Overview
This lecture introduces the course "Physics of Behavior," exploring how simple biological systems like E. coli use universal mathematical principles to regulate their internal states and respond to environmental signals.
Course Introduction and Structure
- The course combines biology and simple mathematics to understand the principles behind complex biological systems.
- Students of varied backgrounds (physics, biology, computer science, etc.) are encouraged to collaborate and learn from each other.
- Weekly exercises start next week; the goal is to train new ways of thinking, not to overload with work.
- Resources include a 2014 lecture video and the book "An Introduction to Systems Biology"; no electronic copy is available.
Relaxation and Learning State
- Being in a relaxed state, supported by deep breathing, improves learning, memory, and concentration.
- The class will periodically practice collective deep sighs to promote relaxation.
Biological Foundations: The Cell as a System
- Focus on E. coli, a single-cell organism capable of sensing and responding to various environmental signals.
- E. coli uses proteinsāmolecular machines encoded by genesāto perform functions like movement and nutrient uptake.
- Proteins are produced in varying quantities based on the cellās needs and environment.
Gene Regulation Mechanisms
- Proteins are made from genes via two steps: transcription (DNA to mRNA) and translation (mRNA to protein).
- Environmental signals activate transcription factors, special proteins that regulate specific genes.
- Transcription factors can act as activators (increase gene expression) or repressors (decrease gene expression).
- Each gene has a promoter region with binding sites for RNA polymerase and transcription factors.
Network Representation & Systems Biology
- Gene regulatory networks (GRNs) map all regulatory interactions between genes and transcription factors.
- GRNs are complex, with thousands of nodes (genes) and arrows (regulatory interactions), but are understandable due to evolutionary pressures and modularity.
- Modern techniques allow mapping and manipulation of these networks, such as using green fluorescent protein (GFP) reporters.
Mathematical Modeling of Gene Expression
- The rate of protein production depends on activator concentration via the Hill function:
( \text{Production} = \frac{\beta x^n}{K^n + x^n} ), where K is the concentration for half-maximal activity, n is the Hill coefficient.
- Input functions illustrate how activators and repressors affect gene expression; when multiple inputs exist, the function becomes multidimensional (e.g., AND/OR gates).
Dynamics of Gene Expression: Equations & Response Times
- The basic equation for protein concentration Y:
( \frac{dY}{dt} = \beta - \alpha Y ), where Ī² is production rate, Ī± is removal (degradation/dilution) rate.
- Steady-state protein level: ( Y_{ss} = \frac{\beta}{\alpha} ).
- Response time (time to half steady-state): ( t_{1/2} = \frac{\ln 2}{\alpha} ), determined mainly by removal rate.
- Most proteins are stable, so response times are limited by cell division ratesāleading to slow responses unless proteins are deliberately made unstable.
Key Terms & Definitions
- Transcription ā Process converting DNA to mRNA.
- Translation ā Process converting mRNA to protein.
- Transcription Factor ā Protein that regulates gene expression by binding DNA.
- Promoter ā DNA region controlling gene transcription.
- Activator ā Transcription factor that increases gene expression.
- Repressor ā Transcription factor that decreases gene expression.
- Gene Regulatory Network (GRN) ā Network illustrating gene and transcription factor interactions.
- Hill Function ā Equation describing saturation kinetics in gene regulation.
Action Items / Next Steps
- Introduce yourself to classmates with different backgrounds.
- Review the assigned textbook "An Introduction to Systems Biology" from the library.
- Prepare for weekly exercises beginning next week.
- Reflect on how GRNs govern protein production and consider questions for biologists or physicists in class.