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

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.Comment: 4 pages, 3 figure

Feynman's ratchet and pawl: an exactly solvable model

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio

Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle

The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than $1/(4\pi)$. We study human ability to simultaneously judge the frequency and the timing of a sound. Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity. Our results establish a lower bound for the nonlinearity and complexity of the algorithms employed by our brains in parsing transient sounds, rule out simple "linear filter" models of early auditory processing, and highlight timing acuity as a central feature in auditory object processing.Comment: 4 pages, 2 figures; Accepted at PR

Noise in neurons is message-dependent

Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that such variability is a function of the input, and can be made arbitrarily large or small by a suitable choice of inputs. Our considerations are expected to extend to virtually any mechanism of spike generation, and we illustrate them with data from the visual pathway. Thus, a simplification usually made in the application of information theory to neural processing is violated: noise {\sl is not independent of the message}. However, we also show the existence of {\sl error-correcting} topologies, which can achieve better timing reliability than their components.Comment: 6 pages,6 figures. Proceedings of the National Academy of Sciences (in press

Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment

Negative Resistance in Brownian Transport

We prove that negative incremental resistance cannot occur on 1D spaces like the circle or the line; we construct an explicit two-dimensional model on the cylinder, and its collapse into a branched 1D backbone. We derive an accurate numerical method for solving our 2D model, and discuss the relevance of the model to biological ion channels.Comment: 3 separate figure

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available in postscript form http://cmtw.harvard.edu/~deniz

Quantum Ratchets

The concept of thermal ratchets is extended to the system governed by quantum mechanics. We study a tight-binding model with an asymmetric periodic potential contacting with a heat bath under an external oscillating field as a specific example of quantum ratchet. Dynamics of a density operator of this system is studied numerically by using the quantum Liouville equation. Finite net current is found in the non-equilibrium steady state. The direction of the current varies with parameters, in contrast with the classical thermal ratchets.Comment: 7 pages, Latex, 4 ps figures; No change in the text by this replacement. only the figures are replaced with higher quality ones (but smaller size

Driven lattice glass as a ratchet and pawl machine

Boundary-induced transport in particle systems with anomalous diffusion exhibits rectification, negative resistance, and hysteresis phenomena depending on the way the drive acts on the boundary. The solvable case of a 1D system characterized by a power-law diffusion coefficient and coupled to two particles reservoirs at different chemical potential is examined. In particular, it is shown that a microscopic realisation of such a diffusion model is provided by a 3D driven lattice-gas with kinetic constraints, in which energy barriers are absent and the local microscopic reversibility holds.Comment: 12 pages, 4 figures, minor change