Random-walk enzymes

Chi H. Mak, Phuong Pham, Samir A. Afif, and Myron F. Goodman

Phys. Rev. E 92, 032717 – Published 17 September 2015

Abstract

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The $C \to U$ deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

Received 27 April 2015

DOI:https://doi.org/10.1103/PhysRevE.92.032717

Authors & Affiliations

Chi H. Mak^1,2, Phuong Pham³, Samir A. Afif³, and Myron F. Goodman^1,3

¹Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
²Center for Applied Mathematical Sciences, University of Southern California, Los Angeles, California 90089, USA
³Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 92, Iss. 3 — September 2015

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Diagrammatic representation of the perturbation series for scanning-coupled catalysis. Single lines represent scanning trajectories. Circles labeled U represent mutation events. Loop diagrams correct for paths with multiple mutations on the same motif. The full propagator, represented by the double line, is the sum over all possible paths.
Reuse & Permissions
Figure 2
Computed mutation probabilities on a hot- ${hot}^{'}$ –hot-cold test cassette. (a) Intrinsic mutations rates $u_{i}$ on the 63-motif hot- ${hot}^{'}$ –hot-cold cassette for AID-catalyzed $C \to U$ mutations on ssDNA. (b) Mutation probabilities predicted by the passive model as a function of sequence position are directly proportional to the intrinsic mutation rates. (c) Mutation probabilities predicted by the intrusive model shows contextual dependence, where the computed mutation probability of a site is influenced by surrounding motifs. (d) Probability $ρ_{i}$ of finding the enzyme on the cassette corresponding to (c), decomposed into contributions from the four lowest eigenfunctions in the order red, green, blue, and black. (e) Mutation probabilities predicted by the intrusive picture in the rapid diffusion limit where the system reduces to the passive picture. (f) Mutation probabilities predicted by the intrusive picture in the slow diffusion limit, which also reduces to the passive picture.
Reuse & Permissions
Figure 3
Experimental setup and results. (a) Deamination assay reports AID-catalyzed deaminations on target cassettes with multiple trinucleotide motifs NNC embedded in lacZ $α$ reporter gene. Examples of deaminated mutant clones with $C \to U$ deaminations shown as Ts. (b) Elements of the scanning transition matrix $W_{i j}$ as a function of distance $i - j$ derived from mutation correlation analysis on a homogeneous (AGC) $_{56}$ cassette [12]. (c) Motif-dependent intrinsic deamination rates along the DNA sequence for an inhomogeneous hot- ${hot}^{'}$ –hot-cold cassette, (d) the experimentally observed mutation frequencies showing sequence-dependent deamination probabilities, and (e) the mutation frequencies predicted by the intrusive model after $t = 45$ s, the length of the experiments. (f) Intrinsic deamination rates along the DNA sequence for a hot- ${hot}^{'}$ –hot-frigid–hot-frigid cassette, (g) the observed mutation frequencies, and (h) the frequencies predicted by the intrusive model after $t = 60$ s. Experimental variability in (d) and (g), $\sim$ (number of mutations) $^{1 / 2}$ , are typically $< 5$ , whereas the sequence-dependent effects are generally $> 20$ . Dashed lines in (e) and (h) indicate expected hot-motif mutation counts from the passive model which exhibit no sequence context dependence. (Other details of the passive model results are not shown.)
Reuse & Permissions
Figure 4
Computed mutation probabilities on a hot- ${hot}^{'}$ –hot-frigid–hot-frigid test cassette. (a) The site-dependent intrinsic mutation rates $u_{i}$ on this 96-motif cassette, which corresponds to the experiment in Fig. 3. (b) Mutation probabilities computed by Monte Carlo simulations. (c) Probability of finding the enzyme $ρ_{i}$ as a function of sequence position on the substrate from the Monte Carlo simulations.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics