Understanding Ion Channel Currents in Terms of Mechanisms
Analysis and interpretation of single ion channel records and macroscopic currents using matrix methods.
The 2013 course ran from 8 – 12 July, 2013. Course photo here.
Every summer since 2003 we have run a summer school. The aim of the school is to teach how to understand enough matrix algebra to understand the theoretical papers written by Colquhoun & Hawkes, and others. The use of our programs is also demonstrated, and extra practice can be arranged for those who want to use them.
When we started this course, we thought the aims were impossible to achieve in 5 days. But morning lectures, combined with afternoon tutorials where you do things youself (with MathCad) have proved successful. By the end of the course, you won’t be scared by the general matrix expression for the distribution of the length of bursts of openings (on the course mug. design above). You will be able to evaluate it numerically, and understand more or less how it was derived.
The synopsis of the course can be found below.
A workshop on analysis and interpretation of single ion channel records and
macroscopic currents using matrix methods.
Aim of the workshop
The aim of this workshop is to explain the theoretical background that is needed to interpret ion channel experiments in terms of physical receptor mechanisms.
In order to do this, in any case apart from the very simplest, it is essential to know some basic ideas about matrices, and the workshop explains how to do it. We also demonstrate the set of computer programs that we have developed for the analysis and interpretation of single channel recordings. Apply as below.
Background of applicants
No particular qualification is needed other than enthusiasm, and the most elementary calculus. In particular no knowledge of matrices will be assumed. People of any age or rank are welcome, as are applicants from industry as well as from Universities.
Please apply by email as below(see below). We will only be able to
take 12 – 16 people because of the need for individual attention in tutorials. Last year we were heavily oversubscribed. Applicants will be contacted directly by the organisers for more details about their background and reasons for interest in the workshop.
Some people will follow the mathematical derivations better than others, but at the end of the course everyone will be able to get numerical results.
Because people from outside UCL may be interested, the workshop will be run full time for one week, immediately after the end of term. Each day will be divided into lectures (with some computer demonstrations as part of the lectures) and tutorials. Each set of lectures will be followed by a tutorial session (up to four students per tutor) in which the material in the lectures will be explained and exemplified using programs such as Mathcad (to a lesser extent we can also cope with Maple and Matlab), as well as our own programs. The use of our own programs for calculations and fitting will also be shown in the tutorials. In last year’s workshop, even those with no previous experience of matrices were able to compute (in Mathcad) things like a burst length distribution for some specified mechanism by the end of the workshop.
Information in advance
It would be useful to have in advance a description of each student’s experience
with (a) ion channels and (b) mathematics. It is also important that if students bring a laptop computer with them (if you can bring Mathcad too, so much the better). The laptop should have enough disk space to allow us to install the programs and other material that you’ll need.
(a) Introductory section for those with no prior knowledge of matrix algebra
- Definition of a matrix
- Addition, subtraction and multiplication of matrices. Commutation
- Matrices as a convenient notation for simultaneous equations and as a convenient way of multiplying and adding probabilities, illustrated by a simple Markov chain.
- Inversion of matrices, and definition of determinant.
- Partitioned matrices
- Characteristic polynomial of a matrix: eigenvalues and eigenvectors
- Differentiation of a matrix and exponential of a matrix.
(b) Introductory section on statistics for those who need it
- Continuous and discrete distributions
- Probability density functions (the other meaning of ‘pdf’) and cumulative distribution functions
- Rate constants, probabilities and derivation of simple exponential distribution
- Convolution: meaning, done explicitly, and by Laplace transform method.
- Description of macroscopic (‘whole-cell) currents in matrix notation: a single equation for any sort of experiment.
- A simple ion channel mechanism analysed without matrices.
(c) Single ion channel analysis
- Distributions of open and shut times using matrices -comparison with the same simple case as done above without matrices.
- Division of single channel records into bursts and clusters of channel openings.
- Number of openings per burst: simple case, geometric distribution.
- Generalisation: sets of states and why matrices are useful; definition of Q matrix, and its partitioned forms.
- Generalisation of analysis of bursts of openings.
- What are the ubiquitous GAB and GAB(t) matrices?
- The distribution of the number of openings per burst: general form.
- The distribution of the open time, burst length and open time per burst; general forms.
- Equilibrium occupancies and macroscopic currents.
- The crucial role of entry probabilities: how to define the initial vectors for openings, $ \varphi_o $, and for bursts, $ \varphi_b $
- How to calculate things like exp(QAAt): eigenvalues, eigenvectors and the beautiful spectral expansion theorem.
- Correlations between open times and shut times (and the rank of a matrix). Bivariate and conditional distributions. Implications for connectivity of reaction schemes.
- Single channels after a jump. Non-stationary single channel behaviour.
- The relationship between single channel behaviour and macroscopic currents.
(d) Analysis and fitting of single channel data:
- Use of programs for analysis of experimental data, particularly direct fitting of a mechanism with HJCFIT.
By the end of the workshop you should be able to understand the formula for the burst length distribution that appears on the workshop mug, at least well enough to evaluate it, and at best to be able to derive it.
(Note: in 2007 there was still a Department of Pharmacology at UCL)
Apply for a place
The sessions take place in the Pharmacology seminar room from 9
This workshop gets no support whatsoever from UCL. That means we have to charge of £150 to cover expenses and travel for tutors. If you can’t find this amount please email and we’ll try to help.
- Workshop Directors Prof David Colquhoun and Prof Lucia Sivilotti (Pharmacology)
- Tutors: Remigijus Lape and Andrew Plested.
Or download as pdf file, with labels.
Earlier course pictures
Pictures taken on previous workshops from 2003 to 2010 are here.