Living cells, either prokaryote or eukaryote, can be integrated within whole-cell biochips (WCBCs) for various applications. We investigate WCBCs where information is extracted from the cells via a cascade of biochemical reactions that involve gene expression. The overall biological signal is weak due to small sample volume, low intrinsic cell response, and extrinsic signal loss mechanisms. The low signal-to-noise ratio problem is aggravated during initial detection stages and limits the minimum detectable signal or, alternatively, the minimum detection time. Taking into account the stochastic nature of biochemical process, we find that the signal is accompanied by relatively large noise disturbances. In this work, we use genetically engineered microbe sensors as a model to study the biochips output signal stochastic behavior. In our model, the microbes are designed to express detectable reporter proteins under external induction. We present analytical approximated expressions and numerical simulations evaluating the fluctuations of the synthesized reporter proteins population based on a set of equations modeling a cascade of biochemical and genetic reactions. We assume that the reporter proteins decay more slowly than messenger RNA molecules. We calculate the relation between the noise of the input signal (extrinsic noise) and biochemical reaction statistics (intrinsic noise). We discuss in further details two cases: (1) a cascade with large decay rates of all biochemical reactions compared to the protein decay rate. We show that in this case, the noise amplitude has a positive linear correlation with the number of stages in the cascade. (2) A cascade which includes a stable enzymatic-binding reaction with slow decay rate. We show that in this case, the noise strongly depends on the protein decay rate. Finally, a general observation is presented stating that the noise in whole-cell biochip sensors is determined mainly by the first reactions in the genetic system with weak dependence on the number of stages in the cascade.

A peculiar and undesirable current-voltage characteristic of nanoporous membranes is that it exhibits a voltage window with a near-constant limiting-current density when bulk ions near one surface of the membrane are depleted. We show both theoretically and experimentally that this interval disappears for an isolated circular nanopore (or narrow nanoslot) because radial field focusing at the pore entrance enhances the depletion effect and drives an ejecting hydrodynamic vortex pair that amplifies ion flux into the nanopore. This vortex pair is distinct from the vortex arrays that appear in front of a wide nanoslot or a nanoporous membrane with small inter-nanopore separation. It hence suggests that an optimal pore radius/separation ratio exists for maximum current density across a membrane.

For Pearson’s model of Bénard-Marangoni convection, the Nusselt number Nu is proven to be bounded as a function Marangoni number Ma according to $\text{Nu}\le 0.838\times {\text{Ma}}^{2/7}$ for infinite Prandtl number and according to $\text{Nu}\lesssim {\text{Ma}}^{1/2}$ uniformly for finite Prandtl number. The analysis is also used to raise the lower bound for the critical Marangoni number for energy stability of the conduction solution from 56.77 to 58.36 when the Prandtl number is infinite.

Grazing incidence x-ray scattering techniques and Monte Carlo (MC) simulations are combined to reveal the influence of molecular structure (genetic mutation) and divalent cations on the survival of gram negative bacteria against cationic peptides such as protamine. The former yields detailed structures of bacterial lipopolysaccharide (LPS) membranes with minimized radiation damages, while the minimal computer model based on the linearized Poisson-Boltzmann theory allows for the simulation of conformational changes of macromolecules (LPSs and peptides) that occur in the time scale of ms. The complementary combination of the structural characterizations and MC simulation demonstrates that the condensations of divalent ions (${\text{Ca}}^{2+}$ or ${\text{Mg}}^{2+}$) in the negatively charged core saccharides are crucial for bacterial survival.

Building on the work [C. R. Doering, P. S. Hagan, and P. Rosenau, Phys. Rev. A 36, 985 (1987)] we present a regularized Fokker-Planck equation for discrete-state systems with more accurate short-time behavior than its standard, Kramers-Moyal counterpart. This regularization leads to a quasicontinuum Fokker-Planck equation with several key features: it preserves crucial aspects of state-space discreteness ordinarily lost in the standard Kramers-Moyal expansion; it is well posed, and it is more amenable to analytical and numerical tools currently available for continuum systems. In order to expose the basic idea underlying the regularization, it suffices for us to focus on two simple problems—the chemical reaction kinetics of a one-component system and a two-dimensional symmetric random walk on a square lattice. We then describe the path to applying this approach to more complex, discrete-state stochastic systems.

The modularity maximization model proposed by Newman and Girvan for the identification of communities in networks works for general graphs possibly with loops and multiple edges. However, the applications usually correspond to simple graphs. These graphs are compared to a null model where the degree distribution is maintained but edges are placed at random. Therefore, in this null model there will be loops and possibly multiple edges. Sharp bounds on the expected number of loops, and their impact on the modularity, are derived. Then, building upon the work of Massen and Doye, but using algebra rather than simulation, we propose modified null models associated with graphs without loops but with multiple edges, graphs with loops but without multiple edges and graphs without loops nor multiple edges. We validate our models by using the exact algorithm for clique partitioning of Grötschel and Wakabayashi.

We show that the dynamics of a doubly excited Heisenberg spin chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked $XXZ$ model we investigate how the anisotropy parameter—which controls the strength of the magnon-magnon interaction—changes the nature of the coupling between the two “image” coupled kicked rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other.

A variational theory is developed to study electrolyte solutions, composed of interacting pointlike ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and nonlinear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image-charge repulsion. Our variational equations thus go beyond the mean-field theory, or weak coupling limit, where thermal fluctuations overcome electrostatic correlations, and allows one to reach the opposite strong coupling limit, where electrostatic interactions induced by interfaces dominate. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. (i) A single neutral dielectric interface (e.g., air-water or electrolyte-membrane) with an asymmetric electrolyte. A charge separation and thus an electrostatic field get established due to the different image-charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, in contact with the surface and with size proportional to the logarithm of the coupling parameter, strong image forces and strong coupling impose a total ion exclusion, while in the second zone the mean-field approach applies. (ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores in membranes. The competition between image-charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. For strong coupling and small pore size, coion exclusion is total and the counterion partition coefficient is solely determined by global electroneutrality. A quantitative comparison is made with a previous approach, where image and surface charge effects were smeared out in the pore. It is shown that the variational method allows one to go beyond the constant Donnan potential approximation, with deviations stronger at high ion concentrations or small pore sizes. The prediction of the variational method is also compared with MC simulations and good agreement is observed.

The electron transfer kinetics of redox proteins adsorbed on metal electrodes coated with self-assembled monolayers (SAMs) of mercaptanes shows an unusual distance-dependence. For thick SAMs, the experimentally measured electron transfer rate constant $k_{\text{exp}}$ obeys the behavior predicted by Marcus theory [R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265 (1985)], whereas for thin SAMs, $k_{\text{exp}}$ remains virtually constant [Z. Q. Feng et al., J. Chem. Soc., Faraday Trans. 93, 1367 (1997)]. In this work, we present a simple theoretical model system for the redox protein cytochrome c electrostatically bound to a SAM-coated electrode. A statistical average of the electron tunneling rate is calculated by accounting for all possible orientations of the model protein. This approach, which takes into account the electric field dependent orientational distribution, allows for a satisfactory description of the “saturation” regime in the high electric field limit. It further predicts a nonexponential behavior of the average electron transfer processes that may be experimentally checked by extending kinetic experiments to shorter sampling times, i.e., $⪡1/k_{\text{exp}}$. For a comprehensive description of the overall kinetics in the saturation regime at sampling times of the order of $1/k_{\text{exp}}$, it is essential to consider the dynamics of protein reorientation, which is not implemented in the present model.

We calculate rigorous lower bounds for the ground-state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-$q$ series expansions for the sq and sc lattices and also present numerical comparisons.

We obtained Pearson’s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by $m$ edges. We found that the Pearson coefficient is exactly zero in the infinite network limit for the recursive trees $\left(m=1\right)$. If the number of connections of new vertices exceeds one $\left(m>1\right)$, then the Pearson coefficient in the infinite networks equals zero only when the degree distribution exponent $\gamma$ does not exceed 4. We calculated the Pearson coefficient for finite networks and observed a slow power-law-like approach to an infinite network limit. Our findings indicate that Pearson’s coefficient strongly depends on size and details of networks, which makes this characteristic virtually useless for quantitative comparison of different networks.

We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behaviors of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit $\left(t\to \infty \right)$ is taken seems to assume significance.

The Hodgkin-Huxley treatment of the dynamics of a nerve impulse on a cell membrane is combined with a phenomenological description of molecular hyperpolarizabilities to develop a closed-form model of an action-potential-sensitive second-harmonic response of membrane-bound chromophores. This model is employed to understand the key properties of the map between the action potential and modulation of the second harmonic from a cell membrane stained with hyperpolarizable chromophore molecules.

In this work, we build an electronic syrinx, i.e., a programmable electronic device capable of integrating biomechanical model equations for the avian vocal organ in order to synthesize song. This vocal prosthesis is controlled by the bird’s neural instructions to respiratory and the syringeal motor systems, thus opening great potential for studying motor control and its modification by sensory feedback mechanisms. Furthermore, a well-functioning subject-controlled vocal prosthesis can lay the foundation for similar devices in humans and thus provide directly health-related data and procedures.

We study charge transport in an ionic solution in a confined nanoscale geometry in the presence of an externally applied electric field and immobile background charges. For a range of parameters, the ion current shows nonmonotonic behavior as a function of the external ion concentration. For small applied electric field, the ion transport can be understood from simple analytic arguments, which are supported by Monte Carlo simulations. The results qualitatively explain measurements of ion current seen in a recent experiment on ion transport through a DNA-threaded nanopore [D. J. Bonthuis et al., Phys. Rev. Lett, 97, 128104 (2006)].

Motivated by experimental results on the interplay between molecular motors and tau proteins, we extend lattice-based models of intracellular transport to include a second species of particle which locally influences the motor-filament attachment rate. We consider various exactly solvable limits of a stochastic multiparticle model before focusing on the low-motor-density regime. Here, an approximate treatment based on the random-walk behavior of single motors gives good quantitative agreement with simulation results for the tau dependence of the motor current. Finally, we discuss the possible physiological implications of our results.

We report on electrical properties of the two sensing proteins: bacteriorhodopsin and rat olfactory receptor OR-I7. As relevant transport parameters we consider the small-signal impedance spectrum and the static current-voltage characteristics. Calculations are compared with available experimental results and the model predictability is tested for future perspectives.

The interaction between multiple pathogens spreading on networks connecting a given set of nodes presents an ongoing theoretical challenge. Here, we aim to understand such interactions by studying bond percolation of two different processes on overlay networks of arbitrary joint degree distribution. We find that an outbreak of a first pathogen providing immunity to another one spreading subsequently on a second network connecting the same set of nodes does so most effectively if the degrees on the two networks are positively correlated. In that case, the protection is stronger the more heterogeneous the degree distributions of the two networks are. If, on the other hand, the degrees are uncorrelated or negatively correlated, increasing heterogeneity reduces the potential of the first process to prevent the second one from reaching epidemic proportions. We generalize these results to cases where the edges of the two networks overlap to arbitrary amount, or where the immunity granted is only partial. If both processes grant immunity to each other, we find a wide range of possible situations of coexistence or mutual exclusion, depending on the joint degree distribution of the underlying networks and the amount of immunity granted mutually. These results generalize the concept of a coexistence threshold and illustrate the impact of large-scale network structure on the interaction between multiple spreading agents.