Noise and Bistability 12/10/07

Noisy gene expression at single cell level Elowitz 2002

Noise distribution of protein concentration Bar-Even 2006

Dependence of noise level on protein concentration Bar-Even 2006

Proteins are produced in bursts Cai 2006

Proteins are produced in bursts Cai 2006

Intrinsic and extrinsic noise extrinsic noise: fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene intrinsic noise: The inherent stochasticity of biochemical processes such as transcription and translation Elowitz 2002

Intrinsic and extrinsic noise extrinsic noise: fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene intrinsic noise: The inherent stochasticity of biochemical processes such as transcription and translation Elowitz 2002

Distinguishing intrinsic from extrinsic noise Average over cell population For a fixed time t, Total noise level, Average over time Swain 2002

Distinguishing intrinsic from extrinsic noise Average over cell population For a fixed time t, Total noise level, Average over time Swain 2002

Measuring intrinsic and extrinsic noise Swain 2002

Measuring intrinsic and extrinsic noise Simultaneously measure the expression levels of two copies of a single gene, controlled by the same promoter. Elowitz 2002

Measuring intrinsic and extrinsic noise Elowitz 2002

Controlling noise Noise can hamper the precision of decision making by a cell. Noise can be controlled by using negative feedback loops. Essential genes are less noisy than other genes, suggestive of selection pressure. AB A B t t

Benefit of noise Noise can diversify phenotypic responses. Different pheontypes may be adapted for different environmental conditions. Population diversity can help the population to survive as a whole.

Alternative ways to adapt to environmental changes Leibler 2005

Noise-induced drug resistance Balaban 2004

Noise-induced drug resistance Observation No mutation is identified. “Resistant” cells can be further killed by antibiotics. Balaban 2004

Noise-induced drug resistance Observation No mutation is identified. “Resistant” cells can be further killed by antibiotics. Explanation Genetically identical cells have different responses to environment due to noise. A subpopulation of cells “persisters” escape the antibiotics by initiating the “right” response. Balaban 2004

Bistability Veening 2006 Gene activities can be regulated by on- off switches. Large-scale continuous response can be due to change of proportions of responsive cells.

Bistability Bistability is characterized by bimodal distribution. Single stable state corresponds to a unimodal distribution. Veening 2006

Positive feedback loops and bistability AB A B t t

AB A B t t

Ordinary differential equations y t

y1y1 t y2y2 y1y1 phase diagram

Steady states y2y2 y1y1

y2y2 y1y1 unstable y2y2 y1y1 stable

Bistability y2y2 y1y1

Modeling positive feedback loops AB The positive feedback loops can be modeled by ODEs

AB The solution is The only possible stable states are 0 and infinity. Therefore, nonlinear models are required to model bistability. Modeling positive feedback loops

Ferrell & Xiong 2001

Single stable steady states in simple Michaelis-Menen systems Ferrell & Xiong 2001

Hysterisis Ferrell & Xiong 2001

Readling List Elowitz et al –Defined intrinsic and extrinsic noise Balaban et al –Noise-induced drug resistance Ferrell and Xiong 2001 –Introduction to bistability