Calculate Energy Barriers for Ion Conduction

Overview and Methodology

What It Does

This tool estimates the free energy barriers that ions must overcome to traverse binding sites in a channel's selectivity filter (SF). It calculates these barriers based on the average dwell time of ions at each site, using a Boltzmann-like relationship between dwell duration and energy.

How It Works

• Ion Dwell Time ($\tau$):

  • Calculated as the mean number of consecutive frames an ion remains within the threshold distance of each binding site.

• Free Energy Barrier ($\Delta G$):

  • For each site, the relative free energy is calculated as:

  $[ \Delta G_i = RT \cdot \ln \left( \frac{\tau_i}{\Delta t} \right) ]$

  Where:

  • $\tau_i$: average dwell time at site $i$
  • $\Delta t$: simulation timestep (duration per frame)
  • $R$: gas constant ($1.987 \times 10^{-3}$ kcal/mol·K)
  • $T$: temperature in Kelvin (e.g., 310.15 K)

• Reference Normalization:

  • If outside_offset > 0, the average dwell time outside the SF is used as a reference ($\Delta G = 0$), and all barriers are shifted accordingly:

  $[ \Delta G_i^{\text{relative}} = \Delta G_i - \Delta G_{\text{outside}} ]$

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Configuration and Inputs

Prerequisites

• Requires a loaded trajectory aligned to the ion conduction axis.

Key Configuration Options

• Selections:

  • sf_sel: Atom selection for SF oxygen atoms (e.g., Kv: 5 residues; NaV: 4 acidic residues).
  • ion_sel: Ions to be tracked (e.g., resname POT for potassium).

• Binding Site Definitions:

  • site_mode:
    • Kv: Defines 5 sites from midpoints of oxygen atom layers.
    • Residue: Uses center of each residue’s oxygen atoms.
  • binding_site_names: Labels for each site, from intracellular to extracellular.

• Distance Threshold:

  • Defines proximity for ion–site assignment (e.g., 4.5 Å).

• Outside Reference:

  • outside_offset: Distance beyond extracellular-most site to define “outside SF” region for energy zero-point.

• Temperature:

  • Affects the magnitude of calculated $\Delta G$ via $RT$ scaling.

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Output

Plot

• Energy Barriers
  • File: SF_energy_barriers.png
  • X-axis: Transitions (e.g., S4➔S3, S3➔S2, etc.)
  • Y-axis: $\Delta G$ in kcal/mol

Console Output

• Ion Occupancy: Percent time each site is occupied.
• Dwell Time: Mean duration of occupancy at each site.
• Energy Barriers: $\Delta G$ values per site.
• Reference Energy (if outside region is included).

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Interpreting the Results

• Higher $\Delta G$:

  • Indicates a kinetic barrier; ions spend longer in that site before exiting.

• Lower or Negative $\Delta G$:

  • Easier escape from the site; rapid transitions observed.

• Flat $\Delta G$ Profile:

  • Uniform conduction — all sites have similar dwell times.

• Relative $\Delta G = 0$:

  • Defined at the outside region if outside_offset > 0.

Example:

If site dwell times increase from S4 to S0:

Site	$\tau$ (ns)	$\Delta G$ (kcal/mol)
S4	1.0	0.0
S3	1.5	+0.13
S2	2.5	+0.30
S1	4.0	+0.50
S0	5.0	+0.58

Interpretation: Strongest retention near S0 (extracellular), weakest at S4.

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Example Scenarios

Knock-On Mechanism

• Observation: Flat $\Delta G$ across inner sites; slight drop at exit site.
• Interpretation: Facilitated conduction via coordinated movement.

Pore Collapse

• Observation: Extremely high $\Delta G$ (>5 kcal/mol) at central site.
• Interpretation: Functional blockade or inactivation.

Entry Barrier

• Observation: First site (S4) has highest $\Delta G$.
• Interpretation: Channel resists ion entry from intracellular side.

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Usage Tips

• Timestep Accuracy:

  • Ensure time_total and step match trajectory metadata for proper $\Delta G$ values.

• Outside Region:

  • Use outside_offset to define a free-energy zero point (extracellular solvent where ions freely traverse), especially useful when comparing channels with varying SF depth.

• Filtering:

  • Adjust threshold_distance to balance site sensitivity vs. noise.

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