Enrique Munoz

Ballistic Thermal Conductance of Graphene Ribbons

An elastic-shell-based theory for calculating the thermal conductance of graphene ribbons of arbitrary width w is presented. The analysis of vibrational modes of a continuum thin plate leads to a general equation for ballistic conductance sigma. At low temperature, it yields a power law sigma approximately T(beta), where the exponent beta varies with the ribbon width w from beta = 1 for a narrow ribbon (sigma approximately T, as a four-channel quantum wire) to beta = (3)/(2) (sigma approximately wT(3/2)) in the limit of wider graphene sheets. The ballistic results can be augmented by the phenomenological value of a phonon mean free path to account for scattering and agree well with the reported experimental observations.

Quasispecies theory for multiple-peak fitness landscapes.

We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.

Quasispecies theory for finite populations

We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations in our description. We show that the fluctuation of the population numbers about the average values is exceedingly large in these physical models of evolution. We further show that horizontal gene transfer reduces by orders of magnitude the fluctuations in the population numbers and reduces the accumulation of deleterious mutations in the finite population due to Mullers ratchet. Indeed, the population sizes needed to converge to the infinite population limit are often larger than those found in nature for smooth fitness functions in the absence of horizontal gene transfer. These analytical results are derived for the steady state by means of a field-theoretic representation. Numerical results are presented that indicate horizontal gene transfer speeds up the dynamics of evolution as well.

Microarray and EST database estimates of mRNA expression levels differ: The protein length versus expression curve for C. elegans

BackgroundVarious methods for estimating protein expression levels are known. The level of correlation between these methods is only fair, and systematic biases in each of the methods cannot be ruled out. We here investigate systematic biases in the estimation of gene expression rates from microarray data and from abundance within the Expressed Sequence Tag (EST) database. We suggest that length is a significant factor in biases to measured gene expression rates.As a specific example of the importance of the bias of expression rate with length, we address the following evolutionary question: Does the average C. elegans protein length increase or decrease with expression level? Two different answers to this question have been reported in the literature, one method using expression levels estimated by abundance within the EST database and another using microarrays. We have investigated this issue by constructing the full protein length versus expression curve for C. elegans, using both methods for estimating expression levels.ResultsThe microarray data show a monotonic decrease of length with expression level, whereas the abundance within the EST database data show a non-monotonic behavior. Furthermore, the ratio of the expression level estimated by the EST database to that measured by microarrays is not constant, but rather systematically biased with gene length.ConclusionsIt is suggested that the length bias may lie primarily in the abundance within the EST database method, being not ameliorated by internal standards as it is in the microarray data, and that this bias should be removed before data interpretation. When this is done, both the microarray and the abundance within the EST database give a monotonic decrease of spliced length with expression level, and the correlation between the EST and microarray data becomes larger. We suggest that standard RNA controls be used to normalize for length bias in any method that measures expression.

Quasispecies theory for horizontal gene transfer and recombination.

We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic recombination on the steady-state mean fitness and distribution of individuals in the population, through an analytic field theoretic mapping. We investigate both horizontal gene transfer from a population and recombination between pairs of individuals. Somewhat surprisingly, these nonlinear generalizations of quasispecies theory to modern biology are analytically solvable. For two-parent recombination, we find two selected phases, one of which is spectrally rigid. We present exact analytical formulas for the equilibrium mean fitness of the population, in terms of a maximum principle, which are generally applicable to any permutation invariant replication rate function. For smooth fitness landscapes, we show that when positive epistatic interactions are present, recombination or horizontal gene transfer introduces a mild load against selection. Conversely, if the fitness landscape exhibits negative epistasis, horizontal gene transfer or recombination introduces an advantage by enhancing selection towards the fittest genotypes. These results prove that the mutational deterministic hypothesis holds for quasispecies models. For the discontinuous single sharp peak fitness landscape, we show that horizontal gene transfer has no effect on the fitness, while recombination decreases the fitness, for both the parallel and the Eigen models. We present numerical and analytical results as well as phase diagrams for the different cases.

Universal out-of-equilibrium transport in Kondo-correlated quantum dots: renormalized dual fermions on the Keldysh contour.

The nonlinear conductance of semiconductor heterostructures and single molecule devices exhibiting Kondo physics has recently attracted attention. We address the observed sample dependence of the measured steady state transport coefficients by considering additional electronic contributions in the effective low-energy model underlying these experiments that are absent in particle-hole symmetric setups. A novel version of the superperturbation theory of Hafermann et al. in terms of dual fermions is developed, which correctly captures the low-temperature behavior. We compare our results with the measured transport coefficients.

Solution of the Crow-Kimura and Eigen Models for Alphabets of Arbitrary Size by Schwinger Spin Coherent States

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an h-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary h and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler’s theorem for homogeneous functions is used to derive this ‘thermodynamic’ formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine h=2 alphabet and the nucleic acid h=4 alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the h=4 and h=20 cases. We also derive the maximum principle for the Eigen model for general h. The general result for the Eigen model reduces to a known result for h=2. Examples are presented for the nucleic acid h=4 and the amino acid h=20 alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.

Magnetostrain-driven quantum engine on a graphene flake.

We propose an alternative conceptual design for a graphene-based quantum engine, driven by a superposition of mechanical strain and an external magnetic field. Engineering of strain in a nanoscale graphene flake creates a gauge field with an associated uniform pseudomagnetic field. The strain-induced pseudomagnetic field can be combined with a real magnetic field, leading to the emergence of discrete relativistic Landau levels within the single-particle picture. The interlevel distance and hence their statistical population can be modulated by quasistatically tuning the magnetic field along a sequence of reversible transformations that constitute a quantum mechanical analog of the classical Otto cycle.

Transport characterization of Kondo-correlated single-molecule devices

A single-molecule break junction device serves as a tunable model system for probing the many-body Kondo state. The low-energy properties of this state are commonly described in terms of a Kondo model, where the response of the system to different perturbations is characterized by a single emergent energy scale, kBTK . Comparisons between different experimental systems have shown issues with numerical consistency. With a new constrained analysis examining the dependence of conductance on temperature, bias, and magnetic field simultaneously, we show that these deviations can be resolved by properly accounting for background, non-Kondo contributions to the conductance that are often neglected. We clearly demonstrate the importance of these non-Kondo conduction channels by examining transport in devices with total conductances exceeding the theoretical maximum due to Kondo-assisted tunneling alone.

Magnetically-Driven Quantum Heat Engines: The Quasi-Static Limit of Their Efficiency

The concept of a quantum heat engine (QHEN) has been discussed in the literature, not only due to its intrinsic scientific interest, but also as an alternative to efficiently recover, on a nanoscale device, thermal energy in the form of useful work. The quantum character of a QHEN relies, for instance, on the fact that any of its intermediate states is determined by a density matrix operator. In particular, this matrix can represent a mixed state. For a classical heat engine, a theoretical upper bound for its efficiency is obtained by analyzing its quasi-static operation along a cycle drawn by a sequence of quasi-equilibrium states. A similar analysis can be carried out for a quantum engine, where quasi-static processes are driven by the evolution of ensemble-averaged observables, via variation of the corresponding operators or of the density matrix itself on a tunable physical parameter. We recently proposed two new conceptual designs for a magnetically-driven quantum engine, where the tunable parameter is the intensity of an external magnetic field. Along this article, we shall present the general quantum thermodynamics formalism developed in order to analyze this type of QHEN, and moreover, we shall apply it to describe the theoretical efficiency of two different practical implementations of this concept: an array of semiconductor quantum dots and an ensemble of graphene flakes submitted to mechanical tension.