Bernardo A. Mello

Quantitative modeling of sensitivity in bacterial chemotaxis: The role of coupling among different chemoreceptor species

We propose a general theoretical framework for modeling receptor sensitivity in bacterial chemotaxis, taking into account receptor interactions, including those among different receptor species. We show that our model can quantitatively explain the recent in vivo measurements of receptor sensitivity at different ligand concentrations for both mutant and wild-type strains. For mutant strains, our model can fit the experimental data exactly. For the wild-type cell, our model is capable of achieving high gain while having modest values of Hill coefficient for the response curves. Furthermore, the high sensitivity of the wild-type cell in our model is maintained for a wide range of ambient ligand concentrations, facilitated by near-perfect adaptation and dependence of ligand binding on receptor activity. Our study reveals the importance of coupling among different chemoreceptor species, in particular strong interactions between the aspartate (Tar) and serine (Tsr) receptors, which is crucial in explaining both the mutant and wild-type data. Predictions for the sensitivity of other mutant strains and possible improvements of our model for the wild-type cell are also discussed.

Perfect and Near-Perfect Adaptation in a Model of Bacterial Chemotaxis

The signaling apparatus mediating bacterial chemotaxis can adapt to a wide range of persistent external stimuli. In many cases, the bacterial activity returns to its prestimulus level exactly, and this perfect adaptability is robust against variations in various chemotaxis protein concentrations. We model the bacterial chemotaxis signaling pathway, from ligand binding to CheY phosphorylation. By solving the steady-state equations of the model analytically, we derive a full set of conditions for the system to achieve perfect adaptation. The conditions related to the phosphorylation part of the pathway are discovered for the first time, while other conditions are generalizations of the ones found in previous works. Sensitivity of the perfect adaptation is evaluated by perturbing these conditions. We find that, even in the absence of some of the perfect adaptation conditions, adaptation can be achieved with near-perfect precision as a result of the separation of scales in both chemotaxis protein concentrations and reaction rates, or specific properties of the receptor distribution in different methylation states. Since near-perfect adaptation can be found in much larger regions of the parameter space than that defined by the perfect adaptation conditions, their existence is essential to understand robustness in bacterial chemotaxis.

Developed profile of holographically exposed photoresist gratings

A simulation of the profile of holographically recorded structures in photoresists is performed. In addition to its simplicity this simulation can be used to take into account the effects that arise from exposure, photosensitization, development, and resolution of positive photoresists. We analyzed the effects of isotropy of wet development, nonlinearity of the photoresist response curve, background light, and standing waves produced by reflection at the film-substrate interface by using this simulation, and the results agree with the experimentally recorded profiles.

Topological Defects with Long-Range Interactions

We investigate a modified sine-Gordon equation which possesses soliton solutions with long-range interaction. We introduce a generalized version of the Ginzbug-Landau equation which supports long-range topological defects in D = 1 and D > 1. The interaction force between the defects decays so slowly that it is possible to enter the non-extensivity regime. These results can be applied to non-equilibrium systems, pattern formation and growth models.

Phase transitions in simplified models with long-range interactions

We study the origin of phase transitions in several simplified models with long-range interactions. For the self-gravitating ring model, we are unable to observe a possible phase transition predicted by Nardini and Casetti [Phys. Rev. E 80, 060103R (2009).] from an energy landscape analysis. Instead we observe a sharp, although without any nonanalyticity, change from a core-halo to a core-only configuration in the spatial distribution functions for low energies. By introducing a different class of solvable simplified models without any critical points in the potential energy we show that a behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features for the simplified models and show that the first-order phase transition comes from the maximization of the entropy of the system as a function of energy and an order parameter, as previously discussed by Hahn and Kastner [Phys. Rev. E 72, 056134 (2005); Eur. Phys. J. B 50, 311 (2006)], which seems to be the main mechanism causing phase transitions in long-range interacting systems.

Bifurcations of kink dynamics in the presence of special inhomogeneities

Abstract We investigate the bifurcations that can occur in kink dynamics in the presence of special external forces and impurities. We have found the existence of soliton explosions. The length scale competition between the “width” of the inhomogeneities, the distance between them and the “width” of the kink leads to unexpected stability changes.

Growth exponents of the etching model in high dimensions

In this work we generalize the etching model (Mello et al 2001 Phys. Rev. E 63 041113 )t o + d 1 dimensions. The dynamic exponents of this model are compatible with those of the Kardar–Parisi–Zhang universality class. We investigate the roughness dynamics with surfaces up to = d 6. We show that the data from all substrate lengths and for all dimensions can be collapsed into one common curve. We determine the dynamic exponents as a function of the dimension. Moreover, our results suggest that = d 4 is not an upper critical dimension for the etching model, and that it fulfills the Galilean invariance.

Physiological aging as an infinitesimally ratcheted random walk.

The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker-Planck equations. A major problem with these equations is that they allow the physiological age to move back in time. This paper proposes an Infinitesimally ratcheted random walk as a way to solve that problem. Two mathematical representations are proposed. One of them uses a nonlocal scalar field. The other one is local, but involves a multicomponent field of speed states. These two formulations are compared to each other and to the Fokker-Planck equation. The relevant properties are discussed. The dynamics of the mean and variance of the population age resulting from the two proposed formulations are obtained.

Controlled transport of solitons and bubbles using external perturbations

We investigate generalized soliton-bearing systems in the presence of external perturbations. We show the possibility of the transport of solitons using external waves, provided the waveform and its velocity satisfy certain conditions. We also investigate the stabilization and transport of bubbles using external perturbations in 3D-systems. We also present the results of real experiments with laser-induced vapor bubbles in liquids.

Scaling transformation of random walk and generalized statistics

We use a decimation procedure in order to obtain the dynamical renormalization group transformation (RGT) properties of random walk distribution in a 1+1 lattice. We obtain an equation similar to the Chapman–Kolmogorov equation. First we show the existence of invariants of the RGT, and that the Tsallis distribution Rq(x)=[1+b(q−1)x2]1/(1−q) (q>1) is a quasi-invariant of the RGT. We obtain the map q′=f(q) from the RGT and show that this map has two fixed points: q=1, attractor, and q=2, repellor, which are the Gaussian and the Lorentzian, respectively. Finally we use those concepts to show that the nonadditivity of the Tsallis entropy needs to be reviewed.