**QUB**:

**Q**uantify

**U**nknown

**B**iophysics

QUB represents a molecule or other mechanism using a state model, like the one below. It's called a Hidden Markov model, because it can have multiple states with the same apparent measurement, and because the probability of a transition from one state to another depends only on which state it's in, and not on its history.

The boxes are "states," and the arrows are labeled with the transition rate per second. Here, the transition rate from state 0 to state 1 is pressure-sensitive. A rate constant can be sensitive to ligand concentration, voltage, or pressure, or any other stimulus that fits this Eyring-type formula for the effective rate constant k:

k = k0*L * exp(k1*V + k2*P)

We use color to group states into "conductance classes" ("classes" for short). By convention, class 0 (black) states are closed/non-conducting. The conductance (measurement) is assumed to be normally distributed, either as a constant (mean +/- std), or as a function of voltage and reversal potential.

*Simulated PIEZO1 channel response to a pressure pulse:*

This PIEZO1 model was published in (Bae et al, 2013). Above it is an energy landscape visualizing states as low-energy wells, with a ball indicating the current state. Notice how states 0 and 2 are both non-conducting.

*Simulated ensemble response of 100 PIEZO1 channels:*

The rate constants form the matrix **Q** (G in some literature), from which we can derive:

- sampled transition probabilities
- equilibrium state occupancy probabilities
- simulated time courses
- likelihood of a particular state sequence given sampled data
- likelihood of a sampled dataset given particular rate constants

The likelihood calculations are the heart of QUB. By maximizing likelihood, we can **idealize** data
with the SKM algorithm,
recovering the most likely state sequence and detecting events in the presence of substantial noise.
We can also **optimize** with the **MIL** and **MAC** algorithms, finding the most likely rate constants
and conductance distributions for a given dataset. Voltage- and pressure-sensitivity constants can be recovered
from data recorded with multiple stimulus levels.

Optimized rate constants provide a quantitative description of behavior, which can add rigor to comparisons, for example, with or without a point mutation. They enable simulations to plan and compare against future experiments, or where experiments would be impractical. They also open up some advanced analyses.

People use QUB for these problems because it's the most complete package of its kind. While some programs share a subset of our features, QUB is the only software that can

- read data files from pClamp, AxoGraph, Patchmaster, TAC, and others,
- pre-process data, including piecewise-linear interactive baseline subtraction,
- find the best rate constants for ensemble (macroscopic) data, using a maximum likelihood approach that goes beyond least-squares fitting,
- solve for rates and stimulus-dependence from data with a time-varying stimulus signal,
- resample a dataset adaptively, keeping fewer data points where the record is flat (to prioritize modeling of the active response instead of the equilibrium resting level),
- detect single-molecule events (idealize) quickly, with a noise model to minimize false positives,
- find the most likely rate constants for a single-molecule recording, using MIL and/or HJC formulas,
- correct for missed events due to limited time resolution (the correction is approximate — valid only when relatively few events are missed),
- fit globally, finding the most likely rate constants for a set of files recorded across different voltages, pressures, or ligand concentrations,
- impose constraints on rate constants, such as holding a constant ratio between two rates, or maintaining detailed balance (microscopic reversability) for all cycles,
- build models with more than two conductance classes,
- simulate a model's response to arbitrary stimuli,
- generate and fit amplitude and duration histograms,
- find and classify
*bursts*(event clusters separated by long inactivity) based on statistics like p_{open}*(desktop QUB only)*, and - search a model database, optimizing rates under all possible state connection schemes
to find the most likely
*(desktop QUB only)*

Please cite our papers when you use this software. Thanks.

### Online Apps:

- QUB Online — Hidden Markov modeling and simulation
- Fitness — Nonlinear least-squares regression (curve fitting) with weights, parameter limits, multi-column fitting, and the ability to enter custom fitting and weighting functions
- X-Means — Finds clusters which minimize members' distance from their centroid, using the K-Means algorithm, with tools to help pick the optimal number of clusters
- Movie Maker — Animates a sequence of events, with a scrolling data trace, sound, and animated graphics

### Books and Articles:

- Sivilotti, L., Colquhoun, D. 2016. In praise of single channel kinetics
*J. Gen. Physiol. 148(2):79-88* - Spies, M., Chemla, Y.R. 2016. Single-Molecule Enzymology: Fluorescence-Based and High-Throughput Methods (Methods in Enzymology)
- How to satisfy cycle (im)balance
- Multi-channel p
_{open} - Maximum Subinterval Likelihood (MSL)
- Simplex state machine with Promises (JavaScript function optimization)
- typedefStruct.js - read and write C structs in JavaScript
- qubtrace.js - plot large sampled datasets