Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.
Biochemical networks experience both intrinsic fluctuations, generated by the stochasticity inherent to biochemical reactions within the network, and extrinsic fluctuations arising from the interactions of the network with other stochastic systems in the cell or its environment. Both types of fluctuations can be controlled or exploited by cells. Intrinsic fluctuations are relatively well understood. They arise from random collisions of reacting molecules with other molecules. Such collisions stochastically alter the time for two reactants to meet and their time to cross a reaction's energy barrier. Intrinsic fluctuations can be described mathematically by a master equation or simulated using a stochastic simulation algorithm, such as the Gillespie algorithm. Despite usually being the dominant fluctuations in experimental measurements of in vivo protein levels, extrinsic fluctuations have been much less studied. They have been measured to have a lifetime comparable to the cell cycle, but their source is largely speculative. Here, we extend the Gillespie algorithm to include extrinsic fluctuations with any properties and so enable their systematic study, at least by simulation. Extrinsic fluctuations have a significant lifetime, and, because their lifetime is greater than zero, they are called ‘colored’. We show that their color causes extrinsic fluctuations to have a nonlinear effect on the dynamics of a network. They can shift the mean number of proteins and can alter the intrinsic noise found in protein levels. Intrinsic noise is measured by the variation in the difference between two distinguishable reporters, each expressed by a separate copy of the network under study. We describe how these effects, arising from the lifetime of extrinsic fluctuations, can help explain trends seen in high‐throughput measurements of stochasticity in gene expression. Extrinsic fluctuations are also nonspecific and can potentially simultaneously affect many cellular components. We show that extrinsic fluctuations in different components of a network can combine destructively to negate each other or constructively to amplify fluctuations in the network's output. These interference effects are likely to be exploited by cells in feedforward loops: some types of feedforward loops can attenuate stochasticity because they channel extrinsic fluctuations in the levels of the network's master transcription factor to combine destructively with those of the other regulating transcription factor and so decrease fluctuations in the network's output. Others can cause constructive extrinsic fluctuations in the network's transcription factors and so can amplify fluctuations in the network's output. Our results show that the lifetime of extrinsic fluctuations increases their co‐dependence with intrinsic fluctuations. More generally, they address how to model one stochastic system embedded in and interacting with a larger stochastic system. Mathematically, these interactions, or extrinsic fluctuations, cause the parameters of an already stochastic system to become stochastic themselves. Measurements of the stochasticity in the output of the system will have an intrinsic component, arising from the dynamics of the system itself, and an extrinsic component, arising from fluctuations in the system's parameters. For example, in gene expression, the rate of initiation of translation is stochastic because it is a function of the number of free ribosomes which is itself stochastic. Although the empirical definitions of extrinsic and intrinsic noise do not change, we show that the colored character of extrinsic fluctuations does alter their theoretical justification. Our simulation algorithm and the concepts we propose should help to quantitatively understand endogenous networks and to design effective synthetic ones.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Colored extrinsic fluctuations and stochastic gene expression ; volume:4 ; number:1 ; year:2008 ; extent:9 ; Molecular systems biology ; 4, Heft 1 (2008) (gesamt 9)

Contributors, Places and Time

• Creator: Shahrezaei, Vahid ; Ollivier, Julien F. ; Swain, Peter S.

Further information

• DOI: 10.1038/msb.2008.31
• URN: urn:nbn:de:101:1-2023073104483410958493
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 11:04 AM CEST