In this work, we have developed a method that can quantitatively map the misincorporation landscapes of error-prone polymerases as a function of environmental signals. Specifically, we quantified how the concentrations of environmental Mg2+, Mn2+ and Ca2+ affect the fidelity of Dpo4 and Klenow exo−. Mn2+ has the strongest influence on misincorporation rates in comparison to the other cations. Our method resolves the misincorporation by spatial position and nucleotide-to-nucleotide transition. We find that, for Dpo4 and Klenow exo−, Mn2+ and Mg2+ change misincorporation rates but leave the distribution across incoming misincorporated nucleotides untouched. We have further shown that polymerase misincorporation rates exhibit sequence dependences. The development of a DNAP-based cation sensor, then, necessitates calibration of misincorporation rates at specific template positions, within specific sequence contexts, and at specific buffer conditions. The buffer-specificity of some DNAPs suggests that polymerase-based sensors might work best within controlled buffer environments, e.g. within living cells expressing ion channels, which can maintain buffer integrity, but selectively allow targeted ions to permeate. Our experiments quantify the transfer function of misincorporation from cations, through processing, all the way to DNA sequence data.
Our assay differs in important ways from the bacterial assays that have been used for the quantification of DNAP behavior 
. Through deep sequencing we can readily observe polymerase trajectories with single molecule and single base resolution while simultaneously generating large datasets, both of which are critical for achieving the comprehensive analyses necessary for establishing polymerase data encoding transfer functions. Single base pair resolution allows quantifying the template dependence of misincorporations, while single molecule resolution allows quantification of the correlation structure of misincorporations.
The method introduced here does have limitations, some of which can be mitigated. For example, the measured background noise level is likely dominated by errors introduced during the chemical synthesis of the oligonucleotides used as templates. The use of clonal isolates should dramatically lower that noise level and may prove necessary in adapting this method to the characterization of high fidelity DNAPs. In addition, GLM analysis indicates that the spatial dependence of the observed misincorporation rates may be in part due to the secondary structure of the ssDNA template. Using a nicked, double stranded template would reduce this source of variance, but would limit the applicability of the method to DNAPs with strand displacement or nick translation activity. While sophisticated molecular counting methods 
and clonal substrates are necessary to quantify the low misincorporation rates of proofreading polymerases using sequencing 
, in this study, we have investigated error-prone polymerases, and are therefore readily able to measure strong effects despite the limitations of our method.
Certain limitations of the method cannot be mitigated without resorting to engineered polymerase variants. For example, we have shown that neither DNAP studied here can act as a Ca2+ sensor in physiologically relevant conditions. Furthermore, these biologically-based recording devices are limited to conditions that enable efficient enzymatic activity; such devices will not work, without modification, in environments of extreme pH, temperature, oxidative stress, proteolysis, etc.
While we have demonstrated how a static ion concentration can be measured by a polymerase copying DNA, it would ultimately be useful to have polymerase-based sensors for time-dependent as well as static signals. To do so, it will be necessary to optimize the sensing polymerase for speed (for temporal resolution), processivity (for recording time), low pause probability (for linearity of temporal readout), total misincorporation rate (for information density) and dynamic range of misincorporation rate (for signal to noise ratio). We have shown that divalent ion concentration can be a potent, yet continuously tunable, modulator of polymerase misincorporation rates, and that such modulation can be restricted to particular template bases and base-to-base transitions. Based on its >15-fold change in misincorporation rate over the Mn2+ range tested here, Dpo4 could act as a high resolution Mn2+ sensor. The fact that misincorporations are largely localized to certain template bases makes it possible in principle to preserve relevant features of the template (on the non-error-prone template bases) while transmitting information at the same time (on the other bases).
Advances in fields such as neuroscience impose spatial, temporal, and combinatorial challenges of unparalleled scope, associated with the three-dimensional recording and analysis of complex cellular systems. A molecular device capable of measuring and recording sub-cellular signals, which can be manufactured and delivered to target environments in a scalable fashion, may emerge as an optimal platform for biological signal recording. However, the basic principles for designing and testing such molecular recording devices in vitro
have not yet been established. This study measures a static environmental signal – divalent cation concentration – by using DNA polymerases as molecular recording devices. The synthesized DNA strand can be considered as an archival medium, which stores the measured signal in the form of a misincorporation rate with respect to the known template. Indeed, the use of DNA as an information storage medium leverages the rapid improvement of sequencing technology, which is currently outpacing the Moore's law rate of improvement of microelectronic technology 
, and which promises to make DNA sequencing a preferred method for extracting data from biological and bio-molecular systems 
. Extension of the techniques described here to time-varying signals and engineered polymerases could lead to molecular sensing technologies of unprecedented scalability.