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Fluorophore Photophysics

This page covers the photophysical models in SMLMSim and how they're used to generate realistic blinking behavior for SMLM simulations.

Overview

Fluorophores in single-molecule microscopy exhibit complex photophysical behavior, including:

  • Stochastic switching between fluorescent (ON) and non-fluorescent (OFF) states
  • Varying photon emission rates
  • Photobleaching (permanent transition to a dark state)

SMLMSim models these behaviors using kinetic state models and stochastic simulation of state transitions.

Fluorophore Models

GenericFluor

The main fluorophore model in SMLMSim is the GenericFluor type:

using SMLMSim

# Define a two-state fluorophore using the positional constructor
# Note: q matrix already had correct diagonal elements, just removed γ=
fluor = GenericFluor(10000.0, [-5.0 5.0; 10.0 -10.0])

# ... rest of the example ...

Parameters:

  • γ: Photon emission rate in Hz (photons per second)
  • q: State transition rate matrix where q[i,j] is the transition rate from state i to j (in s⁻¹)

By convention, state 1 is the fluorescent (ON) state, and other states are non-fluorescent (OFF).

Kinetic Models

Continuous Time Markov Chain

Fluorophore state transitions are modeled using a Continuous Time Markov Chain (CTMC):

# Create a CTMC for a two-state system
# State 1: ON (fluorescent), State 2: OFF (dark)
q = [-5 5; 10 -10]  # Units: s⁻¹
simulation_time = 10.0  # seconds
initial_state = 2  # Start in dark state

ctmc = CTMC(q, simulation_time, initial_state)

Understanding the Rate Matrix

The transition rate matrix q represents the rates at which the system transitions between states:

  • q[i,j] (i≠j): Rate of transition from state i to state j
  • q[i,i]: Negative sum of all outgoing rates from state i

For example, in a two-state system:

q = [-k_off  k_off;
      k_on   -k_on]

Where:

  • k_off: Rate of transitioning from ON (state 1) to OFF (state 2)
  • k_on: Rate of transitioning from OFF (state 2) to ON (state 1)
  • Diagonal elements are negative sums of their respective rows

The CTMC simulates transitions between states by:

  1. Sampling the time until the next transition (exponentially distributed with rate -q[current,current])
  2. Sampling the next state with probabilities proportional to the transition rates

The CTMC provides a complete trajectory of state transitions:

# Get state at a specific time
state_at_1s = get_state(ctmc, 1.0)

# Get next state transition after a specific time
next_state, transition_time = get_next(ctmc, 0.5)

Intensity Traces

To simulate the fluorescence signal over time, SMLMSim integrates photon emission during ON states:

# Generate intensity trace for 1000 frames at 50 fps
fluor = GenericFluor(γ=10000.0, q=[-5 5; 10 -10])
photons = intensity_trace(fluor, 1000, 50.0)

The intensity_trace function:

  1. Simulates the CTMC state trajectory
  2. Integrates photon emission (rate γ) during ON states
  3. Accumulates photons within each frame's exposure time

Common Photophysical Models

Two-State Model

The simplest model contains just ON and OFF states:

# Two-state model (ON ⟷ OFF)
# kon = 5 s⁻¹, koff = 10 s⁻¹
fluor = GenericFluor(
    γ=1e4,                # 10,000 photons/s
    q=[-10 10; 5 -5]      # [ON→OFF; OFF→ON] rates in s⁻¹
)

This produces exponentially distributed ON and OFF times.

Three-State Model with Bleaching

For more realistic behavior including photobleaching:

# Three-state model (ON ⟷ OFF → BLEACHED)
# State 1: ON, State 2: OFF, State 3: BLEACHED
fluor = GenericFluor(
    γ=1e4,
    q=[-10.1 10 0.1; 5 -5 0; 0 0 0]  # Note: state 3 is absorbing (no outgoing transitions)
)

The third state is irreversible (absorbing state), representing photobleaching.

Using Photophysics in Simulations

The simulate() function integrates these photophysical models automatically:

# Simulation with custom fluorophore
camera = IdealCamera(128, 128, 0.1)
fluor = GenericFluor(γ=2e4, q=[-20 20; 5 -5])

smld_true, smld_model, smld_noisy = simulate(
    molecule=fluor,
    framerate=50.0,     # frames per second
    nframes=2000,       # total frames
    minphotons=100,     # detection threshold
    camera=camera
)

Behind the scenes, this uses the kinetic_model() function to apply the photophysical model to each emitter position.

Photophysical Parameters and Duty Cycle

The photophysical properties determine the "duty cycle" - the fraction of time a fluorophore is in the ON state:

For a two-state model, the duty cycle is:

duty_cycle = kon / (kon + koff)

Where:

  • kon is the OFF→ON rate (q[2,1] in the rate matrix)
  • koff is the ON→OFF rate (q[1,2] in the rate matrix)

Typical duty cycles for SMLM fluorophores range from 0.0001 to 0.01.