Optical Lattices: Theory

This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already appeared in the literature (see, for instance, [1-3] and references therein). For this reason, and because of the huge amount of published results, we do not pretend here to be comprehensive, but we will be content to provide a flavor of the richness of this subject, together with some useful references. On the other hand, there are good reasons for our effort. Probably, the most significant is that BEC in periodic potentials is a truly interdisciplinary problem, with obvious connections with electrons in crystal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.Comment: Chapter 13 in Part VIII: "Optical Lattices" of "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer Series on Atomic, Optical, and Plasma Physics, 2007) - pages 247-26

Universality of protein reentrant condensation in solution induced by multivalent metal ions

The effective interactions and phase behavior of protein solutions under strong electrostatic coupling conditions are difficult to understand due to the complex charge pattern and irregular geometry of protein surfaces. This distinguishes them from related systems such as DNA or conventional colloids. In this work, we discuss the question of universality of the reentrant condensation (RC) of proteins in solution induced by multivalent counterions, i.e., redissolution on adding further salts after phase separation, as recently discovered (Zhang et al., Phys Rev Lett 2008; 101:148101). The discussion is based on a systematic investigation of five different proteins with different charge patterns and five different multivalent counterions. Zeta potential measurements confirm the effective charge inversion of proteins in the reentrant regime via binding of multivalent counterions, which is supported by Monte Carlo simulations. Charge inversion by trivalent cations requires an overall negative net charge of the protein. Statistical analysis of a representative set of protein sequences reveals that, in theory, this effect could be possible for about half of all proteins. Our results can be exploited for the control of the phase behavior of proteins, in particular facilitating protein crystallization

Universality of protein reentrant condensation in solution induced by multivalent metal ions.

The effective interactions and phase behavior of protein solutions under strong electrostatic coupling conditions are difficult to understand due to the complex charge pattern and irregular geometry of protein surfaces. This distinguishes them from related systems such as DNA or conventional colloids. In this work, we discuss the question of universality of the reentrant condensation (RC) of proteins in solution induced by multivalent counterions, i.e., redissolution on adding further salts after phase separation, as recently discovered (Zhang et al., Phys Rev Lett 2008; 101:148101). The discussion is based on a systematic investigation of five different proteins with different charge patterns and five different multivalent counterions. Zeta potential measurements confirm the effective charge inversion of proteins in the reentrant regime via binding of multivalent counterions, which is supported by Monte Carlo simulations. Charge inversion by trivalent cations requires an overall negative net charge of the protein. Statistical analysis of a representative set of protein sequences reveals that, in theory, this effect could be possible for about half of all proteins. Our results can be exploited for the control of the phase behavior of proteins, in particular facilitating protein crystallization

Pharmacological inactivation of the prion protein by targeting a folding intermediate

Recent computational advancements in the simulation of biochemical processes allow investigating the mechanisms involved in protein regulation with realistic physics-based models, at an atomistic level of resolution. These techniques allowed us to design a drug discovery approach, named Pharmacological Protein Inactivation by Folding Intermediate Targeting (PPI-FIT), based on the rationale of negatively regulating protein levels by targeting folding intermediates. Here, PPI-FIT was tested for the first time on the cellular prion protein (PrP), a cell surface glycoprotein playing a key role in fatal and transmissible neurodegenerative pathologies known as prion diseases. We predicted the all-atom structure of an intermediate appearing along the folding pathway of PrP and identified four different small molecule ligands for this conformer, all capable of selectively lowering the load of the protein by promoting its degradation. Our data support the notion that the level of target proteins could be modulated by acting on their folding pathways, implying a previously unappreciated role for folding intermediates in the biological regulation of protein expression