Hespanha

Steady state value of the mean auto regulatory

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s response-time (with feedback) CV [x] = StdDev[x] = E[x] ￿ Tr N Tp E[x] “unregulated” intrinsic noise Tr Tp 1 2.25 protein’s half-live (response time without feedback) Negative feedback reduces Tr with respect to Tp ' decreases noise experimental study using a synthetic gene circuit in which the repressor TetR fused to GFP represses its own promoter Rosenfeld et al, J. Molecular Biology, 2002 Exogenous Noise http://en.wikipedia.org transcription event g(x,z) dt x ￿→ x + N In practice, transcription rate also depends on exogenous species (e.g., RNA polymerase and other enzymes) g(x, z) % transcriptional response (stochastic rate at which transcription events occur) exogenous species (with stochastic fluctuations) dxdt decay event x ￿→ x − 1 Exogenous Noise http://en.wikipedia.org transcription event g(x,z) dt x ￿→ x + N ￿ T ￿2 Tr N r C V [ x] ≈ + CV [z ]2 Tp E[x] Tp 2 intrinsic noise extrinsic noise (as before) dxdt decay event x ￿→ x − 1 CV of extrinsic species Tr % protein’s response-time (with feedback) Tp % protein’s half-live (response time without feedback) Negative feedback reduces Tr with respect to Tp ! attenuates both intrinsic and extrinsic noise Tr 1 Tp 2.25 ! more efficient at reducing extrinsic noise ! surprisingly good matches with experimental results… ! offers a new technique to discover sources of extrinsic noise (solve for CV[z] !) [Singh et al, 2009; related results by Paulsson 2004] Summary 1. SHS models that find use in several areas (network traffic modeling, networked control systems, distributed estimation, biochemistry, population dynamics in ecosystems) 2. The analysis of SHSs is challenging but there are tools available (stability conditions for linear time-triggered SHS, Lyapunov methods, moment dynamics, linearization, truncations) 3. Lots of work to be done …...
View Full Document

Ask a homework question - tutors are online