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Please cite the software interface as follows:

Milescu, L.S., Nicolai, C., Bannen, J., 2000-2013 QuB Software.

Nicolai, C., Sachs, F. 2013. Solving Ion Channel Kinetics with the QuB Software. *Biophysical Reviews and Letters* **08**:03 1-21. doi:10.1142/S1793048013300053

Also, please cite the appropriate publication for each algorithm utilized:

**Dynamic Clamp:**

Milescu, L.S., T. Yamanishi, K. Ptak, M.Z. Mogri, and J.C. Smith. 2008. Real-time kinetic modeling of voltage-gated ion channels using dynamic clamp. *Biophysical J*. **95(1)**:66-87.

**MacRates** (ensemble optimization):

Milescu, L.S., G. Akk, and F. Sachs. 2005. Maximum likelihood estimation of ion channel kinetics from macroscopic currents. *Biophysical J*. **88(4)**:2494-2515.

**MIL** (single-channel idealized optimization):

Qin, F., A. Auerbach, and F. Sachs (1997) Maximum likelihood estimation of aggregated Markov processes.
* Proceedings of the Royal Society B ***264:**375-383.

Qin, F., A. Auerbach, and F. Sachs (1996) Estimating single-channel kinetic parameters from idealized patch clamp data.
containing missed events. * Biophysical Journal * **70:**264-280.

**MPL** (single-channel direct optimization):

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.

**RDF**:

Flomenbom, O.
Mathematical Treatments That Solve Single Molecules
*Biophysical Reviews and Letters* 2013 **08**:109-36
doi: 10.1142/S1793048013300016

**SKM** (idealization):

Qin, F. 2004.
Restoration of Single-Channel Currents Using the Segmental k-Means Method Based on Hidden Markov Modeling
*Biophys. J.* 2004 **86(3)**:1488-501

**Staircase methods**:

Milescu, L.S., A. Yildiz, P.R. Selvin, and F. Sachs. 2006. Extraction of dwell-time sequences from processive molecular motor data. *Biophysical J*. **91(9)**:3135-3150.

Milescu, L.S., A. Yildiz, P.R. Selvin, and F. Sachs. 2006. Maximum likelihood estimation of molecular motor kinetics from staircase data. *Biophysical J*. **91(4)**:1156-1168.

**other:**

Li, L., Qin, F. 2004.
Model-Based Fitting of Single-Channel Dwell-Time Distributions
* Biophys J*. **87(3)**:1657-71.

Defintion of a Markovian Chain from the Web Dictionary of Cybernetics and Systems

A brief biography of Andrei Andreyevich Markov

Applications of Hidden Markov Models to Single Molecule and Ensemble Data Analysis by Lorin Milescu. Definition and analysis of several QuB algorithms.

A recent paper on microscopic reversibility, similar to the technique in the 1996 MIL paper :

Colquhoun, D., Dowsland, K., Beato, M. & Plested, A.
How to Impose Microscopic Reversibility in Complex Reaction Mechanisms Biophys. J. 2004 86: 3510-3518

Paul H. Edelman & Jim Chen, “Duel Diligence:” Second Thoughts about the
Supremes as the Sultans of Swing,
70 S. Cal. L. Rev. 219
(1996), 227

Edelman and Chen use Markovian theory to analyse the outcome of Supreme Court decisions.

Fun with Markov Chains Simulated literature using word transition probabilities from classic texts.

Markov Chains as Tools for Jazz Improvisation Analysis of John Coltrane's *Giant Steps*

Capturing and comparing writers' profiles through Markov chains

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