Constraining f(T) teleparallel gravity by big bang nucleosynthesis: f(T) cosmology and BBN.

We use Big Bang Nucleosynthesis (BBN) observational data on the primordial abundance of light elements to constrain f(T) gravity. The three most studied viable f(T) models, namely the power law, the exponential and the square-root exponential are considered, and the BBN bounds are adopted in order to extract constraints on their free parameters. For the power-law model, we find that the constraints are in agreement with those obtained using late-time cosmological data. For the exponential and the square-root exponential models, we show that for reliable regions of parameters space they always satisfy the BBN bounds. We conclude that viable f(T) models can successfully satisfy the BBN constraints.

Classical evolution of fractal measures on the lattice.

We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

A model for enhanced nucleation of protein crystals on a fractal porous substrate.

The phenomenon of enhanced nucleation and crystallization of proteins on porous silicon (PS) is theoretically studied and explained. The PS layer is treated as a fractal structure, and a new mechanism of local supersaturation associated with the fractality is proposed. It is shown that the number of adsorbed molecules on a fragment with a fractal surface significantly exceeds that on one with flat surfaces. For a fractal PS surface, a local concentration of molecules that is sufficient for nucleation is possible inside and in the close vicinity of the pores, even when the average conditions in the bulk of the solution correspond to metastability. The wide distribution of fractal pore size is favorable for the crystallization of a wide range of macromolecules using the same sample. In addition, the PS technology is very flexible, allowing tailoring the pore size and concentration as well as the fractal properties to specific proteins by changing the fabrication conditions.

Nucleation of protein crystals in a wide continuous supersaturation gradient.

By using a supersaturation gradient along a protein solution contained in a glass capillary tube, we modified the classical double pulse technique, thus substantially accelerating the procedure of measurement of nucleation parameters. Data for the number of crystal nuclei, n vs nucleation time, t, were obtained for hen-egg-white lysozyme, chosen as a model because of the availability of reliable solubility data in the literature. The stationary nucleation rate and the nucleation time lag have been measured. Quantitative data for the work required for nucleus formation (A(k) = 4.3 x 10 (-1)3 erg) and the size of the critical cluster (three molecules) were also obtained. Besides, it was observed that Ostwald ripening seems to play an important role for nucleation times longer than 150 min. Using the same technique, semi-quantitative investigations were performed with porcine pancreatic trypsin.

Porous silicon: an effective nucleation-inducing material for protein crystallization.

Protein crystals play a pivotal part in structural genomics, hence there is an urgent requirement for new and improved methodology to aid crystal growth. Considerable effort has been invested in the search of substances (nucleants) that will induce efficient nucleation of protein crystals in a controlled manner. To date, nucleation has been facilitated mainly by seeding, epitaxy, charged surfaces or mechanical means. A different approach is introduced here, involving the use of a mesoporous material that is likely to constrain protein molecules and thereby encourage them to aggregate in crystalline order. Large single crystals were obtained using porous silicon at conditions that are not sufficient for spontaneous nucleation, for five out of six proteins that were investigated. We propose that this success is due to the size distribution of pores in the specially designed porous silicon.

Improving protein crystal quality by decoupling nucleation and growth in vapor diffusion.

A simple method for growing protein crystals in the metastable zone using the vapor diffusion technique is described. The coverslips holding the hanging drops are transferred, after being incubated for some time at conditions normally giving many small crystals, over reservoirs at concentrations that normally yield clear drops. Fewer, much larger and better diffracting crystals are obtained, compared with conventional crystallization at similar conditions. To our knowledge, this is the first report of a significant crystal improvement due to "backing off" from nucleation conditions, using the hanging drop method. A correlation of the transfer time with published results for vapor diffusion equilibration of poly(ethylene glycol) solutions is also presented.

Optimization of the critical nuclear size for protein crystallization: a note.

It was observed that for some proteins the best crystals for X-ray diffraction have been obtained at supersaturation ratios of ca 2.5-3 (in experiments without seeding). It was then noticed that under certain conditions specific to the protein such values are close to a local minimum of the critical radius for nucleation. A relation between the two observations is proposed.

Crystallization and initial X-ray analysis of beta-crustacyanin, the dimer of apoproteins A2 and C1, each with a bound astaxanthin molecule.

Crystals of beta-crustacyanin, a carotenoid-binding protein from lobster carapace, have been grown under oil from solutions containing sodium potassium phosphate as precipitant. They grow slowly over a period of months to reach maximal dimensions of 0.5 x 0.1 x 0.1 mm, and belong to space group P622 with cell dimensions: a = b = 124.39, c = 188.86 A and gamma = 120 degrees. The crystals diffract to beyond 3 A but are very radiation sensitive, limiting the resolution of usable data. The unit-cell volume suggests that there are two beta-crustacyanin molecules per asymmetric unit.

Control of nucleation of protein crystals.

Control of nucleation may be needed to obtain a reliable supply of large protein crystals, when standard techniques give many small or twinned crystals. Heterogeneous nucleation may be controlled by the use of fine filters, with the elimination of airborne contaminants by working under paraffin oil. The area of contact with the supporting vessel also has an important effect. A heterogenous nucleant for lysozyme (identified earlier) has been shown to be effective for carboxypeptidase G2. Control of homogeneous nucleation (previously demonstrated by dilutions of a nucleating sample after various times of incubation) may also be achieved by incubating a sample at 1 temperature, where nucleation can occur, and changing the temperature to conditions where there is growth but no nucleation.

Phase diagram and dilution experiments in the crystallization of carboxypeptidase G2.

The automated microbatch technique developed at Imperial College has been used to establish a phase diagram for crystallization. The concentrations of the protein (carboxypeptidase G2) and precipitant (PEG 4000) were varied, while pH and temperature were kept constant. The diagram consists of an undersaturation and a supersaturation zone, the latter being subdivided into the metastable, nucleation and precipitation zones. In the metastable zone, crystals may grow but nucleation of crystals does not occur. It is the best zone for growth of X-ray diffraction quality crystals because of the slower growth rate and the avoidance of uncontrolled nucleation, which uses up protein in the formation of tiny crystals. Nevertheless, in practice, it is rarely well defined or used because nuclei must be introduced artificially into the system. The new method used here consists of setting crystallization droplets at nucleation conditions and later diluting them to conditions where nucleation has not been observed. Single diffracting crystals of typical dimensions 0.3 x 0.3 x 0.2 mm were routinely obtained in the metastable zone, equivalent to the best (very rarely) obtained crystals in the nucleation zone.