Residuals - initially places
peaks by finding local maxima in a smoothed data stream

Second Derivative - searches
for local minima within a smoothed second derivative data stream

Deconvolution - uses a
Gaussian response function with a Fourier deconvolution/ filtering algorithm.

PeakFit helps you separate overlapping peaks by statistically
fitting numerous peak functions to one data set, which can help you find even
the most obscure patterns in your data. The background can be fit as a separate
polynomial, exponential, logarithmic, hyperbolic or power model. This fitted
baseline is then subtracted before peak characterization data (such as areas) is
calculated, which gives much more accurate results.

PeakFit is the
automatic choice for Spectroscopy, Chromatography or Electrophoresis. AI Experts
throughout the smoothing options and other parts of the program automatically
help you to set many adjustments.PeakFit can even deconvolve your spectral
instrument response so that you can analyze your data without the smearing that
your instrument introduces. By Using 82 nonlinear peak models to choose from,
you're almost guaranteed to find the best equation for your data.

PeakFit
includes 18 different nonlinear spectral application line shapes, including the
Gaussian, the Lorentzian, and the Voigt, and even a Gaussian plus Compton Edge
model for fitting Gamma Ray peaks. As a product of the curve fitting process,
PeakFit reports amplitude (intensity), area, center and width data for each
peak. Overall area is determined by integrating the peak equations in the entire
model.

The Voigt function is a convolution of both the Gaussian and
Lorentzian functions. Most analysis packages that offer a Voigt function use an
approximation with very limited precision. PeakFit actually uses a closed-form
solution to precisely calculate the function analytically. PeakFit has four
different Voigt functions, so you can fit the parameters you're most interested
in, including the individual widths of both the Gaussian and Lorentzian
components, and also the amplitude and area of the Voigt function. PeakFit's
precise calculation of the Voigt function is crucial to the accuracy of your
analysis.

Nonlinear curve fitting is by far the most accurate way to
reduce noise and quantify peaks. Many instruments come with software that only
approximates the fitting process by simply integrating the raw data numerically.
When there are shouldered, or hidden peaks, a lot of noise, or a significant
background signal, this can lead to the wrong results. (For example, a
spectroscopy data set may appear to have a peak with a 'raw' amplitude of 4,000
units -- but may have a shoulder peak that distorts the amplitude by 1,500
units! This would be a significant error.)

PeakFit helps you separate
overlapping peaks by statistically fitting numerous peak functions to one data
set, which can help you find even the most obscure patterns in your data. The
background can be fit as a separate polynomial, exponential, logarithmic,
hyperbolic or power model. This fitted baseline is then subtracted before peak
characterization data (such as areas) is calculated, which gives much more
accurate results. And any noise (like you get with electrophoretic gels or Raman
spectra) that might bias raw data calculations is filtered simply by the
nonlinear curve fitting process. Nonlinear curve fitting is essential for
accurate peak analysis and accurate research.

With PeakFit's visual FFT filter, you can inspect your data
stream in the Fourier domain and zero higher frequency points -- and see your
results immediately in the time-domain. This smoothing technique allows for
superb noise reduction while maintaining the integrity of the original data
stream. PeakFit also includes an automated FFT method as well as Gaussian
convolution, the Savitzky-Golay method, and the Loess algorithm for smoothing.
AI Experts throughout the smoothing options and other parts of the program
automatically help you to set many adjustments. And, PeakFit even has a digital
data enhancer, which helps to analyze your sparse data. Only PeakFit offers so
many different methods of data manipulation.

PeakFit's non-parametric baseline fitting routine
easily removes the complex background of a DNA electrophoresis sample. PeakFit
can also subtract eight other built-in baseline equations, or it can subtract
any baseline you've developed and stored in a file.

If PeakFit's auto-placement features fail on extremely
complicated or noisy data, you can place and fit peaks graphically with only a
few mouse clicks. Each placed function has "anchors" that adjust even the most
highly complex functions, automatically changing that function's specific
numeric parameters. PeakFit's graphical placement options handle even the most
complex peaks as smoothly as Gaussians.

Every publication-quality graph (see above) was created
using PeakFit's built-in graphic engine -- which now includes print preview and
extensive file and clipboard export options. The numerical output is
customizable so that you see only the content you want.

For most data sets, PeakFit does all the work for you.
What once took hours now takes minutes ?with only a few clicks of the mouse! It뭩
so easy that novices can learn how to use PeakFit in no time. And if you have
extremely complex or noisy data sets, the sophistication and depth of PeakFit뭩
data manipulation techniques is unequaled.

PeakFit uses three procedures to automatically place
hidden peaks; while each is a strong solution, one method may work better with
some data sets than the others.

The Residuals procedure initially
places peaks by finding local maxima in a smoothed data stream. Hidden peaks are
then optionally added where peaks in the residuals occur.

The Second Derivative procedure
searches for local minima within a smoothed second derivative data stream. These
local minima often reveal hidden peaks.

The Deconvolution procedure uses a
Gaussian response function with a Fourier deconvolution/ filtering algorithm. A
successfully deconvolved spec-trum will consist of 뱒harpened?peaks of equivalent
area. The goal is to enhance the hidden peaks so that each represents a local
maximum.

GENERAL FEATURES

Data Input

ASCII

Excel

Lotus 123

Quattro Pro Windows

SigmaPlot

AIA Chromatography

dBase III+, IV

DIF

ASCII and Spreadsheet - like Editors

Averaging Digital Filter

Data Preparation

Gaussian Deconvolution to remove Spectrophotometer Instrument Response
smearing

Exponential Deconvolution to remove Chromatographic Detector Response
smearing

Dual Graph Data Sectioning with Graphical data point exclusion

Non - Parametric Digital Filter to Filter or augment data

Compare with Reference

Subtract Baseline Imported from File

Data Transforms

Area Normalization

Inspect Second and Fourth Derivatives

Data Weighting

Peak Autoplacement

Automatic by Local Maxima and Residuals

Automatic by Second Derivatives

Automatic by Deconvolved Local Maxima

Graphical Placement and Adjustments

Manual Parameter Adjustments

Share and Lock Parameters

Constant or Variable Widths and/or Shape in a single step

Non - Linear Curve Fitting

Marquardt - Levenburg Algorithm

Least - Squares and 3 Robust (Maximum Likelihood) methods

Up to 100 Peaks and 1000 Parameters

Intelligent Constraints to insure Fit Integrity

Sparse Curvature Matrix for Faster Fitting

Both Numeric and Graphical Fitting Options

Zoom - in or Toggle Points during Fitting

Output and Export Options

File Export with full Generated Data: Lotus 123, Excel, Quattro Pro Windows,
SigmaPlot, and ASCII.

Graphs to clipboard or file in BMP or WMF formats

All Numeric data in Graph to Clipboard in Spreadsheet Format

SINGLE CHANNEL ANALYSIS - FITTING MULTIPLE SIMULTANEOUS
GAUSSIAN FUNCTIONS :

We are interested in the regulation of large conductance
Ca^{2+}-activated potassium channels of CNS origin. We are using single
channel recording techniques to study the effects of a variety of signal
transduction elements on the activity of these important channels. Regulation of
activity can be compared using the open probability - the amount of time the
channel(s) are open. Experiments are performed under control conditions and in
the presence of the desired bioactive substance in the same patch. When the
patch contains only 1 or 2 channels, the determination of open probability is
relatively simple. However, there are often 4-8 channels in a given patch.
Determination of the open probability requires the deconvolution of an amplitude
histogram comprised of multiple Gaussian distributions. There is a unique
Gaussian distribution associated with each channel state. In the present example
there are 5 channels. Therefore there are 6 Gaussian distributions in the
amplitude histogram; all channels closed (level 0 on the activity records), 1
channel open (level 1), 2 channels open (level 2), 3 channels open (level 3), 4
channels open (level 4) and 5 channels open (level 5). Often there is
significant overlap between distributions and if the time spent with all
channels open is small (in this example all channels are open approximately 1%
of the time) it is difficult to solve for this distribution.

The excised
patch configuration of the patch-clamp technique was used for data acquisition.
Electrodes were fabricated in two steps and were fire polished to a final tip
resistance between 3.0 and 5M . Recordings were performed at room temperature
with a patch clamp amplifier. The recordings in this example were conducted with
the patch depolarized to +20 mV. Single channel data were stored initially on
digital audiotape.

Single channel data were digitized at a sampling rate
of 2 kHz and filtered at 1 kHz using a 4-pole low pass Bessel filter. Each data
file contains approximately 100,000 events. Amplitude histograms are constructed
from the digitized single channel data using commercially available software.
Single channel records and the amplitude histogram data were exported to
SigmaPlot and PeakFit as ASCII files. Line plots were created in SigmaPlot for
the desired number of activity records (3 in the present example) and annotated
as desired.

A vbar graph was created for the amplitude histogram data. The
activity records and amplitude histogram were visually inspected to determine
the most likely number of distributions contained in the data.

The amplitude histogram was imported into PeakFit and fitted
using a sum of Gaussian distribution functions. PeakFit Method 1. was selected
for analysis and several hidden peaks were found. These arise from the overlap
in distributions and were removed to give a function with 6 Gaussian
peaks.

The data were then fit automatically. Estimates for individual
peak areas, means and standard deviations were obtained from the peak fit
results.

Click to View Larger Image

Equation 1. was used to calculate the open probability times
the number of channels (NP_{0}). i is the number of open channels, N is
the total number of channels in the patch and A_{i} is the area
associated with each channel state as determined from the curve-fit individual
peak areas. The open probability (P_{0}) was then calculated as
NP_{0}/N.

In the present example, NP_{0}= 1.11
and P_{0}=0.22.

Author : Donald D. Denson, Ph.D.,
Department of Anesthesiology, Emory University School of
Medicine.