Structure and Reactions of ^{11}Be: Many-Body Basis for Single-Neutron Halo

The exotic nucleus ^{11}Be has been extensively studied and much experimental information is available on the structure of this system. We treat, within the framework of renormalized nuclear field theory in both configuration and 3D space, the mixing of bound and continuum single-particle states through the coupling to collective vibrations of the ^{10}Be core. We also take care of the Pauli principle acting not only between the single valence particle explicitly considered and those participating in the collective states, but also between fermions involved in two-phonon virtual states dressing the single-particle motion. In this way, it is possible to simultaneously and quantitatively account for the energies of the 1/2^{+}, 1/2^{-} low-lying states, the centroid and line shape of the 5/2^{+} resonance and the one-nucleon stripping and pickup absolute differential cross sections involving ^{11}Be as either target or residual nucleus. Also for the dipole transition connecting the 1/2^{+} and 1/2^{-} parity inverted levels as well as the isotopic shift of the charge radius. Theory provides a unified and exhaustive nuclear structure and reaction characterization of the many-body effects which are at the basis of this paradigmatic one-neutron halo system.

Cooper pair transfer in nuclei

The second-order distorted wave Born approximation implementation of two-particle transfer direct reactions which includes simultaneous and successive transfer, properly corrected by non-orthogonality effects, is tested with the help of controlled nuclear structure and reaction inputs against data spanning the whole mass table, and showed to constitute a quantitative probe of nuclear pairing correlations.

Thermodynamics of strongly allosteric inhibition: a model study of HIV-1 protease

Protein inhibitors that shift the thermodynamic equilibrium towards a denatured state escape, in general, the straightforward framework of competitive or allosteric inhibitors. The equilibrium properties of peptides which compete with the folding, or more precisely destabilize the native state, of the human immunodeficiency virus (HIV)-1 protease monomer are studied within a structure-based model. The effect of peptides that disrupt the hydrophobic core of the protein can still be summarized in terms of an inhibition constant, which depends on the thermal stability of the protein. The state of the protein denatured by such a peptide is more structured than its intrinsic denatured state, but displays the same degree of compactness. Peptides that target less buried regions of the protein are less efficient and display a more complex thermodynamics that cannot be captured in a simple way.

Calculation of the transition from pairing vibrational to pairing rotational regimes between magic nuclei ¹⁰⁰Sn and ¹³²Sn via two-nucleon transfer reactions

Absolute values of two-particle transfer cross sections along the Sn-isotopic chain are calculated. They agree with measurements within errors and without free parameters. Within this scenario, the predictions concerning the absolute value of the two-particle transfer cross sections associated with the excitation of the pairing vibrational spectrum expected around the recently discovered closed shell nucleus(50)(132)Sn(82) and the very exotic nucleus (50)(100)Sn(50) can be considered quantitative, opening new perspectives in the study of pairing in nuclei.

Evidence for phonon mediated pairing interaction in the halo of the nucleus ¹¹Li

With the help of a unified nuclear-structure-direct-reaction theory we analyze the reaction ¹H(¹¹Li,⁹Li)³H. The two halo neutrons are correlated through the bare and the induced (medium polarization) pairing interaction. By considering all dominant reaction channels leading to the population of the 1/2⁻ (2.69 MeV) first excited state of ⁹Li, namely, multistep transfer (successive, simultaneous, and nonorthogonality), breakup, and inelastic channels, it is possible to show that the experiment provides direct evidence of phonon mediated pairing.

The molecular evolution of HIV-1 protease simulated at atomic detail

Progress in understanding protein folding allows to simulate, with atomic detail, the evolution of amino-acid sequences folding to a given native conformation. A particularly attractive example is the HIV-1 protease, main target of therapies to fight AIDS, which under drug pressure is able to develop resistance within few months from the starting of therapy. By comparing the results of simulations of the evolution of the protease with the corresponding proteomic data, one can approximately determine the value of the associated evolution pressure under which the enzyme has become and, as a consequence, map out the energy landscape in sequence space of the HIV-1 protease. It is found that there are several families of sequences folding to the native conformations of the enzyme. Each of these families are characterized by different sets of highly conserved ("hot") amino acids which play a critical role in the folding and stability of the protease. There are two main possibilities for the virus to move from one family to a different one: (a) in a single generation, through the concerted mutations of the hot amino acids, a highly unlikely event, (b) through a folding path (if it exists), again a very improbable event. In fact, the number of generations needed by the virus to change stepwise its sequence from one family to another is astronomically large. These results point to the "hot" segments of the protease as promising targets for a nonconventional inhibition strategy, likely not to create resistance.

Identification and characterization of folding inhibitors of hen egg lysozyme: an example of a new paradigm of drug design

Studies of protein folding indicate the presence of native contacts in the denatured state, giving rise to folding elements which contribute to the accomplishment of the native state. The possibility of finding molecules which can interact with specific folding elements of a target protein preventing it from reaching its native state, and hence from becoming biologically active, is particularly attractive. The notion that folding elements not only provide molecular recognition directing the folding process, but also have conserved sequence, implies that targeting such elements will make protein folding inhibitors less susceptible to mutations which, in many cases, abrogate drug effects. The folding-inhibition strategy can lead to a truly novel and rational approach to drug design, aside from providing new insight into folding. This is illustrated in the case of hen egg lysozyme.

Metadynamic sampling of the free-energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free-energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.

Denatured state is critical in determining the properties of model proteins designed on different folds

The thermodynamics of proteins designed on three common folds (SH3, chymotrypsin inhibitor 2 [CI2], and protein G) is studied with a simplified C(alpha) model and compared with the thermodynamics of proteins designed on random-generated folds. The model allows to design sequences to fold within a dRMSD ranging from 1.2 to 4.2 A from the crystallographic native conformation and to study properties that are hard to be measured experimentally. It is found that the denatured state of all of them is not random but is, to different extents, partially structured. The degree of structure is more abundant for SH3 and protein G, giving rise to a weaker stability but a more efficient folding kinetics than CI2 and, even more, than the random-generated folds. Consequently, the features of the unfolded state seem to be as important in the determination of the thermodynamic properties of these proteins as the features of the native state.

Low-throughput model design of protein folding inhibitors

The stabilization energy of proteins in their native conformation is not distributed uniformly among all the amino acids, but is concentrated in few (short) fragments, fragments which play a key role in the folding process and in the stability of the protein. Peptides displaying the same sequence as these key fragments can compete with the formation of the most important native contacts, destabilizing the protein and thus inhibiting its biological activity. We present an essentially automatic method to individuate such peptidic inhibitors based on a low-throughput screening of the fragments which build the target protein. The efficiency and generality of the method is tested on proteins Src-SH3, G, CI2, and HIV-1-PR with the help of a simplified computational model. In each of the cases studied, we find few peptides displaying strong inhibitory properties, properties which are quite robust with respect to point mutations. The possibility of implementing the method through low-throughput experimental screening of the target protein is discussed.

Thermodynamics of beta-amyloid fibril formation

Amyloid fibers are aggregates of proteins. They are built out of a peptide called beta-amyloid (Abeta) containing between 41 and 43 residues, produced by the action of an enzyme which cleaves a much larger protein known as the amyloid precursor protein (APP). X-ray diffraction experiments have shown that these fibrils are rich in beta-structures, whereas the shape of the peptide displays an alpha-helix structure within the APP in its biologically active conformation. A realistic model of fibril formation is developed based on the 17 residues Abeta12-28 amyloid peptide, which has been shown to form fibrils structurally similar to those of the whole Abeta peptide. With the help of physical arguments and in keeping with experimental findings, the Abeta12-28 monomer is assumed to be in four possible states (i.e., native helix conformation, beta-hairpin, globular low-energy state, and unfolded state). Making use of these monomeric states, oligomers (dimers, tertramers, and octamers) were constructed. With the help of short, detailed molecular dynamics calculations of the three monomers and of a variety of oligomers, energies for these structures were obtained. Making use of these results within the framework of a simple yet realistic model to describe the entropic terms associated with the variety of amyloid conformations, a phase diagram can be calculated of the whole many-body system, leading to a thermodynamical picture in overall agreement with the experimental findings. In particular, the existence of micellar metastable states seem to be a key issue to determine the thermodynamical properties of the system.

Thermodynamic features characterizing good and bad folding sequences obtained using a simplified off-lattice protein model

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each beadlike amino acid interacts with the others through a contact potential controlled by a random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical ensembles, namely, a coil-like ensemble, an unfolded globule, and a folded ensemble (plus two other states, frozen and random coils, populated only at extreme temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed.

A folding inhibitor of the HIV-1 protease

Because the human immunodeficiency virus type 1 protease (HIV-1-PR) is an essential enzyme in the viral life cycle, its inhibition can control AIDS. The folding of single-domain proteins, like each of the monomers forming the HIV-1-PR homodimer, is controlled by local elementary structures (LES, folding units stabilized by strongly interacting, highly conserved, as a rule hydrophobic, amino acids). These LES have evolved over myriad generations to recognize and strongly attract each other, so as to make the protein fold fast and be stable in its native conformation. Consequently, peptides displaying a sequence identical to those segments of the monomers associated with LES are expected to act as competitive inhibitors and thus destabilize the native structure of the enzyme. These inhibitors are unlikely to lead to escape mutants as they bind to the protease monomers through highly conserved amino acids, which play an essential role in the folding process. The properties of one of the most promising inhibitors of the folding of the HIV-1-PR monomers found among these peptides are demonstrated with the help of spectrophotometric assays and circular dichroism spectroscopy.

Design of amino acid sequences to fold into Cα-model proteins

In order to extend the results obtained with minimal lattice models to more realistic systems, we study a model where proteins are described as a chain of 20 kinds of structureless amino acids moving in a continuum space and interacting through a contact potential controlled by a 20x20 quenched random matrix. The goal of the present work is to design and characterize amino acid sequences folding to the SH3 conformation, a 60-residue recognition domain common to many regulatory proteins. We show that a number of sequences can fold, starting from a random conformation, to within a distance root-mean-square deviation between 2.6 and 4.0 A from the native state. Good folders are those sequences displaying in the native conformation an energy lower than a sequence-independent threshold energy.

Role of bulk and of interface contacts in the behavior of lattice model dimeric proteins

Some dimeric proteins first fold and then dimerize (three-state dimers) while others first dimerize and then fold (two-state dimers). Within the framework of a minimal lattice model, we can distinguish between sequences following one or the other mechanism on the basis of the distribution of the ground state energy between bulk and interface contacts. The topology of contacts is very different for the bulk than for the interface: while the bulk displays a rich network of interactions, the dimer interface is built up of a set of essentially independent contacts. Consequently, the two sets of interactions play very different roles both, in the folding and in the evolutionary history of the protein. Three-state dimers, where a large fraction of energy is concentrated in few contacts buried in the bulk, and where the relative contact energy of interface contacts is considerably smaller than that associated with bulk contacts, fold according to a hierarchical pathway controlled by local elementary structures, as also happens in the folding of single-domain monomeric proteins. On the other hand, two-state dimers display a relative contact energy of interface contacts, which is larger than the corresponding quantity associated with the bulk. In this case, the assembly of the interface stabilizes the system and leads the two chains to fold. The specific properties of three-state dimers acquired through evolution are expected to be more robust than those of two-state dimers; a fact that has consequences on proteins connected with viral diseases.

Reading the three-dimensional structure of lattice model-designed proteins from their amino acid sequence

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the detailed, biological active, three-dimensional structure of a protein whose sequence is known. Using insight obtained from lattice model simulations of the folding of small proteins (fewer than 100 residues), in particular of the fact that this phenomenon is essentially controlled by conserved contacts (Mirny et al., Proc Natl Acad Sci USA 1995;92:1282) among (few) strongly interacting ("hot") amino acids (Tiana et al., J Chem Phys 1998;108:757-761), which also stabilize local elementary structures formed early in the folding process and leading to the (postcritical) folding core when they assemble together (Broglia et al., Proc Natl Acad Sci USA 1998;95:12930, Broglia & Tiana, J Chem Phys 2001;114:7267), we have worked out a successful strategy for reading the three-dimensional structure of lattice model-designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids.

Designability of lattice model heteropolymers

Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20-letter lattice model of proteins which, relying only on the central limit theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, an energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them.

Energy profile of the space of model protein sequences

A numerical study of the energy landscape of the space of model proteinsequences is carried out. As a consequence of the heterogeneity of thecontact energies among amino acids, the energy landscape displays a veryrough profile, a behaviour typical of frustrated systems. This givesraise to a hierarchical clustering of low-energy sequences and can have evolutionary consequences.

Predicting the tertiary structure of a lattice designed model protein from its primary structure

Through systematic studies of lattice Monte Carlo simulations of thefolding of designed heteropolymers, we have identified a hierarchy ofspecific elementary phenomena which control the way single domain proteinfold: a) formation of few, local elementary structures, b) creation ofthe (post-critical) folding nucleus through the assemblage together ofthe local elementary structures, c) relaxation of the remaining aminoacids to the native conformation. These results, which are consistentwith a two-state kinetics of the folding of small, single domain proteins,where the local elementary structures and the folding nucleus can be viewedas hidden intermediates along the reaction pathway, provide the basis fora strategy to read the tertiary structure of a protein from its aminoacid sequence.

Response function technique for calculating the random-phase approximation correlation energy

We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory [Y. R. Shimizu, J. D. Garrett, R. A. Broglia, M. Gallardo, and E. Vigezzi, Rev. Mod. Phys. 61, 131 (1989)]. It is demonstrated that our formula is equivalent to a contour integral representation recently proposed [F. Donau, D. Almehed, and R. G. Nazmitdinov, Phys. Rev. Lett. 83, 280 (1999)] being numerically more efficient for realistic calculations. Examples are presented for pairing correlations in rapidly rotating nuclei.

Anharmonic properties of the double giant dipole resonance

A systematic microscopic study of the anharmonic properties of the double giant dipole resonance (DGDR) has been carried out, for the first time, for nuclei with mass number A spanning the whole mass table. It is concluded that the corrections of the energy centroid of the Jpi = 0(+) and 2(+) components of the DGDR from its harmonic limit are negative, have a value of the order of a few hundred keV, and follow an A-1 dependence.

Hiking in the energy landscape in sequence space: a bumpy road to good folders

With the help of a simple 20-letter lattice model of heteropolymers, we investigated the energy landscape in the space of designed good-folder sequences. Low-energy sequences form clusters, interconnected via neutral networks, in the space of sequences. Residues that play a key role in the foldability of the chain and in the stability of the native state are highly conserved, even among the chains belonging to different clusters. If, according to the interaction matrix, some strong attractive interactions are almost degenerate (i.e., they can be realized by more than one type of amino acid contacts), sequence clusters group into a few superclusters. Sequences belonging to different superclusters are dissimilar, displaying very small ( approximately 10%) similarity, and residues in key sites are, as a rule, not conserved. Similar behavior is observed in the analysis of real protein sequences.

Effective nucleon mass in deformed nuclei

The coupling of vibrations to nucleons moving in levels lying close to the Fermi energy of deformed rotating nuclei is found to lead to a number of effects: (i) shifts of the single-particle levels of the order of 0.5 MeV towards the Fermi energy and thus to an increase of the level density, (ii) single-particle state depopulation of the order of 30%, and thus spectroscopic factors approximately 0.7, etc. These effects, which we have calculated for 168Yb, can be expressed in terms of an effective mass, the so-called omega mass ( m(omega)), which is approximately 40% larger than the bare nucleon mass in the ground state. It is found that m(omega) displays a strong dependence with rotational frequency, eventually approaching the bare mass for Planck's over 2piomega(rot) approximately 0.5-0.6 MeV.

Folding and aggregation of designed proteins

Protein aggregation is studied by following the simultaneous folding of two designed identical 20-letter amino acid chains within the framework of a lattice model and using Monte Carlo simulations. It is found that protein aggregation is determined by elementary structures (partially folded intermediates) controlled by local contacts among some of the most strongly interacting amino acids and formed at an early stage in the folding process.