Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics
Priyan Bhattacharya1, Karthik Raman2, Arun K Tangirala3,4
1Department of Chemical Engineering, IIT Madras, Chennai, Tamil Nadu, 600036, India.
Bulletin of Mathematical Biology
|July 3, 2024
Summary
This study identifies network architectures enabling perfect adaptation to environmental changes. It reveals two key structures—incoherent feed-forward (IFF) and negative feedback with buffer (NFB)—essential for biological system regulation.
Area of Science:
- Systems biology
- Synthetic biology
- Nonlinear dynamics
Background:
- Biological systems require adaptation to environmental disturbances for stable function.
- Understanding the relationship between network structure and emergent properties like adaptation is crucial.
Purpose of the Study:
- To develop a nonlinear systems theory framework for identifying design principles of perfect adaptation.
- To determine mathematical conditions and network architectures enabling adaptation to external disturbances.
Main Methods:
- Utilizing nonlinear systems theory to derive mathematical conditions for perfect adaptation.
- Translating these conditions into structural requirements for biological networks.
- Analyzing network architectures including incoherent feed-forward (IFF) and negative feedback loops (NFB).
Main Results:
- Identified precise mathematical conditions for perfect adaptation to constant input disturbances.
- Determined that only incoherent feed-forward (IFF) and negative feedback with buffer (NFB) architectures can provide local adaptation across the entire state space.
- Established global asymptotic stability for steady states under constant disturbances.
- Discussed limitations of certain IFF networks with downstream connections.
Conclusions:
- Two fundamental network architectures, IFF and NFB, are necessary for achieving adaptation in biological systems.
- The developed framework provides a systematic approach to understanding and designing adaptive biological networks.
- Simulation studies validate the theoretical findings on network adaptation principles.
Related Concept Videos
01:26Linear Approximation in Frequency Domain
89
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
89
01:07Cell Signaling Feedback Loops
6.2K
Positive and negative feedback loops are crucial for regulating biological signaling systems. These feedback loops are processes that connect output signals to their inputs.
Negative feedback loops
Most signaling systems have negative feedback loops that can perform different functions such as output limiter, and adaptation.
Output limiter
Upon receiving an input signal, the cellular response rapidly increases until a threshold is reached. Beyond this threshold, a negative feedback loop...
Negative feedback loops
Most signaling systems have negative feedback loops that can perform different functions such as output limiter, and adaptation.
Output limiter
Upon receiving an input signal, the cellular response rapidly increases until a threshold is reached. Beyond this threshold, a negative feedback loop...
6.2K
01:22Nonlinear Pharmacokinetics: Bioavailability and Protein-Drug Binding
156
When a drug follows nonlinear pharmacokinetics, its bioavailability, the amount of the drug that reaches the systemic circulation, can change with different doses. This is due to the presence of a saturable pathway. The pathway becomes saturated as the drug concentration increases, decreasing the absorption rate. Consequently, the drug's bioavailability may be lower than expected at higher doses.
To quantify the extent of bioavailability, pharmacologists often use a parameter called .
To quantify the extent of bioavailability, pharmacologists often use a parameter called .
156
01:26Feedback control systems
303
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
303
01:26Classification of Systems-I
179
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
179
01:38Limits to Natural Selection
31.2K
Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.
31.2K