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Noise in biological circuits

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Noise biology focuses on the sources, processing, and biological consequences of the inherent stochastic fluctuations in molecular transitions or interactions that control cellular behavior. These fluctuations are especially pronounced in small systems where the magnitudes of the fluctuations approach or exceed the mean value of the molecular population. Noise biology is an essential component of nanomedicine where the communication of information is across a boundary that separates small synthetic and biological systems that are bound by their size to reside in environments of large fluctuations. Here we review the fundamentals of the computational, analytical, and experimental approaches to noise biology. We review results that show that the competition between the benefits of low noise and those of low population has resulted in the evolution of genetic system architectures that produce an uneven distribution of stochasticity across the molecular components of cells and, in some cases, use noise to drive biological function. We review the exact and approximate approaches to gene circuit noise analysis and simulation, and review many of the key experimental results obtained using flow cytometry and time‐lapse fluorescent microscopy. In addition, we consider the probative value of noise with a discussion of using measured noise properties to elucidate the structure and function of the underlying gene circuit. We conclude with a discussion of the frontiers of and significant future challenges for noise biology. Copyright © 2009 John Wiley & Sons, Inc.

Figure 1.

Noise in molecular populations. (a) A simple birth–death molecular process and (b) the deterministic and stochastic rise to steady‐state molecular population level. (c) A family of possible stochastic trajectories for the birth–death process. The smooth curve represents the average of all possible stochastic trajectories. The noise for any of the possible trajectories is found from the difference between the trajectory and the average of all trajectories.

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Figure 2.

Intrinsic and extrinsic noise in a constitutively expressed gene circuit. The intrinsic noise sources originate from the transcription and translation processes, whereas extrinsic noise originates from resources shared with other gene circuits. (Reprinted, with permission, from Ref. 28. Copyright 2006 AIP.).

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Figure 3.

Noise modulation of the λ switch decision. (a) The red and blue dashed lines represent the average trajectories for the proteins Cro and Cl, respectively. These proteins are in a critical race to their respective thresholds represented by red (Cro) and blue (Cl) horizontal lines at the top. The solid red (Cro) and blue (Cl) lines represent particular trajectories for these proteins. (b) Distributions for the times that Cro (red) and Cl (blue) reach their respective threshold levels. If Cro wins the race, the lytic pathway is chosen, while if Cl wins, the lysogenic pathway is chosen. The cross‐hatched area represents the relatively rare (for this example) case where a stochastic choice of slow Cro and fast Cl accumulation has led to a lysogenic selection. (c) A change in the rate of Cl accumulation makes the selection of the lysogenic pathway more likely as shown in (d).

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Figure 4.

Stochastic representation of a negatively autoregulated gene. (a) Active gene (Ga) is transcribed (R3) to produce mRNA (M), which is in turn translated (R5) to produce protein (P). Repression of transcription results from the conversion of Ga to Gr mediated by the reversible binding of P (R1 and R2). Both M and P are subject to decay/dilution (R4 and R6). (b) Example of possible transitions of one hypothetical state X(t) to other reachable states X(t + Δ τ). The relative likelihood of each reaction and its corresponding state transition are indicated by the thickness of the arrow.

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Figure 5.

Propagation of noise using frequency domain (FD) analysis. The noise power spectral density (PSD) at output nodes E–F is calculated from the noise PSD at the input nodes (A–D) and the transfer functions that connect the inputs to the outputs. For example, the effect of noise in input species A on output species E is given by $H^{2}_{AE}(f)S_{AA}(f)$. (Reprinted, with permission, from Ref. 28. Copyright 2006 AIP.).

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Figure 6.

Scatter plot of flow cytometer data plotted as log CV versus log protein abundance, illustrating the high‐throughput nature and dynamic range of the technique. Gating applied here reduced cell‐cycle variability and hence a major source of extrinsic noise. (Reprinted, with permission, from Ref. 18. Copyright 2006 Nature Publishing.).

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Figure 7.

Measuring noise correlation using time‐lapse fluorescent microscopy. (a) Plasmid containing the constitutive gene circuit, (b) sample micrographs from a single trajectory (arrows) tracked over time, shown in hours, (c) individual noise trajectories extracted from experiment in (b), and (d) their normalized autocorrelation functions. (Reprinted, with permission, from Ref. 11. Copyright 2006 Nature Publishing.).

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Figure 8.

The synchrogram. Nine cell lines with individual GFP‐protein fusions varying in primary cell localization (top to bottom, left axis) shown over time with respect to the percentage of time elapsed during a complete cell cycle (top). Protein localizations were found to change at various times during the cell cycle for several proteins (marked at bottom). Bar = 20 µm. (Reprinted, with permission, from Ref. 24. Copyright 2006 Nature Publishing.).

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Figure 9.

Noise maps and regulation vectors. (a) 3D noise map showing the relationship between CV2, τ1/2 and 〈P〉 (all axes are log scale). Changes in transcription rate cause the noise characteristics of a protein to slide up and down the bias line (shown in black). Colored arrows show how changes in translation rate (blue) or protein half‐life (red) result in displacement from the bias line. (b) 3D noise map of the negative feedback circuit shown in Figure 4(a). Elementary rate constants kj for reactions Rj are k3 = 8E–4, k4 = 5.8E–4, k5 = 0.69, k6 = 9.6E–5.k2 = a × R6 where a = 0.2, 0.5, 1, 5, 10 going from slowest to fastest kinetics. Values of k1 were varied to achieve different levels of repression. The solid black arrows represent the bias line of the nonfeedback model with the arrow pointing in the direction of decreasing transcription efficiency. (c) Regulatory vectors show displacement from any point along the bias line as a result of negative autoregulation. The legend is the same as (b) and repression level increases as one moves clockwise around each plot.

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