Alpha-hemolysin is an exotoxin secreted by the bacterium Staphylococcus aureus. In its active form, the protein is built from 293 water-soluble amino acids that assemble into a heptameric pore, a seven-part barrel that punches through cell membranes. That structure, first resolved in crystallographic detail in the 1990s, has made alpha-hemolysin the workhorse of stochastic sensing: the first and still most widely used biological nanopore for detecting individual molecules. When a single pore is embedded in an artificial membrane bathed in electrolyte and a voltage is applied, a steady ionic current flows through the opening. When an analyte molecule wanders into the pore, it partially obstructs that current, producing a characteristic downward blip. Each blip corresponds to one molecule, and the pattern of blips over time carries information about the analyte’s identity and concentration.

In the new experiments, the team used monodisperse polyethylene glycol of molecular weight 1294, abbreviated PEG 1294, as the analyte. The experimental platform was a solvent-free planar lipid bilayer assembled by the classic Montal and Mueller technique: two monomolecular lipid films were apposed across a hole roughly 100 micrometers in diameter in a Teflon partition, forming a barrier that separated two identical compartments of a Teflon chamber. The synthetic lipid 1,2-diphytanoyl-sn-glycero-3-phosphocholine was used at 2 percent by weight in hexane, and the hole was pretreated with a dilute hexadecane solution to promote stable bilayer formation. Both compartments held a concentrated electrolyte of 4 molar potassium chloride buffered with 5 millimolar Tris-citric acid at pH 7.5. Alpha-hemolysin was added to one side, the cis side, at a concentration tuned so that exactly one pore inserted into the membrane.

The researchers then added PEG 1294 to the opposite, trans side at two concentrations, 400 and 1000 micromolar, and applied voltages ranging from +20 to +100 millivolts in 20 millivolt steps. Ionic currents were recorded with an Axopatch 200B amplifier in voltage clamp mode, using silver/silver chloride electrodes connected through agar salt bridges. The signals were low-pass filtered at 15 kilohertz and digitized at a sampling rate of 250 kilohertz, all at a controlled temperature of 25 degrees Celsius. Under these conditions, the current trace showed the textbook signature of stochastic sensing: stepwise transitions between a fully open level and a partially blocked level, each step corresponding to the entry or exit of a single PEG molecule from the pore lumen.

The novelty of the study lay not in the electrophysiology but in the analysis. Rather than focusing on conventional metrics such as event duration or blocking depth, the team turned to Lempel-Ziv complexity, a measure introduced in 1976 by Abraham Lempel and Jacob Ziv to quantify the randomness of finite sequences. The method works by converting a time series into a binary string: each data point is compared with the average of the entire series, receiving a 1 if it exceeds the average and a 0 if it falls below. The resulting string of ones and zeros is then scanned from left to right, and a counter increments every time a new, previously unseen substring appears. Finally, the counter is normalized by a theoretical upper bound, n divided by the base-2 logarithm of n, yielding a complexity value that ranges from 0 to 1 and is independent of sequence length.

The interpretation of this number is intuitive. A value close to 1 indicates a highly random, unpredictable signal with little internal self-similarity, while a value close to 0 indicates a repetitive, ordered series. Lempel-Ziv complexity has previously found applications in biomedical signal analysis, including studies of electroencephalogram background activity in Alzheimer’s disease patients and the detection of ventricular tachycardia and fibrillation in cardiac recordings. Applying it to nanopore data, however, allowed the researchers to ask a question that conventional event statistics cannot easily answer: how complex, in an information-theoretic sense, is the pattern of molecular blocking events?

The answer depended strongly on how much analyte was present. At the lower PEG concentration of 400 micromolar, complexity values were consistently lower than at 1000 micromolar, across every voltage tested. The full range of measured values stretched from a minimum of 0.45, recorded at 400 micromolar and +40 millivolts, to a maximum of 0.97, recorded at 1000 micromolar and +80 millivolts. The physical explanation is straightforward: higher analyte concentrations produce more frequent blocking events, filling the time series with rapid alternations between open and blocked states and pushing the complexity measure toward its upper limit. At lower concentrations, longer stretches of open-pore current dominate, and the signal becomes more ordered and less random.

To probe whether the apparent order at low concentration reflected genuine structure or simply sparse sampling, the researchers performed a clever control. They segmented the original time series recorded at 400 micromolar, shuffled the segments into a random order, and recalculated the complexity of the resulting randomized series. For every applied potential, the shuffled data yielded higher Lempel-Ziv values than the original recordings. This result is diagnostic: if the original series had already been maximally random, shuffling it would have changed nothing. The fact that randomization increased complexity means the unshuffled sequences contained residual structure, and that the biosensor’s output at low analyte concentration falls short of full stochastic behavior.

The team also compared series built exclusively from blocked periods with series built exclusively from unblocked periods, at both concentrations and all voltages. Statistical analysis using Student’s t-test, with a significance threshold of p less than 0.05, found no meaningful differences between the complexity of the blocked-only and unblocked-only series, nor between those segmented series and the original combined recordings. In other words, the complexity of the signal does not reside preferentially in either the moments when PEG occupies the pore or the intervals between occupations; the stochastic character is distributed across the entire record.

The broader implications reach into a long-standing debate in biology about the role of randomness. Molecular biology has traditionally leaned on deterministic principles, yet stochasticity is now recognized as a genuine feature of living systems rather than mere noise. Ion channel kinetics are widely treated as stochastic events, and some theorists argue that intrinsic randomness in the nervous system may even enable flexible decision-making. As the authors note, biological studies often lack the tools to distinguish chaotic, noisy, deterministic, and probabilistic behavior. Lempel-Ziv complexity offers one such tool. Their conclusion is nuanced: the alpha-hemolysin biosensor behaves in a purely stochastic fashion only at higher analyte concentrations, while at lower concentrations its stochasticity diminishes, though it can be mathematically restored by randomizing the event sequence. For engineers designing nanopore sensors, that finding matters, because the reliability of single-molecule detection depends on understanding when the digital current signature is truly random and when it carries hidden structure that smarter algorithms might exploit.

Subject of Research: Stochastic analysis of alpha-hemolysin nanopore ionic current blocking events using Lempel-Ziv complexity

Article Title: Analyzing alpha-hemolysin nanopore behavior using Lempel-Ziv complexity

Article References: Neves, G. F., Machado, D. C., Consoni, L. H. A., Costa, E. V. L., Carneiro, C. M. M., Rodrigues, C. G., & Nogueira, R. A. (2026). Analyzing alpha-hemolysin nanopore behavior using Lempel-Ziv complexity. Discover Chemistry, 3(1), Article 571. https://doi.org/10.1007/s44371-026-01022-8

Image Credits: AI Generated

DOI: 10.1007/s44371-026-01022-8

Keywords: alpha-hemolysin, nanopore, Lempel-Ziv complexity, stochastic sensing, polyethylene glycol, ion channel, planar lipid bilayer, biosensor, information theory, single-molecule detection, biophysics, stochasticity