128 research outputs found
Exploring the Levinthal limit in protein folding
According to the thermodynamic hypothesis, the native state of proteins is uniquely defined by their amino acid sequence. On the other hand, according to Levinthal, the native state is just a local minimum of the free energy and a given amino acid sequence, in the same thermodynamic conditions, can assume many, very different structures that are as thermodynamically stable as the native state. This is the Levinthal limit explored in this work. Using computer simulations, we compare the interactions that stabilize the native state of four different proteins with those that stabilize three non-native states of each protein and find that the nature of the interactions is very similar for all such 16 conformers. Furthermore, an enhancement of the degree of fluctuation of the non-native conformers can be explained by an insufficient relaxation to their local free energy minimum. These results favor Levinthal's hypothesis that protein folding is a kinetic non-equilibrium process.FCT - Foundation for Science and Technology, Portugal [UID/Multi/04326/2013]; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP); Conselho Nacional de Desenvolvimento Cientia co e Tecnologico (CNPq
Specificity quantification of biomolecular recognition and its implication for drug discovery
Highly efficient and specific biomolecular recognition requires both affinity and specificity. Previous quantitative descriptions of biomolecular recognition were mostly driven by improving the affinity prediction, but lack of quantification of specificity. We developed a novel method SPA (SPecificity and Affinity) based on our funneled energy landscape theory. The strategy is to simultaneously optimize the quantified specificity of the “native” protein-ligand complex discriminating against “non-native” binding modes and the affinity prediction. The benchmark testing of SPA shows the best performance against 16 other popular scoring functions in industry and academia on both prediction of binding affinity and “native” binding pose. For the target COX-2 of nonsteroidal anti-inflammatory drugs, SPA successfully discriminates the drugs from the diversity set, and the selective drugs from non-selective drugs. The remarkable performance demonstrates that SPA has significant potential applications in identifying lead compounds for drug discovery
Discrete Kinetic Models from Funneled Energy Landscape Simulations
A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character
Drug export and allosteric coupling in a multidrug transporter revealed by molecular simulations
Multidrug resistance is a serious problem in current chemotherapy. The efflux system largely responsible for resistance in Escherichia coli contains the drug transporter, AcrB. The structures of AcrB were solved in 2002 as the symmetric homo-trimer, and then in 2006 as the asymmetric homo-trimer. The latter suggested a functionally rotating mechanism. Here, by molecular simulations of the AcrB porter domain, we uncovered allosteric coupling and the drug export mechanism in the AcrB trimer. Allosteric coupling stabilized the asymmetric structure with one drug molecule bound, which validated the modelling. Drug dissociation caused a conformational change and stabilized the symmetric structure, providing a unified view of the structures reported in 2002 and 2006. A dynamic study suggested that, among the three potential driving processes, only protonation of the drug-bound protomer can drive the functional rotation and simultaneously export the drug
Tunable kinetic proofreading in a model with molecular frustration
In complex systems, feedback loops can build intricate emergent phenomena, so
that a description of the whole system cannot be easily derived from the
properties of the individual parts. Here we propose that inter-molecular
frustration mechanisms can provide non trivial feedback loops which can develop
nontrivial specificity amplification. We show that this mechanism can be seen
as a more general form of a kinetic proofreading mechanism, with an interesting
new property, namely the ability to tune the specificity amplification by
changing the reactants concentrations. This contrasts with the classical
kinetic proofreading mechanism in which specificity is a function of only the
reaction rate constants involved in a chemical pathway. These results are also
interesting because they show that a wide class of frustration models exists
that share the same underlining kinetic proofreading mechanisms, with even
richer properties. These models can find applications in different areas such
as evolutionary biology, immunology and biochemistry
The Energy Landscapes of Repeat-Containing Proteins: Topology, Cooperativity, and the Folding Funnels of One-Dimensional Architectures
Repeat-proteins are made up of near repetitions of 20– to 40–amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi–one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete “domain” (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (ΔGwater) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the “coarse-grained” description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are “poised” at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions
An Estimate of the Numbers and Density of Low-Energy Structures (or Decoys) in the Conformational Landscape of Proteins
The conformational energy landscape of a protein, as calculated by known potential energy functions, has several minima, and one of these corresponds to its native structure. It is however difficult to comprehensively estimate the actual numbers of low energy structures (or decoys), the relationships between them, and how the numbers scale with the size of the protein.We have developed an algorithm to rapidly and efficiently identify the low energy conformers of oligo peptides by using mutually orthogonal Latin squares to sample the potential energy hyper surface. Using this algorithm, and the ECEPP/3 potential function, we have made an exhaustive enumeration of the low-energy structures of peptides of different lengths, and have extrapolated these results to larger polypeptides.We show that the number of native-like structures for a polypeptide is, in general, an exponential function of its sequence length. The density of these structures in conformational space remains more or less constant and all the increase appears to come from an expansion in the volume of the space. These results are consistent with earlier reports that were based on other models and techniques
The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
The folding pathway and rate coefficients of the folding of a knotted protein
are calculated for a potential energy function with minimal energetic
frustration. A kinetic transition network is constructed using the discrete
path sampling approach, and the resulting potential energy surface is
visualized by constructing disconnectivity graphs. Owing to topological
constraints, the low-lying portion of the landscape consists of three distinct
regions, corresponding to the native knotted state and to configurations where
either the N- or C-terminus is not yet folded into the knot. The fastest
folding pathways from denatured states exhibit early formation of the
N-terminus portion of the knot and a rate-determining step where the C-terminus
is incorporated. The low-lying minima with the N-terminus knotted and the
C-terminus free therefore constitute an off-pathway intermediate for this
model. The insertion of both the N- and C-termini into the knot occur late in
the folding process, creating large energy barriers that are the rate limiting
steps in the folding process. When compared to other protein folding proteins
of a similar length, this system folds over six orders of magnitude more
slowly.Comment: 19 page
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
We present here a review of the fundamental topics of Hartree-Fock theory in
Quantum Chemistry. From the molecular Hamiltonian, using and discussing the
Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock
equations for the electronic problem. Special emphasis is placed in the most
relevant mathematical aspects of the theoretical derivation of the final
equations, as well as in the results regarding the existence and uniqueness of
their solutions. All Hartree-Fock versions with different spin restrictions are
systematically extracted from the general case, thus providing a unifying
framework. Then, the discretization of the one-electron orbitals space is
reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition
of the basic underlying concepts related to the construction and selection of
Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we
close the review with a section in which the most relevant modern developments
(specially those related to the design of linear-scaling methods) are commented
and linked to the issues discussed. The whole work is intentionally
introductory and rather self-contained, so that it may be useful for non
experts that aim to use quantum chemical methods in interdisciplinary
applications. Moreover, much material that is found scattered in the literature
has been put together here to facilitate comprehension and to serve as a handy
reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and
subeqn package
Static and dynamic characteristics of protein contact networks
The principles underlying protein folding remains one of Nature's puzzles
with important practical consequences for Life. An approach that has gathered
momentum since the late 1990's, looks at protein hetero-polymers and their
folding process through the lens of complex network analysis. Consequently,
there is now a body of empirical studies describing topological characteristics
of protein macro-molecules through their contact networks and linking these
topological characteristics to protein folding. The present paper is primarily
a review of this rich area. But it delves deeper into certain aspects by
emphasizing short-range and long-range links, and suggests unconventional
places where "power-laws" may be lurking within protein contact networks.
Further, it considers the dynamical view of protein contact networks. This
closer scrutiny of protein contact networks raises new questions for further
research, and identifies new regularities which may be useful to parameterize a
network approach to protein folding. Preliminary experiments with such a model
confirm that the regularities we identified cannot be easily reproduced through
random effects. Indeed, the grand challenge of protein folding is to elucidate
the process(es) which not only generates the specific and diverse linkage
patterns of protein contact networks, but also reproduces the dynamic behavior
of proteins as they fold. Keywords: network analysis, protein contact networks,
protein foldingComment: Added Appendix
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