Modeling:MPL

From QuB

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MPL (Maximum Point Likelihood) optimizes the rate constants (with error limits) of a user-defined kinetic model using sampled data. The parameters of the model may be constrained according to detailed balance, fixed rate constants, and proportionality of rate constants. Multiple files, derived from data obtained at different voltages or concentrations can be analysed by MPL simlutaneously to estimate the voltage or concentration dependence (with error estimates) of all rate constants.

MPL maximizes the likelihood of the data at every data point, instead of every interval. The advantage of treating the data in this way, compared with interval methods, is that very busy data (data with residence times on the order of the sampling time) can be analyzed.

In this technique there are no missed events, but the penalty is that it takes longer than working with idealized data. MPL can actually solve the kinetics of data covered by noise. We recommend using it for estimating conductances, characterizing the noise of states, and for kinetic analysis of short pieces of busy data.

MPL can handle correlated noise. Enter the correlation coefficients in State and Class Properties.

MPL generates an idealization in the Data window, by picking $s t a t e t$ that maximizes $Γ s t a t e, t = F o r w a r d s t a t e, t * B a c k w a r d s t a t e, t$ . This idealization is used to show duration histograms in the Results window.

1 Theory
2 Properties
3 Results
4 See Also

Theory

MPL computes the log likelihood (LL) of idealized data given a model. Using the analytical derivative of LL w.r.t. the model parameters, it optimizes LL, finding the most likely rate constants. The LL is calculated with a forward-backward algorithm.

MPL is described in the following papers:

Qin,F., Auerbach,A. & Sachs,F. A Direct Optimization Approach to Hidden Markov Modeling for Single Channel Kinetics. Biophys. J. 2000 79: 1915-1927

Qin,F., Auerbach,A. & Sachs,F. Hidden Markov Modeling for Single Channel Kinetics with Filtering and Correlated Noise. Biophys. J. 2000 79: 1928-1944.

Properties

Data channel index	which A/D channel to work on, typically 0
Data source
Pre-process data	none: use raw data as displayed: use the same baseline correction and filtering as the Data display as such: apply the specified filter and baseline
Max iterations	at most how many times to repeat (calculate LL and gradient, modify parameters)
LL conv	stop if LL increases by less than this much
Grad conv	stop if all gradients are less than this much
Search limit	keep parameters within [initial / searchlimit, initial * searchlimit]
Restarts	if it stops after Max iterations, restart it this many times (works better than increasing Max iterations)
Max step	how much to change parameters each iteration. 1.0 is the natural step size; smaller numbers may be more reliable for sensitive models, but will converge more slowly.
Ligand, Voltage, ...	constant experimental conditions as needed by the model The "Channel" column should be blank; MIP and Mac accept time-varying stimuli recorded in additional A/D channels but MPL needs them to be constant.
Add/Delete/Presets	(ignore these) add/delete experimental variables, and load/save all variables
Use	(column when Data source is File list) whether each file will be part of the file list
Hist bin count	number of bins in the duration histograms in the Results window
Run mode	optimize (maximize LL) or check (compute LL with current parameters)
Use Segments	Separately: Runs MPL separately on each data segment, generating different LL and final rates for each. If Join Segments is checked, runs each file separately. Together: Runs MPL with all the data at once, summing LL and generating one final model
Presets

Results

In the textual Report window:

Rates	along with std deviation estimated from the Hessian matrix
LL	log likelihood
Grad	gradient

In the Results window:

Summary:

LL	of the final rate constants
Gradient	Derivative of LL w.r.t each model parameter. If all are near 0 it's a good fit; a local maximum on the likelihood surface
Iterations	Number of steps taken by the optimizer. 1 means it didn't move, max iterations means it didn't converge
Initial LL	LL using the starting rate constants
ErrorCode	0 is success, anything else makes the result suspect

Segments (and Select, Criteria):

Iterations	Number of optimizer steps if optimizing data segments separately
LL Initial LL	separately: log-likelihood of this segment's final model together: segment's contribution to LL
Gradient i	separately: derivative of LL w.r.t. parameter i together: segment's contribution to Gradient

Models: Initial and Final, per segment if separately

Histograms:

Duration histograms for each conductance class, overlaid with a probability distribution function (PDF) which is computed from the model. Tau and Amp are time constants and weights computed from the Q matrix. Each Tau contributes one exponential component to its class's PDF:

$PDF_i(t) = \frac{Amp_i}{Tau_i} e^{-t/Tau_i}$