Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale
Ovidiu Lipan1, Cameron Ferwerda2
1Department of Physics, University of Richmond, 28 Westhampton Way, Richmond, Virginia 23173, USA.
Physical Review. E
|March 18, 2018
Summary
Stochastic Hill functions account for molecular fluctuations, improving predictions in genetic regulatory networks. This method accurately captures system dynamics, unlike traditional deterministic models.
Area of Science:
- Systems Biology
- Computational Biology
- Biophysics
Background:
- Deterministic Hill functions rely solely on average molecule numbers.
- Fluctuations in molecule numbers are crucial for accurate biological modeling.
- Existing models often fail to capture stochastic effects in gene regulation.
Purpose of the Study:
- To develop a method for constructing stochastic Hill functions.
- To provide a closed analytical form for these functions for easy integration into large models.
- To demonstrate the improved accuracy of stochastic Hill functions over deterministic ones.
Main Methods:
- Deriving stochastic Hill functions from the dynamical evolution of stochastic biocircuits.
- Utilizing means, standard deviations, and correlations in the function's argument.
- Employing Monte Carlo simulations to compare deterministic and stochastic models.
Main Results:
- Stochastic Hill functions were derived in a closed analytical form.
- Deterministic Hill functions inaccurately predicted repression time by two orders of magnitude.
- Stochastic Hill functions accurately predicted repression time by capturing molecular fluctuations.
Conclusions:
- Stochastic Hill functions offer a more accurate representation of gene regulatory dynamics.
- This method enhances the predictive power of models for large genetic regulatory networks.
- Accounting for stochasticity is essential for precise biological system modeling.
Related Concept Videos
02:23Master Transcription Regulators
7.8K
Master transcription regulators are regulatory proteins that are predominantly responsible for regulating the expression of multiple genes. Often these genes work in concert to drive a complex process. Activation of a master transcription regulator can lead to a cascade of transcriptional activation necessary for that outcome. These regulators can directly bind to the regulatory sequences of the various genes involved, or they can indirectly regulate transcription by binding to regulatory...
7.8K
02:23Master Transcription Regulators
2.8K
2.8K
01:20Separable Differential Equations
109
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
109
02:26Protein Networks
4.6K
An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
4.6K
02:02Cis-regulatory Sequences
11.9K
Cis-regulatory sequences are short fragments of non-coding DNA that are present on the same chromosomes as the genes that they regulate. These fragments serve as binding sites for transcriptional regulators, proteins that are responsible for controlling gene transcription and differential gene expression across cell types in eukaryotes. Cis-regulatory sequences can be close to the gene of interest or thousands of bases away in the DNA sequence; however, those sequences that are further away are...
11.9K
01:25Network Function of a Circuit
880
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
880