Theory of Tunneling Spectroscopy in a Mn12_{12} Single-Electron Transistor by Density-Functional Theory Methods

We consider tunneling transport through a Mn$_{12}$ molecular magnet using spin density functional theory. A tractable methodology for constructing many-body wavefunctions from Kohn-Sham orbitals allows for the determination of spin-dependent matrix elements for use in transport calculations. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. The energy splitting of the spin multiplets and the spatial part of their many-body wave functions, describing the orbital degrees of freedom of the excess charge, strongly affect the electronic transport, and can lead to negative differential conductance.Comment: 4 pages, 3 figures, a revised version with minor change

Inelastic fingerprints of hydrogen contamination in atomic gold wire systems

We present series of first-principles calculations for both pure and hydrogen contaminated gold wire systems in order to investigate how such impurities can be detected. We show how a single H atom or a single H2 molecule in an atomic gold wire will affect forces and Au-Au atom distances under elongation. We further determine the corresponding evolution of the low-bias conductance as well as the inelastic contributions from vibrations. Our results indicate that the conductance of gold wires is only slightly reduced from the conductance quantum G0=2e^2/h by the presence of a single hydrogen impurity, hence making it difficult to use the conductance itself to distinguish between various configurations. On the other hand, our calculations of the inelastic signals predict significant differences between pure and hydrogen contaminated wires, and, importantly, between atomic and molecular forms of the impurity. A detailed characterization of gold wires with a hydrogen impurity should therefore be possible from the strain dependence of the inelastic signals in the conductance.Comment: 5 pages, 3 figures, Contribution to ICN+T2006, Basel, Switzerland, July-August 200

Opportunities and limitations of transition voltage spectroscopy: a theoretical analysis

In molecular charge transport, transition voltage spectroscopy (TVS) holds the promise that molecular energy levels can be explored at bias voltages lower than required for resonant tunneling. We investigate the theoretical basis of this novel tool, using a generic model. In particular, we study the length dependence of the conducting frontier orbital and of the 'transition voltage' as a function of length. We show that this dependence is influenced by the amount of screening of the electrons in the molecule, which determines the voltage drop to be located at the contacts or across the entire molecule. We observe that the transition voltage depends significantly on the length, but that the ratio between the transition voltage and the conducting frontier orbital is approximately constant only in strongly screening (conjugated) molecules. Uncertainty about the screening within a molecule thus limits the predictive power of TVS. We furthermore argue that the relative length independence of the transition voltage for non-conjugated chains is due to strong localization of the frontier orbitals on the end groups ensuring binding of the rods to the metallic contacts. Finally, we investigate the characteristics of TVS in asymmetric molecular junctions. If a single level dominates the transport properties, TVS can provide a good estimate for both the level position and the degree of junction asymmetry. If more levels are involved the applicability of TVS becomes limited.Comment: 8 pages, 12 figure

The Smallest Molecular Switch

Ab-initio total energy calculations reveal benzene-dithiolate (BDT) molecules on a gold surface, contacted by a monoatomic gold STM tip to have two classes of low energy conformations with differing symmetries. Lateral motion of the tip or excitation of the molecule cause it to change from one conformation class to the other and to switch between a strongly and a weakly conducting state. Thus, surprisingly, despite their apparent simplicity these Au/BDT/Au nanowires are shown to be electrically bi-stable switches, the smallest two-terminal molecular switches to date. Experiments with a conventional or novel self-assembled STM are proposed to test these predictions.Comment: 8 pages, 3 figure

A family tree of Markov models in systems biology

Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree'' for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.Comment: 18 pages, 2 figure

Stochastic Simulations of the Repressilator Circuit

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.Comment: Accepted to PR

Memory and Modularity in Cell-Fate Decision Making

Genetically identical cells sharing an environment can display markedly different phenotypes. It is often unclear how much of this variation derives from chance, external signals, or attempts by individual cells to exert autonomous phenotypic programs. By observing thousands of cells for hundreds of consecutive generations under constant conditions, we dissect the stochastic decision between a solitary, motile state and a chained, sessile state in Bacillus subtilis. The motile state is memoryless, exhibiting no autonomous control over the time spent in the state, whereas chaining is tightly timed. Timing enforces coordination among related cells in the multicellular state. Further, we show that the three-protein regulatory circuit governing the decision is modular, as initiation and maintenance of chaining are genetically separable functions. As stimulation of the same initiating pathway triggers biofilm formation, we argue that autonomous timing allows a trial commitment to multicellularity that external signals could extend