DNA as a universal substrate for chemical kinetics

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior

On the validity of entropy production principles for linear electrical circuits

We discuss the validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principle are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff's laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables' parity under time-reversal and, in particular, the origin of Landauer's counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.Comment: 19 pages, 1 fi

Bistable Gradient Networks II: Storage Capacity and Behaviour Near Saturation

We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we find evidence of a first-order "memory blackout" phase transition as in the Hopfield network. For weak coupling, on the other hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.Comment: 15 pages, 12 eps figures. Submitted to Phys. Rev. E. Sequel to cond-mat/020356

Antitrust Damages for Consumer Welfare Loss

Section 4 of the Clayton Act provides that any person who is injured in his business or property by reason of anything forbidden in the antitrust laws shall recover threefold the damages by him sustained. The current private enforcement model usually permits plaintiffs to recover damages based upon the excessive prices charged to consumers. However, economists see the real loss to society from an antitrust violation to be the consumer welfare loss which results from reduced output. The authors have been unable to locate any antitrust case which has permitted recovery of damages for this consumer welfare loss. Therefore, this article addresses the following issues: if consumer welfare loss is the true measure of the damage to society from an antitrust violation, should it be included in a damage recovery; if consumer welfare loss is recoverable, who is the proper party to recover for the loss; and what difficulties are there in measuring such a loss for purposes of awarding damages

Massively parallel computing on an organic molecular layer

Current computers operate at enormous speeds of ~10^13 bits/s, but their principle of sequential logic operation has remained unchanged since the 1950s. Though our brain is much slower on a per-neuron base (~10^3 firings/s), it is capable of remarkable decision-making based on the collective operations of millions of neurons at a time in ever-evolving neural circuitry. Here we use molecular switches to build an assembly where each molecule communicates-like neurons-with many neighbors simultaneously. The assembly's ability to reconfigure itself spontaneously for a new problem allows us to realize conventional computing constructs like logic gates and Voronoi decompositions, as well as to reproduce two natural phenomena: heat diffusion and the mutation of normal cells to cancer cells. This is a shift from the current static computing paradigm of serial bit-processing to a regime in which a large number of bits are processed in parallel in dynamically changing hardware.Comment: 25 pages, 6 figure

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

Dynamic separation of suspended solids

A pilot study of a dynamic means of separating suspended solids from a two-phase flow is described. The separation is achieved by passing the two-phase flow through an orifice. The difference in mass between the suspended solids and the fluid causes the path lines of the solids to deviate from the fluid streamlines when flowing through the abrupt contraction. Withdrawal of the center portion of the jet issuing from the orifice results in a primary separation of the solids from the fluid. The utility of this separation technique is indicated.Project # A-015-MO Agreement # 14-01-0001-184

Optimization of operation of a system of flood control reservoirs

Students supported: 1 Graduate StudentOptimization of operation of a system of flood control reservoirs is established by the application of mathematical programming. The mathematical procedure is applied to two different types of systems, reservoirs in parallel and reservoirs in tandem. The operational matrix to be optimized is made up of the objective function and the constraining equations. The objective function that is to be maximized is made up of the time sequence of releases from the reservoirs. The physical, structural and hydrological limitations are described by the constraint equations. All equations in the operational matrix are linear. Inflows to the reservoirs of the system and the initial conditions are assumed to be known, as are the reservoir capacities and downstream-channel maximum and minimum capacities. The objective of the operational matrix is to maximize the sum of releases thus minimizing the storage occupied by flood water. Set up of the operational matrix is carried out using a digital computer program and the optimization is carried out by applying the Linear-Programming algorithm of MPS/360. Results of the procedures are shown for a three reservoir system in the Kansas river basis (U.S.A.) using actual data.Project # B-065-MO Agreement # 14-31-0001-360