An information theory approach to quantifying the sequence-dependent response of nucleic acid motors with applications to nanopore DNA sequencing

Abstract

Motor enzymes that interact with DNA are essential for replicative biological processes. In nanopore sequencing, a motor enzyme controls the motion of a nucleic acid through a protein nanopore, and sequence-dependent blockages of an ion current flowing through the nanopore are used to decode the DNA sequence. The kinetics of these enzymes are sequence-dependent and can serve as an additional source of information during sequencing. Here, we use Mutual Information (MI) to quantify the sequence-dependent kinetics of a Hel308 helicase during nanopore sequencing. We use MI to identify sites in Hel308 that are responsible for sequence-dependent kinetics and develop “k-mer” models of Hel308 kinetics that map kinetics to DNA sequence. We estimate that enzyme kinetics can improve nanopore sequencing accuracy by ~5-fold at high sequencing depth. We mutate Hel308 to identify amino acids involved in DNA translocation and suggest pathways for engineering molecular motors with enhanced responsiveness to DNA sequence.

Motor enzymes that translocate DNA are an essential element of nanopore sequencing. Here, authors use mutual information to quantify the sequence-dependence of helicase kinetics and show that such kinetics can be used to improve the sequencing accuracy of all standard DNA bases.

Introduction

A myriad of biotechnologies use molecular motor enzymes that translocate on or remodel DNA, RNA, or peptides. These enzymes, which include helicases, polymerases, reverse transcriptases, endonucleases and exonucleases, are used in DNA and RNA sequencing techniques, such as nanopore sequencing and sequencing by synthesis; gene editing systems such as CRISPR; and enzymatic DNA synthesis methods. The kinetics of these motors can be strongly dependent on the sequence of the substrate DNA or RNA^1–10.

The sequence dependence of such motors can be particularly useful in single-molecule DNA sequencing technologies such as nanopore sequencing or Pacific biosciences single-molecule real-time (SMRT) sequencing. These technologies measure the kinetics of their motor enzymes simultaneously with a primary observable and can be improved by integrating the information from enzyme kinetics into the primary sequencer. To date, such sequence dependence has been used to detect only base modifications such as N6-methyladenosine and 5-methyl-C using SMRT sequencing^5,6, and pseudo-U¹¹ or unnatural DNA bases¹² in nanopore DNA sequencing. Here, we show that sequence-dependent enzyme kinetics can improve the sequencing of all standard DNA bases in nanopore DNA sequencing and develop a workflow to quantify the sequence information obtained by measurements of enzyme kinetics.

In nanopore sequencing, a single nanopore in a phospholipid bilayer forms the only electrical connection between two salt solutions. A voltage applied across the bilayer causes an ion current to flow through the nanopore. Negatively charged DNA bound to a motor enzyme is threaded through the nanopore until the enzyme comes to rest on the rim of the nanopore (Fig. 1A). The motor enzyme then controls the motion of the DNA through the nanopore. The DNA bases in the constriction of the pore reduce the ion current through the pore depending on the base sequence, and the sequence of ion currents can therefore be decoded into a DNA base sequence^13–20. Each nanopore read is a single-molecule record of motor enzyme kinetics, such as step dwell times and backstepping, as it translocates along the DNA strand. We and others have leveraged this to use nanopore sequencers to resolve sequence-dependent kinetics of the motor enzyme at unmatched spatiotemporal resolution. Every motor enzyme we have run on these “nanopore tweezers” has shown sequence-dependent translocation kinetics, including helicases Hel308^1,4,21,22, RecQ²³, SARS-CoV-2 nsp13²⁴, PcrA²⁵ and transcription by E. coli RNA polymerase²⁶. Others have seen similar results with Phi 29 DNA polymerase²⁷ and UvrD³.

Fig. 1. Nanopore sequencing observables.

A Nanopore sequencing with Hel308. The ion current is determined by the DNA sequence in the MspA constriction, while the Hel308 kinetics are determined by interactions at a distance x, measured in nucleotides, away from the constriction. B Representative ion current vs. time trace from a nanopore sequencing experiment and establishing a coordinate system. The ion current magnitude is determined by the ~4 bases in MspA (gray arrows). Kinetic observables are indicated. C Mean ion current of the helicase open conformation vs. the base at x = 0 nt. Thymine causes a low ion current. D Same as (C) for open conformation. E Mean dwell time of the open conformation vs. DNA base at x = 17 nt. F Same as (E) for the closed conformation. Cytosine causes longer dwell times. G Mean probability of backwards step vs. DNA base at x = 20 nt. Cytosines have a lower probability of a backwards step. For (C–G), each DNA position was measured at least N > 30 times. Error bars are in (C–F) are S.E.M. Error bars for (G) are asymmetric and given by the Wilson interval using z = 1, corresponding to ~67% confidence interval. Source data are provided as a Source Data file.

Figure 1B shows the measured ion current over time as a strand of DNA is stepped through the Mycobacterium smegmatis porin A (MspA) nanopore by the helicase Hel308 from Thermococcus gammatolerans. Hel308 helicase translocates on single-stranded DNA from 3′ to 5′, pulling the DNA out of the pore in two kinetically distinct sub-nucleotide observable steps per nucleotide translocated. We have previously shown that the sub-steps correspond to open and closed conformational states of Hel308, with ATP binding occuring in the open conformation and ATP hydrolysis in the closed conformation^1,23. There are two kinetic observables in the data: (1) step dwell time, t, the time spent at a position on the DNA sequence, and (2) the probability of a backwards step, P_b, at a position on the DNA sequence. We have previously shown that both t and P_b depend upon the DNA sequence that is passing through the helicase^{1,21,23,25,26}.

In this work, we develop methods for understanding how sequence dependence manifests in motor enzymes and to determine how useful such sequence-dependent kinetics can be for improving nanopore sequencing accuracy. We develop an information theory approach to compare the amount of sequence information contained in three nanopore sequencing observables: ion current (I), step dwell time (t), and per-step probability of a backwards step (P_b). We find that kinetic observables contain significant information about the underlying sequence and that these observables, combined, have still more information about the DNA sequence. We show how this information theory approach can be used to develop higher-order “k-mer” models for each of these observables, where k is a collection of nucleotides that together influence the motor enzyme’s kinetics. Integrating this kinetics k-mer model into a sequencer significantly reduces the error rate in the called base sequence compared to sequencing using ion current alone and improves both the magnitude and scaling of sequencing error rate with sequencing depth. We investigate the physical basis that gives rise to sequence-dependent ssDNA translocation kinetics in Hel308 by performing site-directed mutagenesis of amino acids that contact the DNA strand and discuss pathways for engineering enzymes with enhanced responsiveness to the DNA sequence for nanopore sequencing and related biotechnological applications. Finally, we propose using the information-based assessment of sequencing information as a metric by which enzymes can be rapidly screened for useful sequence-dependent behavior.

Results

Quantifying mutual information between nanopore sequencing observables and DNA bases

First, it is important to note that the helicase is displaced from the nanopore constriction, meaning that the DNA bases affecting the ion current are different than the DNA bases affecting the kinetics of the helicase at a given point in time. We define the coordinate x to be the distance, in nucleotides, between the MspA constriction and the base of interest (Fig. 1A, B, glossary, Supplementary Tables 1 and 2). In this convention, the ion current through the pore is determined by the DNA sequence between x = −3 nt and x = +2 nt. For example, Fig. 1C, D shows the ion current versus the DNA base at x = 0 nt for a series of enzyme steps, with thymine at x = −1 or x = 0 nt associated with low ion current states. Figure 1D shows the dwell time of the Hel308 open conformation vs. DNA sequence at x = 17 nt; this variable could not be reliably identified with DNA sequence. However, Fig. 1E shows the dwell time of the closed conformation vs. DNA sequence at x = 17 nt, with cytosines associated with longer dwell times. Figure 1F shows the probability of a backwards step of the closed conformation vs. DNA sequence at x = 20 nt, with cytosines associated with reduced probability of backwards steps. These results are consistent with the results of ref. ¹, which showed more obvious sequence-dependent kinetics in the closed conformation of Hel308.

Figure 2A–E shows the mean ion current (open and closed, 2A/2B), mean dwell time (open and closed 2C/2D) and mean probability of backwards step (closed, 2E) as a function of the displacement, x, and the DNA base at x. The mean ion current responds to changes in b₋₂ through b₁, consistent with previous descriptions^13,14 of the mean ion current in MspA as dependent on the 4 nucleotides in its constriction (k = 4). The mean dwell time of the closed conformation is affected by b₁₇ as well as b₂₀, and the mean probability of a backwards step is affected by b₂₀.

Fig. 2. Sources of information in enzyme-controlled nanopore DNA sequencing.

A Mean ion current vs. x for the open conformation. B Mean ion current vs. x for the closed conformation. C Mean dwell time of Hel308 open conformation vs. x. D Mean dwell time of Hel308 closed conformation vs. x. E Mean probability of a backwards step vs. x. Error bars in (A–E) are SEM (N = 4096 for ion current and N = 288 for kinetics). F–J Mutual information between the continuous variable shown in (A–E) vs. x, using κ = 5. The gray dashed line in each graph sets the 10⁻³ significance level after correcting for multiple testing (Supplementary Discussion 3.2). The mutual information is largest at sites where the corresponding signal changes significantly in response to the base sequence. Source data are provided as a Source Data file.

To determine the strength of the relationship between base sequence and sequencing observables, we turned to mutual information (MI), which quantifies the average information that can be learned about one variable given a measurement of another variable^28,29. MI can answer the question: on average, how much information about the base at position x can be learned from a measurement of ion current? Given a continuously distributed observable y, that can be used to infer a DNA base b by a collection of conditional probability density functions $\rho \left(y\mid b\right)$, the mutual information between y and b is defined as:

$$\mathrm{MI}\left(\mathrm{y},\mathrm{b}\right)={\mathrm{\Sigma }}_{\mathrm{b}}p\left(b\right)\cdot \int \mathrm{d}y\rho \left(y\mid b\right){\log }_2\left(\frac{\rho \left(y\mid b\right)}{\rho \left(y\right)}\right)$$ 1

where $\rho \left(y\right)={\mathrm{\Sigma }}_b\rho \left(y\mid b\right)\cdot p\left(b\right)$ is the sequence-independent distribution of the observable y (Supplementary Discussion 3, glossary). From this definition, if the observable is independent of the base b, then $\rho \left(y\mid b\right)=\rho \left(y\right)$, the expression inside the logarithm is 1, therefore MI(y,b) = 0. Similarly, when the observable y is dependent on base b, then $\rho \left(y\mid b\right)\ne \rho \left(y\right)$ and Eq. 1 becomes non-zero and positive, indicating that the observable y provides information about the base b. MI is a symmetric quantity with MI(y,b) = MI(b,y), and therefore can be thought of as ‘how much can be learned about b given a measurement of y?’, or equivalently as ‘to what extent does b regulate y?’. MI has units of bits when the logarithm base is two, and two bits of information are required to unambiguously identify four different bases from a single measurement of y, under the assumption that each base is equally likely. The value of MI can be used to bound the error rate in determining the identity of b from a measurement of y³⁰.

The expression in eq. [1] is almost always impossible to compute analytically, even for known probability density functions, let alone for empirical data in which the true probability density functions cannot be known. Because of this, there are several methods that have been developed to estimate MI from empirical data. Among these estimators, those using a κ-nearest neighbors approach have been shown to provide robust estimates of the data that are relatively insensitive to choice of parameters^31,32. In calculating MI, it is also essential to consider the discrete/continuous nature of the data in question. Variables such as DNA base take on discrete values A, C, G, or T, while measurements such as ion current or step dwell time are continuous.

We therefore use the discrete-continuous κ-nearest-neighbors estimator of Ross, a bin-free estimator of MI which does not rely upon explicit estimation of the probability density function and has only one parameter, κ³². This calculator builds on the κ-nearest-neighbors calculator of Kraskov et al.³¹, but adapted to the comparison of information between a discrete variable and one or more continuous variables. Briefly, for each data point, we determine the distance (or volume for higher-dimensional data) at which κ other measurements of the same category lie within that distance (e.g., all data associated with A). We then determine how many measurements of all categories (A, C, G, and T), m, lie within that distance (volume). From κ and m, one can estimate the MI using the digamma function. Importantly, Ross’s calculator is relatively insensitive to the choice of κ, as opposed to estimates of MI based on binning the data, which are highly sensitive to the choice of bin width. We perform extensive tests of the calculator in the supplementary information, including estimation of the null hypothesis (Supplementary Figs. 1 and 2), tests of toy models with known answers (Supplementary Figs. 3 and 4), and tests of how κ affects the estimation of MI in our data (Supplementary Figs. 5–11).

Figure 2F–J shows the MI between each observable and b_x (N = 288 sequence contexts for kinetics; N = 4096 sequence contexts for ion current, Supplementary Tables 1 and 2, Supplementary Figs. 1 and 2, Supplementary Discussions 1–3). The MI in each case is maximal where there is significant variation in the observable due to the DNA base. As expected, MI(t_c, b_x) and MI(P_b, b_x) appear to be determined primarily by interactions between the helicase and the DNA sequence at x = 17 nt and x = 20 nt, with limited information about individual DNA bases contained at other sites. To estimate the significance of our results, we calculated the null hypothesis distribution for MI by performing the same calculation as above, but randomly permuting b many times (N = 105,000 for kinetics, N = 2400 for current), leading to uncorrelated data and therefore an estimator for the null hypothesis that the variables are independent of DNA sequence. From there, one can estimate the statistical significance of MI using the empirical cumulative distribution function for the null hypothesis distribution (Supplementary Figs. 1 and 2). In this interpretation, none of the sites for the open conformation dwell time (Fig. 2H) are significant at the 10⁻³ level. Although sequence-dependent kinetics for the open conformation have been established^1,4,21, localizing it to a particular base, or bases, would require more data.

Expanding the mutual information approach to multi-dimensional data

The MI shown in Fig. 2F–J represents the mutual information between individual observables and underlying DNA bases. However, for practical sequencing applications, we would like to use all the observables jointly, which may result in more information than using the individual observables alone. We therefore expanded the mutual information approach to multi-dimensional data (Supplementary Discussion 3.4, Supplementary Figs. 12–14). The MI estimator of Ross uses a nearest-neighbors algorithm to evaluate the expectation value in Eq. 1, which requires calculation of the pairwise distances between points. Because t and P_b have different units, we constructed a dimensionless vector ${\vec{z}}_k$ by subtracting the mean and normalizing each component by the population standard deviation:

$${\vec{\mathit{z}}}_{\mathit{k}}=\left(\frac{t_O-\overline{t_O}}{{\sigma }_O},\frac{t_C-\overline{t_C}}{{\sigma }_C},\frac{P_{\mathrm{b}}-\overline{P_b}}{{\sigma }_P}\right),$$ 2

where σ_O, σ_C, and σ_P are the population standard deviations of t_O, t_C, and P_b, respectively and the bar represents the population average.

Figure 3A shows the mutual information between ${\vec{\mathit{z}}}_{\mathit{k}}$ and b_x. At x = 17 nt, the information about the DNA sequence is mostly contained in t_C. In contrast, at x = 20 nt, t_O, t_C, and P_b individually contain less information about the base, but their joint distribution provides similar total information about the sequence. None of these observables contains significant information individually about b₁₆ or b₂₁, however, their joint distribution does provide a small, but statistically significant, amount of information about the sequence.

Fig. 3. Vector mutual information analysis.

A Mutual information between P_b and b_x (yellow), t_c and b_x (blue), t_o and b_x (purple), ${\vec{z}}_k$ and b_x (green). The gray dashed line sets the 10⁻³ significance level after correcting for multiple testing (Discussion S3.2). B Conditional distributions $\rho \left({\vec{z}}_k\mid C_{17}\right)$ (green), $\rho \left({\vec{z}}_k\mid T_{17}\right)$ (orange). Each data point is the average of d > 20 measurements of each sequence site and contains data from the sequences in (Supplementary Table S1, Supplementary Discussion 6.1.2). The error bars on these data points are omitted for visual clarity. The black dashed line is a hyperplane that optimally separates the two variables based on the conditional distribution alone. The near-vertical line is consistent with our finding that most of the information is contained in the dwell time. C Conditional distributions $\rho \left({\vec{z}}_k\mid C_{20}\right)$ (green), $\rho \left({\vec{z}}_k\mid A_{20}\right)$ (blue). The black dashed line is a hyperplane that optimally separates the two variables based on the conditional distribution alone. The diagonal line is consistent with our finding that the information about the sequence is contained in both t_c and P_b. Source data are provided as a Source Data file.

Figure 3B shows the conditional distributions$,\rho \left({\vec{\mathit{z}}}_{\mathit{k}}\mid b_{17}\right)$, for thymine and cytosine, while Fig. 3C shows $\rho \left({\vec{\mathit{z}}}_{\mathit{k}}\mid b_{20}\right)$ for adenine and cytosine (two-dimensional projection of the three-dimensional distribution). At x = 17 nt, t_c alone provides a reasonable ability to discriminate between individual bases. At x = 20 nt, cytosines have both a short dwell time and a lower probability of backwards step compared to adenine, highlighting the importance of using ${\vec{z}}_k$ for base discrimination. The dashed lines in Fig. 3B, C indicate a hyperplane that enables optimal classification of the DNA base between the two discernible bases using only the conditional distributions. The near-vertical plane in Fig. 3B is consistent with our finding that dwell time contains nearly all the information available about b₁₇, while the diagonal dashed line in Fig. 3C is consistent with there being more available sequence information about b₂₀ in the joint distribution $\rho \left({\vec{\mathit{z}}}_{\mathit{k}}\right)$ as opposed to $\rho \left(t_c\right)$ and $\rho \left(P_{\mathrm{b}}\right)$ alone.

Developing k-mer models for enzyme kinetics using mutual information

In nanopore sequencing, collections of k bases together are used to parameterize the ion current and decode the DNA sequence. In nanopore sequencing with MspA, ion current k-mers of 4–6 consecutive bases have been used for DNA sequencing^14,15. In Hel308, multiple bases within the helicase affect enzyme kinetics, notably at positions x = 17 nt and x = 20 nt. This suggests that a k-mer model for sequence-dependent Hel308 kinetics is formed by non-consecutive bases. Here, we use MI to quantify which k-mers in Hel308 are most informative about the DNA sequence, and can therefore form the basis of a sequence-to-kinetics map that can be used for sequencing.

We defined the dimer D_i,j as the pair of bases (b_i, b_j) (Fig. 4A; k-mer with k = 2) and calculated MI(${\vec{\mathit{z}}}_{\mathit{k}}$, D_x,20), using $\mathrm{MI}\left({\vec{\mathit{z}}}_{\mathit{k}},b_{20}\right)$ as a point of comparison (Fig. 4B, full matrix MI(${\vec{\mathit{z}}}_{\mathit{k}}$, D_i,j) Supplementary Figs. 15 and 16). The mutual information is maximal between ${\vec{z}}_k$ and D_17,20, with ${\vec{z}}_k$ providing ~1 bit about D_17,20. Other dimers also contained enhanced information compared to b₂₀, such as D_16,20 (~0.7 bits) or D_20,21 (~0.7 bits). Similarly, we defined the trimer T_i,j,k as the triplet (b_i, b_j, b_k) and calculated $\mathrm{MI}\left({\vec{\mathit{z}}}_{\mathit{k}},T_{x,\mathrm{17,20}}\right)$, again setting a point of comparison using D_17,20 (Fig. 4C, full matrix T_i,j,k Supplementary Fig. 9). We find enhanced information compared to the D_17,20 dimer in T_16,17,20 (~1.3 bits) and T_17,20,21 (~1.2 bits). These results suggest the primary bases that determine sequence dependent kinetics are located at x = 16, 17, 20 and 21 nt, and that MI can be used to develop k-mer models of enzyme-DNA interactions. Due to the size of the data set, we could not continue further onto quadromers; however, in Supplementary Discussion 5 we analyzed the variance of quadromers for which we had multiple measurements (Supplementary Fig. 17, Supplementary Discussion 5).

Fig. 4. Mutual information approach to k-mer map generation.

A Schematic of the nanopore system showing how multiple bases are used to construct k-mers. B $\mathrm{MI}\left({\vec{z}}_k,b_x\right)$, using κ = 5. C Mutual information between ${\vec{z}}_k$ and dimer D_x,20, using κ = 5. D Mutual information between ${\vec{z}}_k$ and trimer T_x,17,20, using κ = 1. Source data are provided as a Source Data file.

Importantly, because there are 16 dimers, 4 bits of information are required to uniquely specify a dimer (6 bits to specify one of 64 trimers, etc.). However, k-mer based sequencing strategies provide information in the form of constraints on transitions between adjacent k-mers, with up to 2 bits available in the case of the dimers, 4 bits for trimers and so on. For example, let us consider the problem of determining a single unknown base N in the sequence ‘N₁₄C₁₅C₁₆A₁₇C₁₈C₁₉G₂₀’ using a dimer model determined by D_17,20. Here, b₁₇ is A and b₂₀ is G, so D_17,20 = (A, G). If the helicase moves by 3 nucleotides, we now know that b₂₀ must be A, and therefore D_17,20 = (N, A). Because N can only be one of four possibilities, only two more bits are required to specify $D_{\mathrm{17,20}}$. From the kinetics information, we can learn on average ~1 of these 2 bits (at depth d > 20), substantially more than can be learned by analyzing b₁₇ and b₂₀ separately.

Estimating sequencing accuracy using both ion current and Hel308 kinetics data

We next sought to determine how helpful this additional sequence information is for nanopore sequencing. In nanopore sequencing, enzyme stepping errors or unobserved steps can lead to dephasing of the ion current and kinetics signals, due to the ~17-base displacement between the ion current read head in the pore constriction and kinetics read head within Hel308. Fully incorporating kinetic measurements into a nanopore sequencer therefore requires developing tools that can accommodate the uncertainty in this displacement. This is a significant undertaking beyond the scope of this study. Given our current dataset, it is possible to estimate an upper bound on the improvement in sequencing accuracy by incorporating WT Hel308 stepping kinetics and assuming perfect registration between the kinetics and ion current signals, and by not allowing insertions or deletions in the observations or in the called sequence.

To generate samples for sequencing, we simulated ion current data and enzyme kinetics data by generating and sampling the PDFs in Eq. (1) using a kernel density estimator (Fig. 5A, Supplementary Discussion 5, Supplementary Figs. 18 and 19). We used a hidden Markov model to decode the sequence from the simulated data using (i) mean ion current of open and closed conformations $\left({\vec{\mathit{z}}}_{\mathit{c}}\right)$, (ii) enzyme kinetics of open and closed conformations $\left({\vec{\mathit{z}}}_{\mathit{k}}\right)$, and (iii) both ion current and kinetics $\left({\vec{\mathit{z}}}_{\mathit{c}+\mathit{k}}\right)$. The simultaneous inclusion of both data streams led to improved sequencing results, consistent with an increase in MI. Figure 5B highlights a site in which the same sequencing error (A miscalled as G) was made using ion current and kinetics individually, but is corrected by using them simultaneously. Figure 5C shows the mutual information between the base sequence and each of the three $\vec{z}$ discussed above (using k-mer = 4 for ion current; k-mer = 2 for kinetics), as a function of the sequencing depth, d, defined as the number of measurements per sequence context (Supplementary Fig. 20, Supplementary Table 3). The ion current contains more information than kinetics, and the two signals together contain more information than the current alone. As d increases, statistical errors average away, leaving only the systematic errors from variation in different realizations of the k-mers. The maximal information in a k-mer map can be extracted by fitting MI(d) to:

$$\mathrm{MI}\left(d\right)=I_{\infty }\cdot \left(1-a\cdot e^{-bd}\right)$$ 3

Where $I_{\infty }$ is the maximal information that can be extracted from the k-mer model. The exponential decay represents that each measurement provides some random fraction of the remaining total information. We find that $I_{\infty }$ is ~0.9 bits for ${\vec{\mathit{z}}}_{\mathit{k}},$ ~ 2.9 bits for ${\vec{\mathit{z}}}_{\mathit{c}}$ and ~3.4 bits for ${\vec{\mathit{z}}}_{\mathit{c}+\mathit{k}}$.

Fig. 5. Estimate of nanopore sequencing accuracy using ion current and enzyme kinetics.

A Schematic demonstrating how to combine different sources of information into a single feature vector. B Sequencing simulated data of a pseudo-random sequence of length 20,000 nt. Both ion current (red) and kinetics (blue) only sequencers make the same mistake (A miscalled as G), but using the data sources together leads to a correction of multiple errors (purple). C Mutual information as a function of the sequencing depth. $\mathrm{MI}\left({\vec{z}}_k,D_{\mathrm{17,20}}\right)$ (blue), $\mathrm{MI}\left({\vec{z}}_c,Q_{-2,-\mathrm{1,0,1}}\right)$(red) and $\mathrm{MI}\left({\vec{z}}_{c+k},Q_{-2,-\mathrm{1,0,1}}\right)$ (purple, distance corrected). D Sequencing error rate vs. sequencing depth. Colors as in (C). Black dashed lines are fits to Eq. 4. E Correspondence between error rate and mutual information. F Confusion matrices for d = 20 (left), ion current only (middle), enzyme kinetics only (right) both ion current and enzyme kinetics. Source data are provided as a Source Data file.

We then estimated how the sequencing error rate depends on sequencing depth. In nanopore sequencing, a single read of a DNA context is often sufficient to reduce the uncertainty in the mean ion current measurement to negligible levels, because the ion current states are heavily sampled^13,15. This is not the case for kinetics: each enzyme read typically produces only a single measurement of the dwell time and probability of the backwards step. The distribution of a single dwell time measurement is the convolution of two exponential distributions, and the distribution of P_b is a beta distribution (Supplementary Discussion 3.4). Figure 5D shows the estimated error rate as a function of sequencing depth for each of the sequencers described above. The error rate for a random sequencer without insertions or deletions is 0.75. At d = 20, the error rate for a kinetics-based sequencer is ~0.4, and for an ion current-based sequencer is ~0.1. This error rate decreases to ~0.03 when both sources of information are used together. Interestingly, using only d = 3 reads of current and kinetics together leads to a lower error rate than d = 20 reads of ion current alone, suggesting that even the relatively weak information contained in Hel308 kinetics can lead to substantial improvement in error rate and throughput. Figure 5E shows a scatter plot of error rate vs. MI, with higher MI corresponding to a lower error rate (Supplementary Discussion 8, Supplementary Fig. 20). Figure 5F shows confusion matrices for each of the sequencers described above, showing that at high sequencing depth that augmenting an ion current sequencer with WT Hel308 kinetics can result in a 4–5× reduction in error rate.

Effects of mutations to Hel308 on translocation kinetics

The analysis above implies that mutations to Hel308, which increase the mutual information between the kinetics and sequence, could improve sequencing accuracy. To that end, we sought to understand how interactions between amino acids in Hel308 and the DNA influence the kinetics of translocation. We previously used a crystal structure of Hel308 from A. fulgidus conjugated to double-stranded DNA³³, combined with protein sequence alignment between Hel308 T. gammatolerans and Hel308 A. fulgidus¹, to map contacts between Hel308 and the template ssDNA sequence (Fig. 6A, B). We hypothesized that by changing the amino acids interacting with the DNA sequence that the kinetics of helicase translocation would be altered. We made 11 point-mutations in which a single amino acid residue interacting with the ssDNA was changed to alanine, effectively removing an interaction between the protein and DNA one at a time. We also expressed Hel308Δ5, in which all of domain 5 was removed.

Fig. 6. Mutations to Hel308 identify key residues in ssDNA translocation.

A Crystal structure of Hel308 from A. fulgidus. Protein domains are: RecA1 (green), RecA2 (cyan), Beta-hairpin (pink), Winged-helix (orange), Ratchet helix (burgundy). B Schematic showing the contacts between Hel308 and the DNA sequence, translated from A. fulgidus to T. gammatolerans using protein sequence alignment. C Mean dwell time of the closed conformation in Hel308 mutants; each data point is the mean and SEM taken over 20 sequence positions (Supplementary Figs. 23 and 24). *p < 0.01 (p = 0.004, K78A; p = 0.003, R349A; two sided 2-sample t-test corrected for 11 tests). The dashed line is the mean value of WT Hel308. The number of events for each mutant is given in Supplementary Table 2 (N > 10 for each mutant/sequence combination). Each data point shown here is the average taken over all sequence-contexts for a given enzyme/sequence combination. Each mutant enzyme was run on at least 3 DNA sequences (except for K124A, which was run on two sequences and the Δ5 variant, which was run on one sequence). D Mean probability of the backwards step of the closed conformation. *p < 0.01 (p = 0.002, K78A), two-sided 2-sample t-test corrected for 11 tests. E Mean dwell time of the open conformation. F Mean probability of the backwards step of the open conformation. Error bars in (C–F) are S.E.M. G $MI\left({\vec{z}}_k,D_{\mathrm{17,20}}\right)$ vs sequencing depth for WT Hel308 (blue) and K78A mutant (yellow). H Information rate, defined as $\mathrm{MI}\left[\frac{\mathrm{bits}}{\mathrm{nt}}\right]\cdot \mathrm{velocity}\cdot \left[\frac{\mathrm{nt}}{\mathrm{s}}\right].$ Although K78A has slightly more information per step, its reduced velocity (17 nt/s vs 20 nt/s for WT) leads to a similar information rate to WT. Source data are provided as a Source Data file.

We screened Hel308 variants using nanopore experiments on three DNA sequences and measured the dwell time and probability of a backwards step (Fig. 6C–F). Most of the mutations resulted in almost no change in Hel308 kinetics (K124A, R310A, Y350A, E603 A, D606A, W607A, Hel308Δ5). Several others mutants may have had small effects which do not rise to the level statistically significant from just 3 measured sequences, such as R248A and R600A which had a modest increase in the probability of a backwards step of the closed conformation and D154A which had a small increase in the dwell time and probability of a backwards step of the open conformation The most dramatic effects on kinetics of the closed conformation were observed in mutants R349A and K78A (p < 0.01; 2-sample t-test corrected for multiple testing). The mutation R349A resulted in a decrease in the average dwell-time at each sequence position compared to WT Hel308, whereas K78A had both a large decrease in the dwell time and a large increase in the probability of a backwards step at each sequence position compared to WT. Despite these changes in kinetics, the relative response to sequence for both R349A and K78A is similar to WT (Supplementary Figs. 21–24). For example, in K78A cytosines at b₂₀ result in lower P_b compared to the mean, despite the overall increase in P_b from ~20% to ~50%, suggesting that sequence-dependent kinetics seen with WT Hel308 are the result of the full environment of the helicase in the vicinity of the R349 and K78 amino acids in addition to specific interactions between amino acids and particular DNA bases.

These results are striking when compared with the MI. In Fig. 3A, we showed that the sequence-dependent response to b₁₇ is primarily in the dwell time, whereas the sequence-dependent response to b₂₀ is in both the dwell time and P_b. The mutation R349A affects only dwell time, whereas the mutation K78A affects both dwell time and P_b, and these amino acids contact the DNA with a 3-nt separation (Fig. 6B), identical to the separation observed in MI. We therefore suggest an association of b₁₇ with the amino acid R349 and b₂₀ with the amino acid K78. Each of the mutations that significantly altered Hel308 kinetics interacts with the DNA sequence between the +4 to +7 sites in the structure (K78A, D154A, R248A, R349A, R600A, shaded box Fig. 6B), suggesting these are the primary DNA-amino acid contacts responsible the translocation kinetics of Hel308 and that this is a region of the helicase that could be fruitful for making mutations that alter sequence-dependent translocation. Intriguingly, most of these amino acids, except for R349, interact primarily with the DNA backbone rather than directly with the DNA bases themselves.

We next measured the relative sequence-dependent response of Hel308 WT to Hel308 K78A, because K78A showed the largest change in kinetic parameters relative to WT, with t_c and P_b both changing in response to the mutation. Figure 6G shows MI(${\vec{z}}_k$,D_17,20) as a function of the sequencing depth. Hel308 K78A has a slightly higher information content on a per-step basis compared to Hel308 WT. However, K78A is, on average, slower than WT. Figure 6H shows the information rate, $\overline{\mathrm{MI}}$ in terms of $\mathrm{MI}$ and the helicase velocity, v:

$$\overline{\mathrm{MI}}\left[\frac{bit}{s}\right]=\mathrm{MI}\left[\frac{bit}{nt}\right]\cdot v\left[\frac{nt}{s}\right]$$ 4

with K78A having a similar information rate to WT due to its reduced speed, despite a slightly larger information per step. Enzyme mutations can be selected to optimize for either maximum per-step information or maximal information rate.

Discussion

These results have applications in the study of enzyme-nucleic acid interactions and in developing motor enzymes for sequencing nucleic acids, in which the enzyme kinetics yield information about the nucleic acid sequence. The information theory approach is a holistic approach to understanding the sequence-dependent behavior of motor enzymes. Rather than asking a specific question such as “what sequence motifs cause the enzyme to slow down?,” our approach determines the strength of the relationship between a given observable and the underlying nucleic acid sequence, making it sensitive to more complex relationships between enzyme behavior and DNA sequence. This approach can quickly evaluate the sequencing power for a range of experimental conditions. The experimental parameter space for optimization of nanopore sequencing is vast, including salinity, temperature, pH, choice of nanopore and choice of motor enzyme. The pore and enzyme can also be modified via many possible mutations at several sites. This approach allows for quick evaluation and comparison across a vast parameter space without the need to collect massive datasets and train sequencing models for each configuration.

Every motor enzyme we have observed using nanopore tweezers has shown some degree of sequence dependence, including monomeric helicases^3,21,24,25, DNA & RNA polymerases^13,26,27,34, and a reverse transcriptase³⁵. Nanopore tweezers make the detection of these phenomena straightforward because an enzyme’s nucleic acid position is measured via sequencing of the DNA. Still, other experiments using magnetic tweezers and optical tweezers have also observed sequence-dependent behavior in a range of enzymes^36–40. This suggests that sequence dependence may be the rule rather than the exception for motors that translocate on DNA and RNA. In many cases, the biological significance and physical mechanisms of such behavior are not well understood, and therefore, MI can be a useful tool to quantify sequence-specific interactions and to interpret their roles in biology.

Using MI, we identified sites which are responsible for controlling the sequence-dependence of kinetic observables, dwell time and probability of backwards step, parameters which we have previously shown can provide substantial insights into the biology of how helicases unwind DNA and interact with other biomolecules²³. Here, we used mutual information to identify two primary sites in Hel308 at x = 17 nt and x = 20 nt and secondary sites at x = 16 nt and x = 21 nt as responsible for their roles in ssDNA translocation and in determining sequence-dependent kinetics. Through point mutations and mutual information analysis, we identified the amino acids K78 and R349 for their central role in the kinetics of ssDNA translocation and suggest an association of R349 with the x = 17 nt displacement and K78 with the x = 20 nt displacement, although the physical basis for ssDNA sequence dependence remains unclear.

MI has value to the continued development of nanopore sequencing in several ways. Using MI, we identified a k-mer model for Hel308 kinetics that can improve nanopore DNA sequencing accuracy and provide substantially improved scaling with sequencing depth compared to ion current alone. Because this work was done with wild-type Hel308, we suspect that an engineered Hel308 with enhanced response to DNA sequence could be used to significantly enhance sequencing accuracy. Due to the combinatorially large set of possible mutations, future work to alter the sequence-dependent kinetics of Hel308 will necessarily include computational approaches. Molecular dynamics simulations or other approaches to calculate the energy of the interactions between the amino acids and DNA sequence in apo, ATP-bound and ADP-bound helicase states could reveal the energetics of sequence-dependent translocation and help generate predictions for how mutations to Hel308 could result in modified sequence-dependent kinetics^41–55. From there, promising mutants can be expressed and tested with nanopore tweezers. Because of the association between MI and sequencing accuracy (Supplementary Fig. 20), comparisons of the strength of the sequence-dependence of particular helicase mutants for sequencing can be quickly evaluated using a relatively small number of measurements (N ~ 300 enzyme steps along random, known DNA templates with sequencing depth d ≥ 20), and without the need to develop sequencing algorithms, obviating the need to measure complete k-mer maps for enzyme evaluation. It is important to note that MI does not have a 1–1 association with sequencing accuracy, instead providing upper and lower bounds on error rate^29,30,56, however, our results suggest that MI can be useful as a proxy for the order-of-magnitude error rate of an ideal sequencer. Information theory could potentially be extended to analyze error rates for more realistic sequencing devices by combining the MI approach here with an understanding of how sequencing errors, such as inserts or deletions, result in information loss. Similar analysis could also be used to further optimize mutations to the nanopore or variations to other experimental parameters such as salinity, ATP concentration, pH, temperature, or applied voltage.

Because of the displacement between the site where the ion current is determined (x = −3 to +2 nt) and where the Hel308 kinetics (x = 16–21 nt) are determined, integrating the information from sequence-dependent enzyme kinetics could further improve de novo nanopore sequencing by enabling correction of common error modes such as insertions and deletions. For example, if we simultaneously observed a long dwell time of the helicase and a high probability of a backwards step, we would know that we are more likely to have a cytosine at x = 17 nt and an adenine at x = 20 nt, constraining the possible sequences in between the constriction and the helicase to have exactly 16 nt. This second read head will also aid in resolving the length of long homopolymer sections and dinucleotide repeats, both due to an increased effective k-mer size and by accounting for sequence-dependent dwell times of the motor on long homopolymer sequences. It is also important to consider the kinetics of the read head’s performance in concert with the primary ion current read head. One could imagine a scenario in which the information contained in the kinetics signal is entirely redundant to sequence information contained in the ion current amplitude, thus combining them would yield no extra information, or in another scenario, the kinetics information could be completely complementary to the ion current information. The combined vector formulation of nanopore observables used here is useful for summarizing the sequence information contained in all nanopore observables combined for a given experimental configuration.

Commercially available nanopore sequencers developed by Oxford Nanopore Technologies (ONT) use sequencing algorithms based on machine learning algorithms, which take in raw ion current reads and return the DNA sequence. While it is difficult to know what information is “learned” by the sequencing model, it is likely these models learn to use kinetic information present within the nanopore signal. Even with machine learning approaches, our results suggest that engineering a motor enzyme to maximize the information encoded in its sequence-dependent behavior should yield significant gains in sequencing accuracy. Engineering a motor enzyme to go significantly slower via pauses and backsteps can significantly increase the single-molecule read accuracy while reducing the speed at which strands are read. Still, the results of Fig. 5D suggest this is a net gain in throughput even for applications in which multiple reads are combined into a consensus read, because lower coverage is necessary to achieve a given accuracy, and the achievable accuracy is higher with individual reads that are more informative. As shown in Fig. 5D, there are diminishing returns for re-reads of the same sequence using ion current alone because most of the information is already available in the first read. Subsequent reads provide a fraction of the remaining information and do not efficiently resolve ambiguous signals in which the signals for the incorrect and correct sequence appear nearly identical; bases that are hard to distinguish in a single read are still hard to distinguish the second time. The additional sequence information embedded in the motor enzyme kinetics provides an independent source of information that can help resolve ambiguous signals, producing both higher single-molecule and consensus accuracy.

For applications such as sequencing nucleic acids with modifications or additional bases, this additional source of information could prove crucial due to the increased information density of the nucleic acid and the relatively little room for improving the ion current signal dynamic range. For example, in sequencing an 8-letter genetic alphabet, 3 bits of information would be required to achieve high sequencing accuracy. Recent work has suggested that Hel308 responds strongly to non-standard DNA bases¹², suggesting that kinetic information could be a major contributor to sequencing expanded genetic alphabets.

The ability to make informed mutations that result in specific altered properties of enzymes is an important aspect of optimizing enzyme-based biotechnologies. This work suggests significant increases in sequencing accuracy can be obtained by optimizing the motor enzyme for nanopore sequencing and provides tools for probing the sequence-dependent kinetics of motor enzymes essential to life.

Methods

Lipid bilayer and nanopore establishment

Lipid bilayers (1,2-di-O-phytanyl-sn-glyscero-3-phosphocoline, Avanti Polar Lipids) were established across an ~20 µm Teflon aperture by mixing desiccated lipid with hexadecane and painting with a single-bristle paintbrush. M2-NNN MspA nanopores (accession CAB56052.1) were added to the cis well. Upon insertion of a single nanopore, the volume was perfused to remove any excess MspA. A single nanopore is recognized by characteristic asymmetric ion currents of +145 pA/−180 pA at 180 mV/−180 mV applied voltage, respectively, in conditions of 23 ± 1 °C, with 400 mM KCl, 10 mM HEPES buffered to pH 8.

Experimental conditions

Once a single nanopore had been established, a buffer containing pH 8.00 ± 0.05, 400 mM KCl, 10 mM MgCl2, 10 mM HEPES and 1 mM ATP was perfused to the cis reaction volume. Hel308, DNA and DTT were then added to final concentrations of 20 nM, 10 nM and 1 mM, respectively. The trans reaction volume was buffered at pH 8.00 ± 0.05, 400 mM KCl, and 10 mM HEPES. All experiments were performed at 37 ± 1 °C. DNA sequences used in this study are listed in supplementary table 1 and discussed in detail in Supplementary Discussion 6.1.2. Each DNA sequence was annealed with a common complement with sequence 5’ CCTGCATGAGAATGCGATAGTGAGATTTTTTTTTTTTTTTTTTTTZ 3’ where Z is a cholesterol base designed to insert into the bilayer.

Data acquisition and ion current recording

Data was acquired with custom LabVIEW software on an Axopatch 200B amplifier at 50 kHz sampling frequency, and downsampled by averaging to 5000 Hz. The LabVIEW software is provided with the figshare repository. Ion current patterns were compiled into a consensus sequence previously¹; briefly, many traces of a known sequence are recorded, a prediction for the expected ion current pattern is produced using the ion current-to-sequence map from ref. ¹⁴, and then alignments of the raw data are iteratively aligned to the prediction which is updated to form a new prediction. Raw data were aligned to this consensus sequence as described in ref. ¹⁴, and corrected by hand for errors.

Kinetics methods

Kinetic analysis follows the methods described in refs. ^21,22, and are available in the Supplementary Information

Protein expression and purification

The gene for Hel308 from Thermococcus Gammatolerans was assembled by GenScript in the pET28b+ expression vector between NdeI and NotI restriction sites with a 6× His tag and a thrombin cleavage site. The plasmid was transformed into BL21 DE3 cells and grown in 0.5 L of auto-induction media. Because Hel308 is thermostable, the cells were lysed and then heat-shocked at 80 °C to denature the endogenous E. coli proteins, followed by cooling. This sample was centrifuged at 60,000g for 30 min to form an aggregate, and the supernatant was collected. Hel308 was then purified using a nickel column, and the His tag was cleaved using thrombin.

Statistics and reproducibility

We sought to measure each enzyme/DNA combination at least 10 times to obtain estimates of the mean and standard error of the dwell time and probability of a backwards step. For enzymes such as the WT and K78A mutants, we sought to understand the scaling of MI with sequencing depth, and so we included only sequence contexts with at least N = 20 measurements. These were interpreted in the context of the well-established kinetic model of Hel308²¹ (Supplementary Discussion 3.4, Supplementary Fig. 12) and single-molecule enzyme-kinetics theory (Supplementary Discussions 3.4.2–3.4.3).

Some ion current vs time data is rejected in this study. The most common reasons for data rejection are: (1) errors in the DNA sequence, such as a mutation or a deletion. Mutations are recognized by a sequence of 6–8 ion current states that differ systematically from the empirical prediction. Deletions are recognized by successive missed ion current states. These errors can affect the measured kinetics or the registration between kinetics and current signals and are therefore rejected. (2) Sometimes nanopores undergo a phenomenon known as pore gating, in which the conductance is spontaneously reduced to ~1–10% of its original value. If a large amount of gating is present (typically >50% of a read), then it can be rejected. Some traces with minimal amounts of gating only have the data in the gated region removed. In these cases, any ion current states that display gating are rejected. No randomization was performed in this study. Each nanopore experiment had only a single enzyme/DNA sequence combination included in the experiments. The investigators were not blinded to allocation during experiments and outcome assessments.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

Designed experiments: J.M.C., A.H.L., and S.K.M. Background research: J.M.C., A.H.L., H.B., and J.H.G. Plasmid design, protein expression and purification: J.M.C. and S.K.M. Collected data: J.M.C., E.F.L., S.J.A., M.C.F., J.R.H., H.C.K., and J.D.C. Analyzed data: J.M.C., A.H.L., H.B., and C.A.T. Wrote and edited paper: J.M.C., A.H.L., H.B., C.A.T., and J.H.G.

Peer review

Peer review information

Nature Communications thanks Maria Spies and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The raw data, intermediate analysis products, results and code generated in this study have been deposited in the figshare database (10.6084/m9.figshare.31100482)⁵⁷. Source data are provided with this paper.

Code availability

A code repository containing all code necessary to analyze the data has been made available in figshare (10.6084/m9.figshare.31100482)⁵⁷.

Competing interests

J.M.C., A.H.L., H.B., and J.H.G. and the University of Washington have US patent 10359395 “Nanopore-based analysis of protein characteristics” on the nanopore tweezers technology, which covers methods discussed herein, including the use of a nanopore to measure kinetic states of an enzyme, and to correlate that behavior with the DNA sequence in the enzyme. The remaining authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-69867-2.