Issue: Enhance `Enzyme` Class to Model Signal Transduction Cascades and Feedback Loops

Summary

The current Enzyme class lacks the capability to accurately model signal transduction pathways, especially concerning activation cascades and feedback loops. To make the class more realistic and accurate for biochemical simulations, we propose a series of enhancements that will allow it to:

Represent activation states and participate in cascades.
Incorporate positive and negative feedback mechanisms.
Improve kinetic modeling with advanced catalytic processes.
Simulate time-dependent changes in enzyme activities and metabolite concentrations.

Proposed Enhancements

1. Implement Activation States and Cascades

Activation State: Introduce an active attribute to represent whether the enzyme is active or inactive.
Activation Methods: Add activate() and deactivate() methods to manage the enzyme's state.
Cascades: Allow enzymes to activate or deactivate other enzymes via a regulate_enzyme() method, simulating cascade effects.
Downstream Enzymes: Include a downstream_enzymes list to hold enzymes that are regulated by the current enzyme.

2. Incorporate Feedback Mechanisms

Feedback in calculate_rate(): Modify the method to account for feedback from downstream metabolites or products.
Positive and Negative Feedback: Implement mechanisms where metabolite concentrations can enhance or inhibit enzyme activity.

3. Enhance the Catalytic Process

catalyze() Method: Define a method that updates metabolite concentrations over time, considering the reaction's stoichiometry.
Multiple Substrates and Products: Extend support for reactions involving multiple substrates and products.

4. Improve Kinetic Modeling

Inhibition Types: Refine inhibition modeling to include competitive and non-competitive inhibition.
Cooperative Binding: Introduce cooperative effects using models like the Hill equation for more complex kinetics.

5. Add Time Dynamics

Time-Dependent Simulations: Incorporate a time step dt in the catalyze() method to simulate dynamic changes over time.

Proposed Implementation

Here is the updated Enzyme class incorporating the proposed enhancements:

from typing import Dict, List, Optional

from .metabolite import Metabolite

class Enzyme:
    """
    Represents an enzyme that can catalyze reactions and participate in signal transduction pathways.

    Parameters
    ----------
    name : str
        The name of the enzyme.
    k_cat : float
        The catalytic constant (turnover number) of the enzyme.
    k_m : Dict[str, float]
        The Michaelis constants for multiple substrates.
    inhibitors : Dict[str, float], optional
        The inhibition constants for multiple inhibitors.
    activators : Dict[str, float], optional
        The activation constants for multiple activators.
    active : bool, optional
        The current activation state of the enzyme. Defaults to True.
    downstream_enzymes : List['Enzyme'], optional
        Enzymes that are activated or deactivated by this enzyme.

    Methods
    -------
    activate()
        Activates the enzyme.
    deactivate()
        Deactivates the enzyme.
    regulate_enzyme(target_enzyme: 'Enzyme', action: str)
        Activates or deactivates a target enzyme.
    calculate_rate(metabolites: Dict[str, Metabolite]) -> float
        Calculates the rate of the reaction catalyzed by the enzyme.
    catalyze(metabolites: Dict[str, Metabolite], dt: float)
        Simulates the catalysis over a time step dt.
    """

    def __init__(
        self,
        name: str,
        k_cat: float,
        k_m: Dict[str, float],
        inhibitors: Optional[Dict[str, float]] = None,
        activators: Optional[Dict[str, float]] = None,
        active: bool = True,
        downstream_enzymes: Optional[List['Enzyme']] = None,
    ):
        self.name = name
        self.k_cat = k_cat
        self.k_m = k_m
        self.inhibitors = inhibitors or {}
        self.activators = activators or {}
        self.active = active
        self.downstream_enzymes = downstream_enzymes or []

    def activate(self):
        """Activates the enzyme."""
        self.active = True

    def deactivate(self):
        """Deactivates the enzyme."""
        self.active = False

    def regulate_enzyme(self, target_enzyme: 'Enzyme', action: str):
        """
        Activates or deactivates a target enzyme.

        Parameters
        ----------
        target_enzyme : Enzyme
            The enzyme to regulate.
        action : str
            The action to perform ('activate' or 'deactivate').
        """
        if action == 'activate':
            target_enzyme.activate()
        elif action == 'deactivate':
            target_enzyme.deactivate()

    def calculate_rate(self, metabolites: Dict[str, Metabolite]) -> float:
        if not self.active:
            return 0.0  # Inactive enzymes do not catalyze reactions

        rate = self.k_cat

        # Michaelis-Menten kinetics
        for substrate, k_m in self.k_m.items():
            metabolite = metabolites.get(substrate)
            if metabolite is None:
                return 0.0  # Required substrate is missing
            conc = metabolite.quantity
            rate *= conc / (k_m + conc)

        # Inhibition effects
        for inhibitor, k_i in self.inhibitors.items():
            metabolite = metabolites.get(inhibitor)
            if metabolite:
                conc = metabolite.quantity
                rate /= (1 + conc / k_i)

        # Activation effects
        for activator, k_a in self.activators.items():
            metabolite = metabolites.get(activator)
            if metabolite:
                conc = metabolite.quantity
                rate *= (1 + conc / k_a)

        # Feedback regulation (example for negative feedback)
        # You can customize this section based on specific feedback mechanisms
        # Example: Product inhibition
        # for product_name in self.products:
        #     product = metabolites.get(product_name)
        #     if product:
        #         conc = product.quantity
        #         rate /= (1 + conc / feedback_constant)

        return rate

    def catalyze(self, metabolites: Dict[str, Metabolite], dt: float):
        """
        Simulates the catalysis over a time step dt.

        Parameters
        ----------
        metabolites : Dict[str, Metabolite]
            The metabolites involved in the reaction.
        dt : float
            The time step for the simulation.
        """
        rate = self.calculate_rate(metabolites)
        if rate == 0.0:
            return  # No reaction occurs

        # Update metabolite concentrations
        # Assuming a simple reaction: Substrate -> Product
        # Modify this section based on the actual reaction stoichiometry
        substrates = list(self.k_m.keys())
        if not substrates:
            return

        # For simplicity, assume one substrate and one product
        substrate_name = substrates[0]
        substrate = metabolites.get(substrate_name)
        product_name = f"{substrate_name}_product"  # Define how to get product name
        product = metabolites.get(product_name)

        delta = rate * dt
        substrate.quantity = max(substrate.quantity - delta, 0.0)
        if product:
            product.quantity += delta
        else:
            # Create new product if it doesn't exist
            metabolites[product_name] = Metabolite(name=product_name, quantity=delta)

        # Trigger downstream enzymes in the cascade
        for enzyme in self.downstream_enzymes:
            self.regulate_enzyme(enzyme, 'activate')

Additional Considerations

Stoichiometry

Multiple Substrates and Products: Modify the catalyze() method to handle reactions with multiple substrates and products.
Stoichiometric Coefficients: Use coefficients to accurately update metabolite quantities based on reaction stoichiometry.

Advanced Kinetics

Inhibition Types: Implement different inhibition models such as competitive and non-competitive inhibition by adjusting rate equations.

Cooperative Binding: Use the Hill equation to model cooperative binding effects:

# Example for cooperative binding
n = 2  # Hill coefficient
conc = metabolite.quantity
rate *= conc**n / (k_m + conc**n)

Simulation Framework

Time Steps: Incorporate a simulation loop that updates enzyme states and metabolite concentrations over discrete time steps.

Example Simulation Loop:

def simulate_pathway(enzymes: List[Enzyme], metabolites: Dict[str, Metabolite], total_time: float, dt: float):
  time = 0.0
  while time < total_time:
      for enzyme in enzymes:
          enzyme.catalyze(metabolites, dt)
      time += dt

Error Handling

Negative Quantities: Add checks to prevent metabolite quantities from becoming negative.
Missing Metabolites: Handle cases where required substrates or products are missing gracefully.

Example Usage

Here's an example of how the enhanced Enzyme class can be used in a simulation:

from .enzyme import Enzyme
from .metabolite import Metabolite

# Define metabolites
metabolites = {
    'A': Metabolite(name='A', quantity=100.0),
    'B': Metabolite(name='B', quantity=0.0),
    'C': Metabolite(name='C', quantity=0.0),
}

# Define enzymes
enzyme1 = Enzyme(
    name='Enzyme1',
    k_cat=1.0,
    k_m={'A': 10.0},
    downstream_enzymes=[],
)

enzyme2 = Enzyme(
    name='Enzyme2',
    k_cat=1.0,
    k_m={'B': 10.0},
    active=False,  # Initially inactive
    downstream_enzymes=[],
)

# Enzyme1 activates Enzyme2
enzyme1.downstream_enzymes.append(enzyme2)

# List of enzymes in the pathway
enzymes = [enzyme1, enzyme2]

# Simulate the pathway
def simulate_pathway(enzymes, metabolites, total_time, dt):
    time = 0.0
    while time < total_time:
        for enzyme in enzymes:
            enzyme.catalyze(metabolites, dt)
        time += dt

simulate_pathway(enzymes, metabolites, total_time=100.0, dt=1.0)

Benefits

By implementing these enhancements, the Enzyme class will be more capable of:

Simulating complex biochemical pathways with activation cascades.
Modeling feedback loops that are essential in biological regulation.
Providing a foundation for dynamic simulations of metabolite concentrations over time.

References

Michaelis-Menten Kinetics: Wikipedia
Hill Equation: Wikipedia
Signal Transduction Pathways: Alberts et al., Molecular Biology of the Cell

Tasks

[x] Update the Enzyme class with the proposed enhancements.
[x] Modify existing unit tests or write new ones to cover the new functionality.
[x] Update documentation to reflect changes.
[x] Perform simulations to validate the enhanced model.

Note: Please adjust the code and examples as needed to fit the specific context and requirements of your project.: Enhance Enzyme Class to Model Signal Transduction Cascades and Feedback Loops