Michael Zwolak

Colloquium : Physical approaches to DNA sequencing and detection

With the continued improvement of sequencing technologies, the prospect of genome-based medicine is now at the forefront of scientific research. To realize this potential, however, a revolutionary sequencing method is needed for the cost-effective and rapid interrogation of individual genomes. This capability is likely to be provided by a physical approach to probing DNA at the single-nucleotide level. This is in sharp contrast to current techniques and instruments that probe (through chemical elongation, electrophoresis, and optical detection) length differences and terminating bases of strands of DNA. Several physical approaches to DNA detection have the potential to deliver fast and low-cost sequencing. Central to these approaches is the concept of nanochannels or nanopores, which allow for the spatial confinement of DNA molecules. In addition to their possible impact in medicine and biology, the methods offer ideal test beds to study open scientific issues and challenges in the relatively unexplored area at the interface between solids, liquids, and biomolecules at the nanometer length scale. This Colloquium emphasizes the physics behind these methods and ideas, critically describes their advantages and drawbacks, and discusses future research opportunities in the field.

Fast DNA sequencing via transverse electronic transport.

A rapid and low-cost method to sequence DNA would usher in a revolution in medicine. We propose and theoretically show the feasibility of a protocol for sequencing based on the distributions of transverse electrical currents of single-stranded DNA while it translocates through a nanopore. Our estimates, based on the statistics of these distributions, reveal that sequencing of an entire human genome could be done with very high accuracy in a matter of hours without parallelization, that is, orders of magnitude faster than present techniques. The practical implementation of our approach would represent a substantial advancement in our ability to study, predict, and cure diseases from the perspective of the genetic makeup of each individual.

Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm.

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension.

Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems

Using time-dependent current-density functional theory, we derive analytically the dynamical exchange-correlation correction to the dc conductance of nanoscale junctions. The correction pertains to the conductance calculated in the zero-frequency limit of time-dependent density functional theory within the adiabatic local-density approximation. In particular, we show that in linear response, the correction depends nonlinearly on the gradient of the electron density; thus, it is more pronounced for molecular junctions than for quantum point contacts. We provide specific numerical examples to illustrate these findings.

Uncertainty Relations from Simple Entropic Properties

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and as well as being fundamental to our understanding of quantum theory, they have practical applications such as for cryptography and witnessing entanglement. Here we shed new light on the entropic form of these relations, showing that they follow from a few simple properties, including the data-processing inequality. We prove these relations without relying on the exact expression for the entropy, and hence show that a single technique applies to several entropic quantities, including the von Neumann entropy, min- and max-entropies, and the Rényi entropies.

Effect of Noise on DNA Sequencing via Transverse Electronic Transport

Previous theoretical studies have shown that measuring the transverse current across DNA strands while they translocate through a nanopore or channel may provide a statistically distinguishable signature of the DNA bases, and may thus allow for rapid DNA sequencing. However, fluctuations of the environment, such as ionic and DNA motion, introduce important scattering processes that may affect the viability of this approach to sequencing. To understand this issue, we have analyzed a simple model that captures the role of this complex environment in electronic dephasing and its ability to remove charge carriers from current-carrying states. We find that these effects do not strongly influence the current distributions due to the off-resonant nature of tunneling through the nucleotides--a result we expect to be a common feature of transport in molecular junctions. In particular, only large scattering strengths, as compared to the energetic gap between the molecular states and the Fermi level, significantly alter the form of the current distributions. Since this gap itself is quite large, the current distributions remain protected from this type of noise, further supporting the possibility of using transverse electronic transport measurements for DNA sequencing.

Quantized ionic conductance in nanopores

Ionic transport in nanopores is a fundamentally and technologically important problem in view of its occurrence in biological processes and its impact on novel DNA sequencing applications. Using molecular dynamics simulations we show that ion transport may exhibit strong nonlinearities as a function of the pore radius reminiscent of the conductance quantization steps as a function of the transverse cross section of quantum point contacts. In the present case, however, conductance steps originate from the break up of the hydration layers that form around ions in aqueous solution. We discuss this phenomenon and the conditions under which it should be experimentally observable.

Redundant imprinting of information in nonideal environments: Objective reality via a noisy channel

Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, E , is in a non-ideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, S, and an environment fragment, F , is given solely by F ’s entropy increase. This demonstrates that the environment’s capacity for recording the state of S is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with S, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that when decoherence is not complete the deviation of the mutual information from F ’s entropy change is quantified by the quantum discord, i.e., the excess mutual information between S and F is information regarding the initial coherence between pointer states of S. In addition to illustrating these results with a single qubit system interacting with a multi-qubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of S. Our results demonstrate that Quantum Darwinism is robust with respect to non-ideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.

Dehydration and ionic conductance quantization in nanopores

There has been tremendous experimental progress in the last decade in identifying the structure and function of biological pores (ion channels) and fabricating synthetic pores. Despite this progress, many questions still remain about the mechanisms and universal features of ionic transport in these systems. In this paper, we examine the use of nanopores to probe ion transport and to construct functional nanoscale devices. Specifically, we focus on the newly predicted phenomenon of quantized ionic conductance in nanopores as a function of the effective pore radius--a prediction that yields a particularly transparent way to probe the contribution of dehydration to ionic transport. We study the role of ionic species in the formation of hydration layers inside and outside of pores. We find that the ion type plays only a minor role in the radial positions of the predicted steps in the ion conductance. However, ions with higher valency form stronger hydration shells, and thus, provide even more pronounced, and therefore, more easily detected, drops in the ionic current. Measuring this phenomenon directly, or from the resulting noise, with synthetic nanopores would provide evidence of the deviation from macroscopic (continuum) dielectric behavior due to microscopic features at the nanoscale and may shed light on the behavior of ions in more complex biological channels.

Complementarity of quantum discord and classically accessible information

The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. We also prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.