Single Channel Kinetics

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The goal of QuB is to find a model and rate constants that describe your data. For any model, the likelihood optimizers can find the rate constants which maximize the likelihood of the data being generated by the model. To choose between model topologies, you can compare them by likelihood and histograms, and at different experimental conditions. You can also try an additive or exhaustive search of topologies.

Contents

Features

  • optimize using sampled or idealized data
  • correct for missed events
  • constrain rate constants to reduce the number of free parameters or impose detailed balance
  • fit data relaxing from known state(s) to equilibrium
  • "global fit" a model to multiple files at different conditions
  • distinguish two or more types of bursts and fit each type separately
  • build a model by merging two simpler models
  • build linear and star models automatically
  • fit all possible topologies
  • generate an MS Word report for an optimization run

Optimizers

MIL
works with idealized data
corrects for missed events shorter than tdead
can handle a multichannel patch
is very fast
MPL
works with sampled data
can distinguish conductance classes that differ only in noise (same amplitude)
MIP
works with idealized data
corrects for missed events shorter than Δt
can handle variable stimuli

All three can be found on the right-hand button bar, under Modeling. As always, right-click a button for options (common options). This text will focus on MIL.

Results

The results of the last several optimizer runs are listed in the Data window under "Results." The selected result is displayed in the Results window (View -> Results). By default only the most recent few results are kept, but you can right-click an entry in the Results list and Hold it indefinitely.

The [[Results#Summary|Summary] tab includes:

  • LL -- the log likelihood -- higher is better
  • Gradient -- the derivative of LL wrt each free parameter -- 0 is best
  • Iterations -- 1 means it failed to change the rates

The Histograms tab shows duration histograms for each conductance class, overlaid with the predicted distribution of events for this model and rates (PDF). The PDF has one exponential component for each state of that color. You can quickly check the goodness of fit by looking at

  • does the PDF have as many humps (components) as the histogram? If not, add or remove a state.
  • does the PDF fit the histogram closely? If not, try a different connection scheme.
  • For multi-file fits, there are histograms and PDFs for each file. Scroll through and make sure all of them fit well.

The Models tab shows the rate constants in the initial and final models. You can show one in the Model window by clicking its entry.

The Segments tab has a table of LL, gradient, rates, etc per data segment.

The Reports button generates a summary of the optimization as an MS Word document. You can use a standard report or customize what's included. Microsoft Office 2000 or newer required.

Model Building

In the best models, each state and connection has a physical meaning, perhaps inspired by outside structural discoveries. Lacking this knowledge we can still build a decent model:

  • starting with a two-state C-O model, run MIL and note the LL
  • repeatedly add a state, connect it somewhere, and run MIL
    • make the new rate constants small: MIL moves more easily toward larger rates.
    • add states while the PDFs have too few components
    • remove the last state if the change in LL was too small
How much is "too small"? Increasing the number of states or connections increases the number of free parameters that MIL can use to it the data and therefore will frequently increase the LL value by a few points, even if these states or connections are not really required to fit the data. Likewise, increasing the number of events increases the LL. Although it is well known that the LL value must be penalized by the number of free parameters, the means of doing this are still debated, and current opinions will not be discussed here. See the work of _____ Akaike and ______ Schwartz for further details. For the purposes of this tutorial, just keep in mind that when analyzing complex kinetic activity, you may want to make a judgment as to whether or not to include extra free parameters.

This procedure is automated in the Star and Chain buttons. You specify a minimum delta LL for it to keep a new state. Star connects all new states to your chosen state, while Chain connects them all in a line.

If you have built meaningful models, please share your insights here.

Kinetic Constraints

The optimizers can satisfy constraints on the rate constants. You can

  • fix a rate
  • maintain the ratio between two rates
  • maintain a cycle in detailed balance, where the product of forward rates equals the product of backward rates
  • maintain a cycle's imbalance, keeping a constant ratio between the forward and backward products
  • do any of the above with k1, the exponential/voltage-sensitivity rate constant

Enter constraints in the Model Properties dialog.

Uses of Constraints

Identical subunits
For a ligand-gated channel with two binding sites, the rate from 0-bound to 1-bound is twice the rate from 1-bound to 2-bound.
Cooperative effects
A two-channel model created by Modeling:Model Merge has constraints keeping both opening rates equal. If the channels in a patch are not independent, the MIL likelihood of the constrained model is lower than if you remove the constraints.
Runaway or known rate constants
A rate constant could misbehave during optimization, escaping to infinity or zero. You can fix it, solve the other rates, and hope it is less sensitive when the other rates are better.
Detailed balance
See if a cycle is in detailed balance by comparing its likelihood with and without the constraint
(see also How to satisfy cycle (im)balance)

Global Fitting

QuB can optimize a model using the data in multiple files. Each file can have its own experimental conditions, dead time, and even channel count. Use global fitting to develop a model of concentration, voltage or pressure sensitivity.

To begin, set up a model with P or Q dependence. Open all the data files. Choose Data Source: "file list". Right-click MIL. Put a checkmark next to each file and enter its parameter Values. Note that histogram PDFs and time constants will be different for each file.

If you suspect that some rate constants are changing with the ligand concentration, you may try the following trick. Check "Q" for all rate constants and set each k1 to a small nonzero value. Right-click MIL and set the "Voltage" of each file to the natural log of the experimental ligand concentration. Run MIL, and look at the final values for k1. A concentration-independent rate constant should have k1=0, and a concentration dependent one should have k1=1. If k1 is neither zero nor 1, then maybe you are using the wrong model.

Nonstationary Analysis

It has been shown that two models have the same max LL at equilibrium if they differ only in their connection scheme (e.g. C-O-C vs. C-C-O). However, they may be distinguished if we can record them from a known starting state. Set the "starting prob" of possible state(s) to 1 and the rest to 0.

Heterogeneous Bursts

Recordings often have long stretches of baseline punctuated by clusters (bursts) of channel activity. Clusters may come from different channels, which might for example have different combinations of mutant subunits. You can distinguish them statistically for separate analysis. Some clusters might overlap -- you can identify and discard messy multi-channel clusters.

The key step is Preprocessing:Chop Idl. You specify a "burst terminator" and it lists all stretches of data in which the closed events are shorter than that threshold. In the tutorial we use MIL to calculate the burst terminator.

After ChopIdl you can plot the clusters' stats, group them statistically or by eye into separate lists, and work with one list at a time.

Model Merge

Model merge builds a new model by combining two models. The rate constants are constrained to keep the two sub-models independent. You can relax constraints to model cooperative behavior, or "un-merge" solved rate constants back into the original models. (in the model's right-click menu)

Model Search

For a given number and coloring of states, model search runs MIL on all possible connection schemes. The results are shown in the Results window, including a list of all models, ranked by LL (or whatever column header you click). Click an item in the list to see it in the Model window. Due to the huge number of connection schemes, model search is limited to 6 states.

Tutorials


Prev: Tutorial:Single Channel Measurements Outline Next: Tutorial:Single Channel Kinetics
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