Unified Phase Model

This module provides a unified framework that combines all aspects of the microscopic gating model into a single coherent interface.

Transport Type

class microscopic_gating.unified_phase.TransportType(value)

Bases: Enum

An enumeration.

ENHANCEMENT = 1

SUPPRESSION = 2

CRITICAL = 3

Unified Control Parameters

class microscopic_gating.unified_phase.UnifiedControlParameters(beta, kappa0, x_c, chi_kappa, lambda0, epsilon_eff)

Bases: object

Unified control parameters (S5) for the minimal competition form.

Definitions

A = beta * (1/2) * kappa0 * x_c^2 * chi_kappa Gamma = lambda0 * (1 - exp(-beta * epsilon_eff))

transport type: - ENHANCEMENT if A > Gamma - SUPPRESSION if A < Gamma - CRITICAL if A == Gamma (within tolerance)

beta: float

kappa0: float

x_c: float

chi_kappa: float

lambda0: float

epsilon_eff: float

A()

Return type:

float

Gamma()

Return type:

float

transport_type(tol=1e-12)

Parameters:

tol (float) –

Return type:

TransportType

__init__(beta, kappa0, x_c, chi_kappa, lambda0, epsilon_eff)

Parameters:

• beta (float) –

• kappa0 (float) –

• x_c (float) –

• chi_kappa (float) –

• lambda0 (float) –

• epsilon_eff (float) –

Return type:

None

Parameters:

• beta (float) –

• kappa0 (float) –

• x_c (float) –

• chi_kappa (float) –

• lambda0 (float) –

• epsilon_eff (float) –

Unified Model

class microscopic_gating.unified_phase.UnifiedModel(renorm, control, D_star, tau_star)

Bases: object

Unified diffusion model:

Deff(phi) = D_star * exp[(A - Gamma) * G(phi)]

Here G(phi) is obtained from the renormalizer’s gating function.

Parameters:

• renorm (GProvider) –

• control (UnifiedControlParameters) –

• D_star (float) –

• tau_star (float) –

renorm: GProvider

control: UnifiedControlParameters

D_star: float

tau_star: float

Deff(phi)

Parameters:

phi (ndarray) –

Return type:

ndarray

__init__(renorm, control, D_star, tau_star)

Parameters:

• renorm (GProvider) –

• control (UnifiedControlParameters) –

• D_star (float) –

• tau_star (float) –

Return type:

None

Suppression Capture Island

class microscopic_gating.unified_phase.SuppressionCaptureIsland(boundaries, control, tau_star)

Bases: object

Capture island intervals for suppression-type (Gamma > A) using rate-averaged window.

Implements the lambda window via:

lambda_± = ln(tau_± / tau_star) / (1 - exp(-beta * epsilon_eff))

Then map to G-band via g_± = lambda_± / lambda0 and invert to phi intervals using DomePhaseBoundaries.

Parameters:

• boundaries (DomePhaseBoundaries) –

• control (UnifiedControlParameters) –

• tau_star (float) –

boundaries: DomePhaseBoundaries

control: UnifiedControlParameters

tau_star: float

lambda_bounds(tau_net, tau_obs)

Parameters:

• tau_net (float) –

• tau_obs (float) –

Return type:

tuple[float, float]

concentration_intervals(tau_net, tau_obs)

Parameters:

• tau_net (float) –

• tau_obs (float) –

Return type:

list[tuple[float, float]]

__init__(boundaries, control, tau_star)

Parameters:

• boundaries (DomePhaseBoundaries) –

• control (UnifiedControlParameters) –

• tau_star (float) –

Return type:

None

Theory Background

The unified model integrates:

1. Adsorption - Langmuir or Hill isotherms

2. Gating - Symmetric or asymmetric binding

3. Statistics - Poisson bridge distributions

4. Transport - Escape rate averaging

5. Phase behavior - Capture island analysis

This provides a complete end-to-end model from molecular parameters to macroscopic transport properties.