitates kinetic interpretations in terms of the integer-valued random processes that produce the fluctuations.

Reduced IGF-1 signaling delays age-associated proteotoxicity in mice.

The insulin/insulin growth factor (IGF) signaling (IIS) pathway is a key regulator of aging of worms, flies, mice, and likely humans. Delayed aging by IIS reduction protects the nematode C. elegans from toxicity associated with the aggregation of the Alzheimers disease-linked human peptide, Abeta. We reduced IGF signaling in Alzheimers model mice and discovered that these animals are protected from Alzheimers-like disease symptoms, including reduced behavioral impairment, neuroinflammation, and neuronal loss. This protection is correlated with the hyperaggregation of Abeta leading to tightly packed, ordered plaques, suggesting that one aspect of the protection conferred by reduced IGF signaling is the sequestration of soluble Abeta oligomers into dense aggregates of lower toxicity. These findings indicate that the IGF signaling-regulated mechanism that protects from Abeta toxicity is conserved from worms to mammals and point to the modulation of this signaling pathway as a promising strategy for the development of Alzheimers disease therapy.The insulin/insulin growth factor (IGF) signaling (IIS) pathway is a key regulator of aging of worms, flies, mice, and likely humans. Delayed aging by IIS reduction protects the nematode C. elegans from toxicity associated with the aggregation of the Alzheimers disease-linked human peptide, Aβ. We reduced IGF signaling in Alzheimers model mice and discovered that these animals are protected from Alzheimers-like disease symptoms, including reduced behavioral impairment, neuroinflammation, and neuronal loss. This protection is correlated with the hyperaggregation of Aβ leading to tightly packed, ordered plaques, suggesting that one aspect of the protection conferred by reduced IGF signaling is the sequestration of soluble Aβ oligomers into dense aggregates of lower toxicity. These findings indicate that the IGF signaling-regulated mechanism that protects from Aβ toxicity is conserved from worms to mammals and point to the modulation of this signaling pathway as a promising strategy for the development of Alzheimers disease therapy.

Effects of Molecular Memory and Bursting on Fluctuations in Gene Expression

Many cellular components are present in such low numbers per cell that random births and deaths of individual molecules can cause substantial “noise” in concentrations. But biochemical events do not necessarily occur in single steps of individual molecules. Some processes are greatly randomized when synthesis or degradation occurs in large bursts of many molecules during a short time interval. Conversely, each birth or death of a macromolecule could involve several small steps, creating a memory between individual events. We present a generalized theory for stochastic gene expression, formulating the variance in protein abundance in terms of the randomness of the individual gene expression events. We show that common types of molecular mechanisms can produce gestation and senescence periods that reduce noise without requiring higher abundances, shorter lifetimes, or any concentration-dependent control loops. We also show that most single-cell experimental methods cannot distinguish between qualitatively different stochastic principles, although this in turn makes such methods better suited for identifying which components introduce fluctuations. Characterizing the random events that give rise to noise in concentrations instead requires dynamic measurements with single-molecule resolution.

Fundamental limits on the suppression of molecular fluctuations

Negative feedback is common in biological processes and can increase a system’s stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

Non-genetic heterogeneity from stochastic partitioning at cell division

Gene expression involves inherently probabilistic steps that create fluctuations in protein abundances. The results from many in-depth analyses and genome-scale surveys have suggested how such fluctuations arise and spread, often in ways consistent with stochastic models of transcription and translation. But fluctuations also arise during cell division when molecules are partitioned stochastically between the two daughters. Here we mathematically demonstrate how stochastic partitioning contributes to the non-genetic heterogeneity. Our results show that partitioning errors are hard to correct, and that the resulting noise profiles are remarkably difficult to separate from gene expression noise. By applying these results to common experimental strategies and distinguishing between creation versus transmission of noise, we hypothesize that much of the cell-to-cell heterogeneity that has been attributed to various aspects of gene expression instead comes from random segregation at cell division. We propose experiments to separate between these two types of fluctuations and discuss future directions.

Separating intrinsic from extrinsic fluctuations in dynamic biological systems.

From molecules in cells to organisms in ecosystems, biological populations fluctuate due to the intrinsic randomness of individual events and the extrinsic influence of changing environments. The combined effect is often too complex for effective analysis, and many studies therefore make simplifying assumptions, for example ignoring either intrinsic or extrinsic effects to reduce the number of model assumptions. Here we mathematically demonstrate how two identical and independent reporters embedded in a shared fluctuating environment can be used to identify intrinsic and extrinsic noise terms, but also how these contributions are qualitatively and quantitatively different from what has been previously reported. Furthermore, we show for which classes of biological systems the noise contributions identified by dual-reporter methods correspond to the noise contributions predicted by correct stochastic models of either intrinsic or extrinsic mechanisms. We find that for broad classes of systems, the extrinsic noise from the dual-reporter method can be rigorously analyzed using models that ignore intrinsic stochasticity. In contrast, the intrinsic noise can be rigorously analyzed using models that ignore extrinsic stochasticity only under very special conditions that rarely hold in biology. Testing whether the conditions are met is rarely possible and the dual-reporter method may thus produce flawed conclusions about the properties of the system, particularly about the intrinsic noise. Our results contribute toward establishing a rigorous framework to analyze dynamically fluctuating biological systems.

Memory and Modularity in Cell-Fate Decision Making

Genetically identical cells sharing an environment can display markedly different phenotypes. It is often unclear how much of this variation derives from chance, external signals, or attempts by individual cells to exert autonomous phenotypic programs. By observing thousands of cells for hundreds of consecutive generations under constant conditions, we dissect the stochastic decision between a solitary, motile state and a chained, sessile state in Bacillus subtilis. We show that the motile state is ‘memoryless’, exhibiting no autonomous control over the time spent in the state. In contrast, the time spent as connected chains of cells is tightly controlled, enforcing coordination among related cells in the multicellular state. We show that the three-protein regulatory circuit governing the decision is modular, as initiation and maintenance of chaining are genetically separable functions. As stimulation of the same initiating pathway triggers biofilm formation, we argue that autonomous timing allows a trial commitment to multicellularity that external signals could extend.

Fluctuations and Quality of Control in Biological Cells: Zero-Order Ultrasensitivity Reinvestigated

Living cells differ from most other chemical systems in that they involve regulation pathways that depend very nonlinearly on chemical species that are present in low copy numbers per cell. This leads to a variety of intracellular kinetic phenomena that elude macroscopic modeling, which implicitly assumes that cells are infinitely large and fluctuations negligible. It is of particular importance to assess how fluctuations affect regulation in cases where precision and reliability are required. Here, taking finite cell size and stochastic aspects into account, we reinvestigate theoretically the mechanism of zero-order ultrasensitivity for covalent modification of target enzymes ( Proc. Natl. Acad. Sci. USA. 78:6840-6844). Macroscopically, this mechanism can produce a very sharp transition in target concentrations for very small changes in the activity of the converter enzymes. This study shows that the transition is much more gradual in a finite cell or a population of finite cells. It also demonstrates that the switch is exactly analogous to a thermodynamic phase transition and that ultrasensitivity is inevitably coupled to random ultravariation. As a consequence, the average response in a large population of cells will often be much more gradual than predicted from macroscopic descriptions.

Random partitioning of molecules at cell division

Many RNAs, proteins, and organelles are present in such low numbers per cell that random segregation of individual copies causes large “partitioning errors” at cell division. Even symmetrically dividing cells can then by chance produce daughters with very different composition. The size of the errors depends on the segregation mechanism: Control systems can reduce low-abundance errors, but the segregation process can also be subject to upstream sources of randomness or spatial heterogeneities that create large errors despite high abundances. Here we mathematically demonstrate how partitioning errors arise for different types of segregation mechanisms and how errors can be greatly increased by upstream heterogeneity but remarkably hard to avoid through controlled partitioning. We also show that seemingly straightforward experiments cannot be straightforwardly interpreted because very different mechanisms produce identical fits and present an approach to deal with this problem by adding binomial counting noise and testing for convexity or concavity in the partitioning error as a function of the binomial thinning parameter. The results lay a conceptual groundwork for more effective studies of heterogeneity among growing and dividing cells, whether in microbes or in differentiating tissues.