Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Solid-state synthesis and mechanical unfolding of polymers of T4 lysozyme

Recent advances in single molecule manipulation methods offer a novel approach to investigating the protein folding problem. These studies usually are done on molecules that are naturally organized as linear arrays of globular domains. To extend these techniques to study proteins that normally exist as monomers, we have developed a method of synthesizing polymers of protein molecules in the solid state. By introducing cysteines at locations where bacteriophage T4 lysozyme molecules contact each other in a crystal and taking advantage of the alignment provided by the lattice, we have obtained polymers of defined polarity up to 25 molecules long that retain enzymatic activity. These polymers then were manipulated mechanically by using a modified scanning force microscope to characterize the force-induced reversible unfolding of the individual lysozyme molecules. This approach should be general and adaptable to many other proteins with known crystal structures. For T4 lysozyme, the force required to unfold the monomers was 64 ± 16 pN at the pulling speed used. Refolding occurred within 1 sec of relaxation with an efficiency close to 100%. Analysis of the force versus extension curves suggests that the mechanical unfolding transition follows a two-state model. The unfolding forces determined in 1 M guanidine hydrochloride indicate that in these conditions the activation barrier for unfolding is reduced by 2 kcal/mol.

Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K

The conformational space annealing (CSA) method for global optimization has been applied to the 10-55 fragment of the B-domain of staphylococcal protein A (protein A) and to a 75-residue protein, apo calbindin D9K (PDB ID code 1CLB), by using the UNRES off-lattice united-residue force field. Although the potential was not calibrated with these two proteins, the native-like structures were found among the low-energy conformations, without the use of threading or secondary-structure predictions. This is because the CSA method can find many distinct families of low-energy conformations. Starting from random conformations, the CSA method found that there are two families of low-energy conformations for each of the two proteins, the native-like fold and its mirror image. The CSA method converged to the same low-energy folds in all cases studied, as opposed to other optimization methods. It appears that the CSA method with the UNRES force field, which is based on the thermodynamic hypothesis, can be used in prediction of protein structures in real time.

Stretching lattice models of protein folding

A new class of experiments that probe folding of individual protein domains uses mechanical stretching to cause the transition. We show how stretching forces can be incorporated in lattice models of folding. For fast folding proteins, the analysis suggests a complex relation between the force dependence and the reaction coordinate for folding.

Transverse relaxation-optimized NMR spectroscopy with the outer membrane protein OmpX in dihexanoyl phosphatidylcholine micelles

The 2H,13C,15N-labeled, 148-residue integral membrane protein OmpX from Escherichia coli was reconstituted with dihexanoyl phosphatidylcholine (DHPC) in mixed micelles of molecular mass of about 60 kDa. Transverse relaxation-optimized spectroscopy (TROSY)-type triple resonance NMR experiments and TROSY-type nuclear Overhauser enhancement spectra were recorded in 2 mM aqueous solutions of these mixed micelles at pH 6.8 and 30°C. Complete sequence-specific NMR assignments for the polypeptide backbone thus have been obtained. The 13C chemical shifts and the nuclear Overhauser effect data then resulted in the identification of the regular secondary structure elements of OmpX/DHPC in solution and in the collection of an input of conformational constraints for the computation of the global fold of the protein. The same type of polypeptide backbone fold is observed in the presently determined solution structure and the previously reported crystal structure of OmpX determined in the presence of the detergent n-octyltetraoxyethylene. Further structure refinement will have to rely on the additional resonance assignment of partially or fully protonated amino acid side chains, but the present data already demonstrate that relaxation-optimized NMR techniques open novel avenues for studies of structure and function of integral membrane proteins.

Cooperative enhancement of specificity in a lattice of T cell receptors

Two of the most important models to account for the specificity and sensitivity of the T cell receptor (TCR) are the kinetic proofreading and serial ligation models. However, although kinetic proofreading provides a means for individual TCRs to measure accurately the length of time they are engaged and signal appropriately, the stochastic nature of ligand dissociation means the kinetic proofreading model implies that at high concentrations the response of the cell will be relatively nonspecific. Recent ligand experiments have revealed the phenomenon of both negative and positive crosstalk among neighboring TCRs. By using a Monte Carlo simulation of a lattice of TCRs, we integrate receptor crosstalk with the kinetic proofreading and serial ligation models and discover that receptor cooperativity can enhance T cell specificity significantly at a very modest cost to the sensitivity of the response.

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

The relaxation dynamics of the excited electronic states of retinal in bacteriorhodopsin by two-pump-probe femtosecond studies

We present the results of two-pump and probe femtosecond experiments designed to follow the relaxation dynamics of the lowest excited state (S1) populated by different modes. In the first mode, a direct (S0 → S1) radiative excitation of the ground state is used. In the second mode, an indirect excitation is used where the S1 state is populated by the use of two femtosecond laser pulses with different colors and delay times between them. The first pulse excites the S0 → S1 transition whereas the second pulse excites the S1 → Sn transition. The nonradiative relaxation from the Sn state populates the lowest excited state. Our results suggest that the S1 state relaxes faster when populated nonradiatively from the Sn state than when pumped directly by the S0 → S1 excitation. Additionally, the Sn → S1 nonradiative relaxation time is found to change by varying the delay time between the two pump pulses. The observed dependence of the lowest excited state population as well as its dependence on the delay between the two pump pulses are found to fit a kinetic model in which the Sn state populates a different surface (called S′1) than the one being directly excited (S1). The possible involvement of the Ag type states, the J intermediate, and the conical intersection leading to the S0 or to the isomerization product (K intermediate) are discussed in the framework of the proposed model.

Heme oxygenase 2: endothelial and neuronal localization and role in endothelium-dependent relaxation.

Heme oxygenase 2 (HO-2), which synthesizes carbon monoxide (CO), has been localized by immunohistochemistry to endothelial cells and adventitial nerves of blood vessels. HO-2 is also localized to neurons in autonomic ganglia, including the petrosal, superior cervical, and nodose ganglia, as well as ganglia in the myenteric plexus of the intestine. Enzyme studies demonstrated that tin protoporphyrin-9 is a selective inhibitor of HO with approximately 10-fold selectivity for HO over endothelial nitric oxide synthase (NOS) and soluble guanylyl cyclase. Inhibition of HO activity by tin protoporphyrin 9 reverses the component of endothelial-derived relaxation of porcine distal pulmonary arteries not reversed by an inhibitor of NOS. Thus, CO, like NO, may have endothelial-derived relaxing activity. The similarity of NOS and HO-2 localizations and functions in blood vessels and the autonomic nervous system implies complementary and possibly coordinated physiologic roles for these two mediators.

A method for distance determination in proteins using a designed metal ion binding site and site-directed spin labeling: evaluation with T4 lysozyme.

The use of molecular genetics to introduce both a metal ion binding site and a nitroxide spin label into the same protein opens the use of paramagnetic metalnitroxyl interactions to estimate intramolecular distances in a wide variety of proteins. In this report, a His-Xaa3-His metal ion binding motif was introduced at the N terminus of the long interdomain helix of T4 lysozyme (Lys-65 --> His/Gln-69 --> His) of three mutants, each containing a single nitroxide-labeled cysteine residue at position 71, 76, or 80. The results show that Cu(II)-induced relaxation effects on the nitroxide can be quantitatively analyzed in terms of interspin distance in the range of 10-25 A using Redfield theory, as first suggested by Leigh [Leigh, J.S. (1970) J. Chem. Phys. 52, 2608-2612]. Of particular interest is the observation that distances can be determined both under rigid lattice conditions in frozen solution and in the presence of motion of the spins at room temperature under physiological conditions. The method should be particularly attractive for investigating structure in membrane proteins that are difficult to crystallize. In the accompanying paper, the technique is applied to a polytopic membrane protein, lactose permease.

Lattice model for rapidly folding protein-like heteropolymers.

Protein folding is a relatively fast process considering the astronomical number of conformations in which a protein could find itself. Within the framework of a lattice model, we show that one can design rapidly folding sequences by assigning the strongest attractive couplings to the contacts present in a target native state. Our protein design can be extended to situations with both attractive and repulsive contacts. Frustration is minimized by ensuring that all the native contacts are again strongly attractive. Strikingly, this ensures the inevitability of folding and accelerates the folding process by an order of magnitude. The evolutionary implications of our findings are discussed.

Increase of skeletal muscle relaxation speed by direct injection of parvalbumin cDNA.

Parvalbumin (PV) is a high affinity Ca(2+)-binding protein found at high concentration in fast-contracting/relaxing skeletal muscle fibers of vertebrates. It has been proposed that PV acts in the process of muscle relaxation by facilitating Ca2+ transport from the myofibrils to the sarcoplasmic reticulum. However, on the basis of metal-binding kinetics of PV in vitro, this hypothesis has been challenged. To investigate the function of PV in skeletal muscle fibers, direct gene transfer was applied in normal and regenerating rat soleus muscles which do not synthesize detectable amounts of PV. Two weeks after in vivo transfection with PV cDNA, considerable levels of PV mRNA and protein were detected in normal muscle, and even higher amounts were detected in regenerating muscle. Twitch half-relaxation time was significantly shortened in a dose-dependent way in transfected muscles, while contraction time remained unaltered. The observed shortening of half-relaxation time is due to PV and its ability to bind Ca2+, because a mutant protein lacking Ca(2+)-binding capacity did not promote any change in physiology. These results directly demonstrate the physiological function of PV as a relaxing factor in mammalian skeletal muscle.

Oxygen-sensitive calcium channels in vascular smooth muscle and their possible role in hypoxic arterial relaxation.

We have investigated the modifications of cytosolic [Ca2+] and the activity of Ca2+ channels in freshly dispersed arterial myocytes to test whether lowering O2 tension (PO2) directly influences Ca2+ homeostasis in these cells. Unclamped cells loaded with fura-2 AM exhibit oscillations of cytosolic Ca2+ whose frequency depends on extracellular Ca2+ influx. Switching from a PO2 of 150 to 20 mmHg leads to a reversible attenuation of the Ca2+ oscillations. In voltage-clamped cells, hypoxia reversibly reduces the influx of Ca2+ through voltage-dependent channels, which can account for the inhibition of the Ca2+ oscillations. Low PO2 selectively inhibits L-type Ca2+ channel activity, whereas the current mediated by T-type channels is unaltered by hypoxia. The effect of low PO2 on the L-type channels is markedly voltage dependent, being more apparent with moderate depolarizations. These findings demonstrate the existence of O2-sensitive, voltage-dependent, Ca2+ channels in vascular smooth muscle that may critically contribute to the local regulation of circulation.

Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' sector and the U-A(1) anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard SU(3) framework for the octet case and combining the use of the SU(3) framework and the large-Nc expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of U(3) quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.