Scalable, Time-Responsive, Digital, Energy-Efficient Molecular Circuits using DNA Strand Displacement

We propose a novel theoretical biomolecular design to implement any Boolean circuit using the mechanism of DNA strand displacement. The design is scalable: all species of DNA strands can in principle be mixed and prepared in a single test tube, rather than requiring separate purification of each species, which is a barrier to large-scale synthesis. The design is time-responsive: the concentration of output species changes in response to the concentration of input species, so that time-varying inputs may be continuously processed. The design is digital: Boolean values of wires in the circuit are represented as high or low concentrations of certain species, and we show how to construct a single-input, single-output signal restoration gate that amplifies the difference between high and low, which can be distributed to each wire in the circuit to overcome signal degradation. This means we can achieve a digital abstraction of the analog values of concentrations. Finally, the design is energy-efficient: if input species are specified ideally (meaning absolutely 0 concentration of unwanted species), then output species converge to their ideal concentrations at steady-state, and the system at steady-state is in (dynamic) equilibrium, meaning that no energy is consumed by irreversible reactions until the input again changes. Drawbacks of our design include the following. If input is provided non-ideally (small positive concentration of unwanted species), then energy must be continually expended to maintain correct output concentrations even at steady-state. In addition, our fuel species - those species that are permanently consumed in irreversible reactions - are not "generic"; each gate in the circuit is powered by its own specific type of fuel species. Hence different circuits must be powered by different types of fuel. Finally, we require input to be given according to the dual-rail convention, so that an input of 0 is specified not only by the absence of a certain species, but by the presence of another. That is, we do not construct a "true NOT gate" that sets its output to high concentration if and only if its input's concentration is low. It remains an open problem to design scalable, time-responsive, digital, energy-efficient molecular circuits that additionally solve one of these problems, or to prove that some subset of their resolutions are mutually incompatible.Comment: version 2: the paper itself is unchanged from version 1, but the arXiv software stripped some asterisk characters out of the abstract whose purpose was to highlight words. These characters have been replaced with underscores in version 2. The arXiv software also removed the second paragraph of the abstract, which has been (attempted to be) re-inserted. Also, although the secondary subject is "Soft Condensed Matter", this classification was chosen by the arXiv moderators after submission, not chosen by the authors. The authors consider this submission to be a theoretical computer science paper

Selenium-Binding Protein 1 Indicates Myocardial Stress and Risk for Adverse Outcome in Cardiac Surgery

Selenium-binding protein 1 (SELENBP1) is an intracellular protein that has been detected in the circulation in response to myocardial infarction. Hypoxia and cardiac surgery affect selenoprotein expression and selenium (Se) status. For this reason, we decided to analyze circulating SELENBP1 concentrations in patients (n = 75) necessitating cardioplegia and a cardiopulmonary bypass (CPB) during the course of the cardiac surgery. Serum samples were collected at seven time-points spanning the full surgical process. SELENBP1 was quantified by a highly sensitive newly developed immunological assay. Serum concentrations of SELENBP1 increased markedly during the intervention and showed a positive association with the duration of ischemia (ρ = 0.6, p < 0.0001). Elevated serum SELENBP1 concentrations at 1 h after arrival at the intensive care unit (post-surgery) were predictive to identify patients at risk of adverse outcome (death, bradycardia or cerebral ischemia, "endpoint 1"; OR 29.9, CI 3.3-268.8, p = 0.00027). Circulating SELENBP1 during intervention (2 min after reperfusion or 15 min after weaning from the CPB) correlated positively with an established marker of myocardial infarction (CK-MB) measured after the intervention (each with ρ = 0.5, p < 0.0001). We concluded that serum concentrations of SELENBP1 were strongly associated with cardiac arrest and the duration of myocardial ischemia already early during surgery, thereby constituting a novel and promising quantitative marker for myocardial hypoxia, with a high potential to improve diagnostics and prediction in combination with the established clinical parameters

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering

Electron-phonon scattering in quantum point contacts

We study the negative correction to the quantized value $2e^2/h$ of the conductance of a quantum point contact due to the backscattering of electrons by acoustic phonons. The correction shows activated temperature dependence and also gives rise to a zero-bias anomaly in conductance. Our results are in qualitative agreement with recent experiments studying the 0.7 feature in the conductance of quantum point contacts.Comment: 4 pages, no figure

Temperature and magnetic-field dependence of the quantum corrections to the conductance of a network of quantum dots

We calculate the magnetic-field and temperature dependence of all quantum corrections to the ensemble-averaged conductance of a network of quantum dots. We consider the limit that the dimensionless conductance of the network is large, so that the quantum corrections are small in comparison to the leading, classical contribution to the conductance. For a quantum dot network the conductance and its quantum corrections can be expressed solely in terms of the conductances and form factors of the contacts and the capacitances of the quantum dots. In particular, we calculate the temperature dependence of the weak localization correction and show that it is described by an effective dephasing rate proportional to temperature.Comment: 24 pages, 14 figure

The electron lifetime in Luttinger liquids

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp(-t/\tau_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys $\tau_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T\tau_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.Comment: 20 pages, 1 column, 6 figures, 1 Table; expands cond-mat/0110307 and cond-mat/0503652; final version to appear in PR

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

Electron fractionalization induced dephasing in Luttinger liquids

Using the appropriate fractionalization mechanism, we correctly derive the temperature (T) and interaction dependence of the electron lifetime $\tau_F$ in Luttinger liquids. For strong enough interactions, we report that $(T\tau_F)\propto g$, with $g\ll 1$ being the standard Luttinger exponent; This reinforces that electrons are {\it not} good quasiparticles. We immediately emphasize that this is of importance for the detection of electronic interferences in ballistic 1D rings and carbon nanotubes, inducing ``dephasing'' (strong reduction of Aharonov-Bohm oscillations).Comment: 5 pages, 1 figure (Final version for PRB Brief Report

Probe-Configuration-Dependent Decoherence in an Aharonov-Bohm Ring

We have measured transport through mesoscopic Aharonov-Bohm (AB) rings with two different four-terminal configurations. While the amplitude and the phase of the AB oscillations are well explained within the framework of the Landaur-B\"uttiker formalism, it is found that the probe configuration strongly affects the coherence time of the electrons, i.e., the decoherence is much reduced in the configuration of so-called nonlocal resistance. This result should provide an important clue in clarifying the mechanism of quantum decoherence in solids.Comment: 4 pages, 4 figures, RevTe

Energy-time entanglement of quasi-particles in solid-state devices

We present a proposal for the experimental observation of energy-time entanglement of quasi-particles in mesoscopic physics. This type of entanglement arises whenever correlated particles are produced at the same time and this time is uncertain in the sense of quantum uncertainty, as has been largely used in photonics. We discuss its feasibility for electron-hole pairs. In particular, we argue that the recently fabricated 2DEG-2DHG junctions, irradiated with a continuous laser, behave as "entanglers" for energy-time entanglement.Comment: 4 pages, 3 figure