PMC

A) The percent error of the estimated parameters compared to the true parameters (those of DNAP) as a function of the number of template copies. B) The ion concentration estimation error based on polymerase parameters estimated from data using varying numbers of templates. Ion concentration estimation used N = 1000, and . In both panels, solid lines are median estimation errors, and dashed lines are 95% confidence intervals.

Performance of continuous decoding to estimate randomly determined sequences of eight concentrations over 20 minutes of recording, as a function of experimental parameters. Solid lines are median estimation errors, and dashed lines are 95% confidence intervals. A) Varying numbers of templates, with the CMLF fixed at and , and using DNAP kinetic parameters. B) Varying CMLFs, with the number of templates fixed at 1000, and using DNAP kinetic parameters. C, D) Varying DNAP pausing parameters, with a fixed elongation time of 20 ms, a fixed CMLF of and , and 1000 and 100 templates, respectively.

A) Example time-varying ion concentration signal. In a neuron, peaks in calcium concentration occur during neural firing. B) Example products from the simultaneous replication of multiple template strands, showing correct (C) and incorrect (I) nucleotide additions, with the time of incorporation shown on the horizontal axis. Misincorporations are more likely in the presence of higher ion concentration. C) The misincorporation counts from each template copy are summed to calculate the misincorporation probability at every nucleotide position in the template. In this example, approximately 100 nucleotides are replicated per second on average.

A) Estimation error of continuous concentration decoding at 1 second resolution as a function of the time of recording. Parameters are ms, P = 0, N = 1000, , and . B) Estimation error at 6000 seconds (10 minutes) of recording for polymerases that do not start recording simultaneously. Polymerase start-time distributions are drawn from gamma distributions that have almost all values between 0 and twice the average delay time. C) Estimation error of continuous concentration decoding at 100 ms resolution as a function of the time of recording. Parameters are ms, P = 0, N = 10000, , and varying . In all panels, solid lines are median estimation errors, and dashed lines are 95% confidence intervals.

Continuous decoding to estimate sequences of eight concentrations over 20 minutes of recording using varying numbers of templates. The 95% confidence interval of the estimated concentrations (light red) that result from the decoding algorithm presented here on an ion concentration input sequence representing the word “RECORDER” (dark red). Concentrations are mapped to letters via A = 0/25, B = 1/25,,…,Z = 25/25, so that the concentration sequence representing the word RECORDER is 17/25, 4/25…). The numbers of templates used were, from top to bottom, 1000, 100, 10, and 1. For all panels, kinetic parameters are those of DNAP ( ms, ms, ), , and ().

A) DNAP can copy one nucleotide directly after another (top path) or pause between additions (bottom path). B) Dwell-time distributions between nucleotide additions. Distributions for the continuous route and for the pausing route are mixed based on their relative frequencies to create the full dwell time distribution, . For this panel, the parameters are set as ms, ms, and P = 0.3, to best illustrate the concept of distribution mixing. C) Time distributions, , resulting from repeated convolutions of the dwell time distribution, are shown for nucleotides 50, 200, 400, and 600. Iterated convolutions cause the distribution to widen for later times. For this panel and below, parameters are ms, ms, . D) An example time-varying concentration. E) The probability of misincorporation for a polymerase subjected to the input concentration trace from panel B. The misincorporation probability is related to the concentration through a CMLF: here, F) The misincorporation probability of the nucleotide, . The more the nucleotide's incorporation-time distribution overlaps with the concentration peaks in the time-varying input signal, the larger the misincorporation probability at the nucleotide.