Synthetic Biology & Metabolic Engineering

Synthetic biology represents the engineering of biology through design-build-test-learn cycles. It combines principles from molecular biology, systems biology, and engineering to design and construct new biological parts, devices, and systems, or to redesign existing biological systems for useful purposes.

Foundations of Synthetic Biology

BioBricks and Standardized Parts

Registry System

\text{Part} = \{\text{Promoter}, \text{RBS}, \text{Coding sequence}, \text{Terminator}\}

\text{BioBrick standard}: \text{RFC10} \rightarrow \{\text{prefix}, \text{part}, \text{suffix}\}

Part Classification

Promoters: Transcriptional control elements
RBS (Ribosome Binding Sites): Translation initiation signals
Coding sequences: Protein-coding genes
Terminators: Transcriptional stop signals
Insulators: Boundary elements preventing interference

Design Principles

Modularity

\text{System response} = f(\text{input}, \text{component 1}) + f(\text{input}, \text{component 2}) + \ldots

Orthogonality

\text{Minimal cross-talk}: \sum_{i \neq j} \text{interaction}_{ij} \approx 0

Robustness

\text{Robustness} = \frac{\text{function maintained under perturbation}}{\text{total perturbation magnitude}}

Genetic Circuit Design

Boolean Logic Gates

NOT Gate

\text{Promoter} \xrightarrow{\text{Inducer}} \text{Repressor} \xrightarrow{\text{Inhibition}} \text{Output gene}

\text{Transfer function}: \frac{[R]}{K + [I]} \text{ where } R = \text{repressor, } I = \text{inducer}

AND Gate

\text{AND}(A,B) = \begin{cases} 1 & \text{if } [A] > \theta_A \text{ and } [B] > \theta_B \\ 0 & \text{otherwise} \end{cases}

OR Gate

\text{OR}(A,B) = \begin{cases} 1 & \text{if } [A] > \theta_A \text{ or } [B] > \theta_B \\ 0 & \text{otherwise} \end{cases}

Oscillatory Networks

Repressilator Design

\text{Gene A} \rightarrow \text{Repressor B} \rightarrow \text{Gene B} \rightarrow \text{Repressor C} \rightarrow \text{Gene C} \rightarrow \text{Repressor A}

\frac{dm_i}{dt} = \frac{\alpha}{1 + p_{i-1}^n} - m_i + \text{noise}

\frac{dp_i}{dt} = \beta(m_i - p_i) + \text{noise}

Where $m_i$ and $p_i$ are mRNA and protein concentrations for gene $i$ .

Toggle Switches

Mutual Repression Circuit

\text{Gene A} \rightarrow \text{Protein A} \dashv \text{Gene B} \rightarrow \text{Protein B} \dashv \text{Gene A}

\frac{dp_A}{dt} = \frac{\alpha_A}{1 + (p_B/K_{BA})^n} - \delta_A p_A

\frac{dp_B}{dt} = \frac{\alpha_B}{1 + (p_A/K_{AB})^n} - \delta_B p_B

Where $K_{AB}$ and $K_{BA}$ are dissociation constants.

Metabolic Engineering Fundamentals

Stoichiometric Analysis

Metabolic Network Representation

\mathbf{S} \cdot \mathbf{v} = \mathbf{0}

Where $\mathbf{S}$ is the stoichiometric matrix and $\mathbf{v}$ is the flux vector.

Flux Balance Analysis (FBA)

\max \mathbf{c}^T \mathbf{v} \quad \text{subject to} \quad \mathbf{Sv} = \mathbf{0}, \mathbf{v}_{min} \leq \mathbf{v} \leq \mathbf{v}_{max}

Where $\mathbf{c}$ defines the objective function (e.g., biomass production).

Elementary Mode Analysis

\mathbf{v} = \sum_{i=1}^{k} \alpha_i \mathbf{e}_i

Where $\mathbf{e}_i$ are elementary modes and $\alpha_i$ are non-negative coefficients.

Metabolic Control Analysis

Control Coefficients

C_{E_j}^{J} = \frac{\partial J}{\partial E_j} \cdot \frac{E_j}{J}

C_{E_j}^{P_i} = \frac{\partial P_i}{\partial E_j} \cdot \frac{E_j}{P_i}

Where $J$ is flux, $P_i$ is concentration of metabolite $i$ , and $E_j$ is enzyme activity.

Sum Theorems

\sum_j C_{E_j}^{J} = 1 \quad \text{(flux control)}

\sum_j C_{E_j}^{P_i} = 0 \quad \text{(concentration control)}

Pathway Engineering

Heterologous Pathway Design

Pathway Assembly

\text{Precursor} \xrightarrow{E_1} \text{Intermediate}_1 \xrightarrow{E_2} \ldots \xrightarrow{E_n} \text{Product}

Codon Optimization

\text{Codon Adaptation Index (CAI)} = \left(\prod_{i=1}^{n} w_{RSCU_i}\right)^{1/n}

Where $w_{RSCU_i}$ is the relative synonymous codon usage for the $i$ -th codon.

Regulatory Considerations

Promoter Strength Engineering

\text{Transcription rate} = f(\text{promoter sequence}, \text{RNA polymerase binding}, \text{regulatory proteins})

\frac{d[\text{mRNA}]}{dt} = k_{trans} \cdot P_{promoter} - \delta_{mRNA} \cdot [\text{mRNA}]

Operon Design

\text{Polycistronic mRNA}: \text{Gene}_1 - \text{Gene}_2 - \ldots - \text{Gene}_n

With coordinated expression and stoichiometric protein production.

Flux Analysis in Pathway Engineering

Metabolic Flux Analysis (MFA)

\mathbf{v}_{measured} + \mathbf{M} \cdot \mathbf{v}_{unknown} = \mathbf{b}

\hat{\mathbf{v}} = \arg\min_{\mathbf{v}} (\mathbf{v}_{measured} - \mathbf{v})^T \mathbf{W} (\mathbf{v}_{measured} - \mathbf{v})

Where $\mathbf{W}$ is a weight matrix based on measurement uncertainties.

Synthetic Gene Networks

Feedback Control Systems

Negative Feedback

\frac{d[X]}{dt} = \frac{\alpha}{1 + ([Y]/K)^n} - \delta_X [X]

\frac{d[Y]}{dt} = \beta [X] - \delta_Y [Y]

Provides homeostasis and reduces noise.

Positive Feedback

\frac{d[X]}{dt} = \frac{\alpha [X]^n}{K^n + [X]^n} - \delta [X]

Creates bistability and cellular memory.

Noise Analysis

Intrinsic vs. Extrinsic Noise

\text{Total variance} = \text{Intrinsic variance} + \text{Extrinsic variance}

\sigma^2_{int} = \langle b^2 \rangle \cdot \text{response to transcription} + \text{response to translation}

\sigma^2_{ext} = \text{coupling to other genes} + \text{environmental fluctuations}

Biosensor Design

Environmental Sensors

Two-Component Systems

\text{Sensor kinase} + \text{Signal} \rightleftharpoons \text{Phosphorylated sensor} \rightarrow \text{Response regulator phosphorylation}

\frac{d[R-P]}{dt} = k_{phos} [SK-P] [R] - k_{dephos} [R-P] - \delta_{R-P} [R-P]

Transcriptional Reporters

\text{Promoter}_{sensor} \rightarrow \text{Reporter gene} (e.g., GFP, RFP, luciferase)

\text{Output signal} = f(\text{analyte concentration}, \text{sensitivity}, \text{dynamic range})

Computational Tools in Synthetic Biology

Design Software

CAD Software for Biology

SBOL (Synthetic Biology Open Language): Standard for representing designs
SBML (Systems Biology Markup Language): Mathematical models
CellDesigner: Pathway visualization
Cello: Logic circuit to DNA compilation

Simulation Approaches

Ordinary Differential Equations (ODEs)

\frac{d\mathbf{x}}{dt} = \mathbf{f}(\mathbf{x}, \mathbf{u}, t; \theta)

Where $\mathbf{x}$ is state variables, $\mathbf{u}$ is inputs, and $\theta$ is parameters.

Stochastic Simulation

\text{Chemical Langevin Equation}: d\mathbf{x} = \mathbf{f}(\mathbf{x})dt + \mathbf{G}(\mathbf{x})d\mathbf{W}

\text{Gillespie algorithm}: \tau = \frac{1}{a_0} \ln\left(\frac{1}{r_1}\right)

\mu = \text{smallest integer } j \text{ such that } \sum_{i=1}^{j} a_i > r_2 a_0

Where $r_1, r_2$ are random numbers, $a_i$ are propensity functions.

Metabolic Pathway Optimization

Objective Functions

Common Goals

Maximize flux: $\max v_{product}$
Maximize yield: $\max \frac{v_{product}}{v_{substrate}}$
Minimize byproducts: $\min \sum_i v_{byproduct_i}$
Maximize energy efficiency: $\max \frac{\text{ATP produced}}{\text{substrate consumed}}$

Constraint-Based Analysis

Thermodynamic Constraints

\sum_i \nu_i \Delta G_f^0 + RT \ln(Q) < 0

Where $\nu_i$ are stoichiometric coefficients, $\Delta G_f^0$ are formation energies, and $Q$ is reaction quotient.

Capacity Constraints

v_i \leq k_{cat,i}^{eff} [E_i]

Where $k_{cat,i}^{eff}$ is effective turnover number considering cofactors and regulation.

Applications in Biotechnology

Pharmaceutical Production

Antibiotic Synthesis

\text{Acetyl-CoA} \xrightarrow{\text{Polyketide synthases}} \text{Polyketides} \xrightarrow{\text{Modifications}} \text{Antibiotics}

\text{Flux objective}: \max \text{antibiotic flux} \text{ subject to } \sum_i \text{ATP}_i \leq \text{ATP budget}

Biofuel Production

Isoprenoid Pathways

\text{Acetyl-CoA} \xrightarrow{\text{MVA pathway}} \text{IPP/DMAPP} \xrightarrow{\text{Terpene synthases}} \text{Terpenoids}

\text{Biosynthetic pathway}: n \text{Acetyl-CoA} + (3n-1) \text{ATP} + \text{NADPH} \rightarrow \text{Terpene}_n + \text{byproducts}

Chemical Production

Platform Chemicals

\text{Glucose} \xrightarrow{\text{Engineered pathway}} \text{Muconic acid} \rightarrow \text{Adipic acid} \rightarrow \text{Nylon precursors}

\text{Yield}: Y_{chemical/glucose} = \frac{\text{mol chemical produced}}{\text{mol glucose consumed}}

Safety and Containment

Biocontainment Strategies

Genetic Containment

Auxotrophy: Dependence on non-natural amino acids
Kill switches: Programmed cell death circuits
Orthogonal translation: Incorporation of unnatural amino acids

Chemical Containment

\text{Evolutionary safety}: \text{fitness}_\text{wild-type} > \text{fitness}_\text{engineered}

\text{Escape probability} \propto \text{mutation rate}^n \times \text{selection advantage}^m

Risk Assessment

Biosafety Levels

BSL-1: Minimal risk organisms
BSL-2: Moderate risk organisms
BSL-3: High risk pathogens
BSL-4: Dangerous pathogens

\text{Risk} = \text{Likelihood} \times \text{Severity} \times \text{Exposure potential}

Standards and Protocols

Synthetic Biology Standards

Data Standards

SBOL: Synthetic Biology Open Language
SBML: Systems Biology Markup Language
BioPAX: Biological Pathway Exchange
FAIR principles: Findable, Accessible, Interoperable, Reusable

Quality Control

\text{Accuracy} = \frac{\text{correct assemblies}}{\text{total assemblies}}

\text{Efficiency} = \frac{\text{functional circuits}}{\text{total circuits}}

Real-World Application: Biofuel Production Pathway Engineering

Metabolic engineering can optimize cellular pathways to produce biofuels efficiently.

Biofuel Pathway Analysis

# Metabolic pathway engineering for biofuel production
pathway_params = {
    'target_product': 'isobutanol',
    'precursor': 'pyruvate',
    'pathway_steps': 3,  # Number of enzymatic steps
    'theoretical_yield': 0.19,  # g/g glucose (max theoretical)
    'consumed_pathway': 'central_carbon_metabolism',
    'engineered_pathway': 'isobutanol_synthesis',
    'carbon_source': 'glucose',
    'max_specific_growth_rate': 0.7,  # 1/h
    'substrate_uptake_rate': 10,  # mmol/gDW/h
    'product_titer': 5.2,  # g/L
    'productivity': 0.2,  # g/L/h
    'biomass_yield': 0.35  # g/g glucose
}

# Calculate pathway efficiency
# Stoichiometric analysis of isobutanol synthesis
# Glucose + 2NAD+ + 2CoA → 2Isobutanol + 2NADH + 2CoASH + 2ATP

# Calculate carbon conservation
glucose_carbons = 6  # Carbons in glucose
isobutanol_carbons = 4  # Carbons in isobutanol
theoretical_carbon_yield = (2 * isobutanol_carbons) / glucose_carbons  # 8/6 = 1.33 moles isobutanol per mole glucose

# Calculate actual vs. theoretical performance
actual_yield = pathway_params['product_titer'] / (pathway_params['substrate_uptake_rate'] * pathway_params['productivity'] / pathway_params['substrate_uptake_rate'])
theoretical_yield = pathway_params['theoretical_yield']

yield_efficiency = actual_yield / theoretical_yield

# Calculate metabolic burden
# Estimate reduction in growth due to pathway expression
metabolic_burden = 0.15  # Fraction reduction in growth rate (15% burden estimate)
adjusted_growth_rate = pathway_params['max_specific_growth_rate'] * (1 - metabolic_burden)

# Calculate pathway flux requirements
# For desired productivity of 0.2 g/L/h of isobutanol (MW 74.12 g/mol)
product_flux_mol = pathway_params['productivity'] / 74.12  # mol/L/h
glucose_flux_mol = product_flux_mol / theoretical_carbon_yield  # Required glucose flux based on stoichiometry
glucose_flux_mmol = glucose_flux_mol * 1000  # mmol/L/h

# Calculate cofactor requirements
# Each isobutanol molecule requires NADH and ATP
nadh_requirement = 2  # moles NADH per mole isobutanol
atp_requirement = 2   # moles ATP per mole isobutanol

# Calculate cofactor burden
nadh_demand = product_flux_mol * nadh_requirement  # mol/L/h
atp_demand = product_flux_mol * atp_requirement    # mol/L/h

# Assess cellular capacity
atp_regeneration_capacity = 20  # mmol/gDW/h (typical cellular capacity)
nadh_oxidation_capacity = 15    # mmol/gDW/h (typical cellular capacity)

# Calculate limiting factors
atp_burden_fraction = (atp_demand * 1000) / atp_regeneration_capacity  # Fraction of ATP capacity used
nadh_burden_fraction = (nadh_demand * 1000) / nadh_oxidation_capacity  # Fraction of NADH capacity used

# Calculate energy cost
# Maintenance energy for pathway expression
pathway_maintenance = 2.5  # mmol ATP/gDW/h (estimated cost)

# Overall efficiency metrics
energy_efficiency = (pathway_params['productivity'] / pathway_params['substrate_uptake_rate']) / (theoretical_yield * 1.0)  # Adjusted for ATP costs
production_efficiency = pathway_params['productivity'] / (pathway_params['substrate_uptake_rate'] * 0.85)  # Account for metabolic burden

print(f"Biofuel pathway engineering analysis for {pathway_params['target_product']}:")
print(f"  Theoretical carbon yield: {theoretical_carbon_yield:.2f} mol/mol glucose")
print(f"  Actual yield: {actual_yield:.3f} g/g glucose")
print(f"  Yield efficiency: {yield_efficiency:.3f} ({yield_efficiency*100:.1f}%)")
print(f"  Adjusted growth rate: {adjusted_growth_rate:.3f} h⁻¹")
print(f"  Required glucose flux: {glucose_flux_mmol:.2f} mmol/L/h")
print(f"  NADH demand: {nadh_demand*1000:.2f} mmol/L/h ({nadh_burden_fraction*100:.1f}% of cellular capacity)")
print(f"  ATP demand: {atp_demand*1000:.2f} mmol/L/h ({atp_burden_fraction*100:.1f}% of cellular capacity)")
print(f"  Energy efficiency: {energy_efficiency:.3f}")
print(f"  Production efficiency: {production_efficiency:.3f}")

# Optimization recommendations
if yield_efficiency < 0.5:
    optimization_priority = "High - significant pathway optimization needed"
elif atp_burden_fraction > 0.8 or nadh_burden_fraction > 0.8:
    optimization_priority = "Medium - cofactor balancing required"
else:
    optimization_priority = "Low - pathway performing reasonably well"

print(f"  Optimization priority: {optimization_priority}")

# Evaluate alternative strategies
alternative_pathways = {
    'mevalonate_pathway': {'yield': 0.15, 'atp_cost': 3, 'complexity': 'high'},
    'direct_conversion': {'yield': 0.18, 'atp_cost': 1.5, 'complexity': 'medium'},
    'combined_pathway': {'yield': 0.20, 'atp_cost': 2.5, 'complexity': 'high'}
}

# Calculate best alternative
best_alternative = max(alternative_pathways.items(), 
                      key=lambda x: x[1]['yield'] / (1 + x[1]['atp_cost']/5))  # Weighted by ATP cost

print(f"  Best alternative pathway: {best_alternative[0]} (score: {best_alternative[1]['yield'] / (1 + best_alternative[1]['atp_cost']/5):.3f})")

# Metabolic engineering targets
potential_targets = []
if nadh_burden_fraction > 0.5:
    potential_targets.append("NADH regeneration optimization")
if atp_burden_fraction > 0.5:
    potential_targets.append("ATP regeneration optimization")
if yield_efficiency < 0.6:
    potential_targets.append("Pathway optimization")

print(f"  Recommended engineering targets: {potential_targets}")

Pathway Optimization

Designing metabolic pathways for optimal product yield.

Your Challenge: Genetic Circuit Design

Design a synthetic genetic circuit that exhibits specific dynamic behavior and analyze its response characteristics.

Goal: Engineer a genetic toggle switch or oscillator and analyze its stability and response to perturbations.

Circuit Design Parameters

import math

# Genetic circuit design - toggle switch
toggle_params = {
    'promoter_strength_A': 2.5,  # Transcription rate constant (relative units)
    'promoter_strength_B': 2.0,  # Transcription rate constant (relative units)
    'rbs_strength_A': 1.8,       # Translation rate constant
    'rbs_strength_B': 1.5,       # Translation rate constant
    'protein_degradation_A': 0.1, # Degradation rate constant (h⁻¹)
    'protein_degradation_B': 0.12, # Degradation rate constant (h⁻¹)
    'repression_constant_AB': 10,   # Kd for A repressing B promoter
    'repression_constant_BA': 15,   # Kd for B repressing A promoter
    'cooperativity': 2,           # Hill coefficient (n)
    'inducer_concentration': 0,   # Inducer present initially
    'initial_state_A': 10,        # Initial concentration (arbitrary units)
    'initial_state_B': 1          # Initial concentration (arbitrary units)
}

# Simulate the toggle switch behavior using differential equations
def simulate_toggle(toggle_params, time_points):
    """Simulate toggle switch dynamics"""
    results = []
    dt = 0.01  # time step
    
    # Initialize states
    A = toggle_params['initial_state_A']
    B = toggle_params['initial_state_B']
    
    for t in time_points:
        # Calculate repression terms using Hill equation
        repression_B_by_A = toggle_params['repression_constant_AB']**toggle_params['cooperativity'] / \
                           (toggle_params['repression_constant_AB']**toggle_params['cooperativity'] + A**toggle_params['cooperativity'])
        
        repression_A_by_B = toggle_params['repression_constant_BA']**toggle_params['cooperativity'] / \
                           (toggle_params['repression_constant_BA']**toggle_params['cooperativity'] + B**toggle_params['cooperativity'])
        
        # Calculate dynamics
        dA_dt = toggle_params['promoter_strength_A'] * toggle_params['rbs_strength_A'] * repression_A_by_B - \
                toggle_params['protein_degradation_A'] * A
        
        dB_dt = toggle_params['promoter_strength_B'] * toggle_params['rbs_strength_B'] * repression_B_by_A - \
                toggle_params['protein_degradation_B'] * B
        
        # Update states
        A += dA_dt * dt
        B += dB_dt * dt
        
        results.append({'time': t, 'protein_A': A, 'protein_B': B})
    
    return results

# Run simulation
time_range = [i/10 for i in range(0, 500)]  # 0 to 50 hours, 0.1 h resolution
simulation_result = simulate_toggle(toggle_params, time_range)

# Analyze steady states
final_A = simulation_result[-1]['protein_A']
final_B = simulation_result[-1]['protein_B']

# Determine which state is dominant
if final_A > final_B:
    dominant_state = "A ON / B OFF"
    stability = "Stable A state"
elif final_B > final_A:
    dominant_state = "B ON / A OFF"
    stability = "Stable B state"
else:
    dominant_state = "Bistable equilibrium"
    stability = "Metastable - sensitive to initial conditions"

# Calculate relaxation time (time to reach 90% of final value)
target_A_90 = toggle_params['initial_state_A'] + 0.9 * (final_A - toggle_params['initial_state_A'])
target_B_90 = toggle_params['initial_state_B'] + 0.9 * (final_B - toggle_params['initial_state_B'])

# Find relaxation time
relaxation_time = 0
for i, result in enumerate(simulation_result):
    if (abs(result['protein_A'] - final_A) < abs(final_A - toggle_params['initial_state_A']) * 0.1 and
        abs(result['protein_B'] - final_B) < abs(final_B - toggle_params['initial_state_B']) * 0.1):
        relaxation_time = result['time']
        break

# Calculate sensitivity to perturbation
# Simulate with temporary induction of protein A
induced_params = toggle_params.copy()
induced_params['initial_state_A'] = 20  # Double initial A
induced_result = simulate_toggle(induced_params, time_range)

# Analyze memory retention
induced_final_A = induced_result[-1]['protein_A']
induced_final_B = induced_result[-1]['protein_B']

# Check if state was flipped
state_flipped = (final_A > final_B and induced_final_B > induced_final_A) or \
                (final_B > final_A and induced_final_A > induced_final_B)

# Calculate bistability score (measure of toggle stability)
# Compare energy landscape of two possible states
# In a perfect toggle, two stable states should exist with high energy barrier between
if state_flipped:
    bistability_score = 0.9
elif abs(final_A - final_B) > 5:  # Large difference indicates stability in one state
    bistability_score = 0.7
else:
    bistability_score = 0.4  # Similar levels indicate weak bistability

Design and analyze a genetic toggle switch circuit with appropriate parameters.

Hint:

Use Hill equation kinetics to model repression
Analyze steady-state behavior and stability
Consider the effect of cooperativity and repression strength
Evaluate response to perturbations and memory retention

# TODO: Calculate circuit analysis results
steady_state_A = 0      # Protein A concentration at steady state
steady_state_B = 0      # Protein B concentration at steady state
dominant_state = ""     # A-ON/B-OFF or B-ON/A-OFF
relaxation_time = 0     # Time to reach steady state (hours)
bistability_score = 0   # Metric for toggle stability (0-1 scale)
switching_efficiency = 0 # Ability to flip between states (0-1 scale)

# Calculate results from simulation above
steady_state_A = final_A
steady_state_B = final_B
dominant_state = dominant_state
relaxation_time = relaxation_time
bistability_score = bistability_score

# Calculate switching efficiency based on flip experiment
if state_flipped:
    switching_efficiency = 0.9
elif abs(initial_state_A - induced_params['initial_state_A']) > 5:  # Significant perturbation didn't cause flip
    switching_efficiency = 0.3
else:
    switching_efficiency = 0.6  # Moderate switching capability

# Print results
print(f"Toggle switch analysis results:")
print(f"  Steady state A: {steady_state_A:.2f} units")
print(f"  Steady state B: {steady_state_B:.2f} units")
print(f"  Dominant state: {dominant_state}")
print(f"  Relaxation time: {relaxation_time:.2f} hours")
print(f"  Bistability score: {bistability_score:.2f}")
print(f"  Switching efficiency: {switching_efficiency:.2f}")

# Circuit assessment
if bistability_score > 0.8 and switching_efficiency > 0.7:
    circuit_quality = "Excellent toggle switch - stable states with good switching"
elif bistability_score > 0.6:
    circuit_quality = "Good toggle - stable but may need optimization for switching"
elif switching_efficiency > 0.8:
    circuit_quality = "Good switching - but may lack stability"
else:
    circuit_quality = "Poor performance - needs significant design improvements"
    
print(f"  Circuit quality: {circuit_quality}")

# Design recommendations
recommendations = []
if toggle_params['cooperativity'] < 2:
    recommendations.append("Increase cooperativity (n) for sharper switching")
if toggle_params['repression_constant_AB'] < 5 or toggle_params['repression_constant_BA'] < 5:
    recommendations.append("Increase repression strength for better bistability")
if toggle_params['protein_degradation_A'] != toggle_params['protein_degradation_B']:
    recommendations.append("Balance degradation rates for symmetric switching")
    
print(f"  Design recommendations: {recommendations}")

# Biological implications
if dominant_state == "Bistable equilibrium":
    biological_implication = "Circuit may be useful for cellular memory applications"
elif dominant_state.startswith("A ON"):
    biological_implication = "Circuit favors A state - suitable for permanent ON switch"
else:
    biological_implication = "Circuit favors B state - suitable for permanent ON switch"
    
print(f"  Biological implication: {biological_implication}")

How would you modify the genetic circuit design to create an oscillator instead of a toggle switch?