Optimal protein-folding codes from spin-glass theory.
Ontology highlight
ABSTRACT:
SUBMITTER: Goldstein RA
PROVIDER: S-EPMC49199 | BioStudies | 1992-01-01T00:00:00Z
SECONDARY ACCESSION(S): 1ALC
REPOSITORIES: biostudies
Similar Datasets
Project description:Energy landscape theory is used to obtain optimized energy functions for predicting protein structure, without using homology information. At short sequence separation the energy functions are associative memory Hamiltonians constructed from a database of folding patterns in nonhomologous proteins and at large separations they have the form of simple pair potentials. The lowest energy minima provide reasonably accurate tertiary structures even though no homologous proteins are included in the construction of the Hamiltonian. We also quantify the funnel-like nature of these energy functions by using free energy profiles obtained by the multiple histogram method.
2000-01-01 | S-EPMC18901 | BioStudies
Project description:Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.
2016-01-01 | S-EPMC4866778 | BioStudies
Project description:Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
1000-01-01 | S-EPMC5512879 | BioStudies
Project description:The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.
2016-01-01 | S-EPMC4834628 | BioStudies
Project description:Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Configurations are treated where the absolute values of the spin vectors can be considered constant. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to d-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up. The conservative spin-dependent dynamics finds explicit presentation in Hamiltonian form through next-to-next-to-leading-order spin-orbit and spin1-spin2 couplings and to leading-order in the cubic and quartic in spin interactions. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin-orbit and spin1-spin2 couplings. The most important historical issues get pointed out.
1000-01-01 | S-EPMC6133045 | BioStudies
Project description:The time-energy uncertainty relation (TEUR) [Formula: see text] holds if the Hamiltonian is completely unknown, but can be violated otherwise; here we initiate a rigorous study describing when and to what extent such violations can occur. To this end, we propose a computational version of the TEUR (cTEUR), in which ?t is replaced by the computational complexity of simulating the measurement. cTEUR violations are proved to occur if and only if the Hamiltonian can be fast forwarded (FF), namely, simulated for time t with complexity significantly smaller than t. Shor's algorithm provides an example of exponential cTEUR violations; we show that so do commuting local Hamiltonians and quadratic fermion Hamiltonians. A general FF method is ruled out, but finding further examples, as well as experimental demonstrations, are left for future work. We discuss possible connections to sensing and quantum gravity. This work initiates a rigorous theory of efficiency versus accuracy in energy measurements using computational complexity language.
1000-01-01 | S-EPMC5691059 | BioStudies
Project description:Aminoacyl-tRNA synthetases recognize tRNA anticodon and 3' acceptor stem bases. Synthetase Urzymes acylate cognate tRNAs even without anticodon-binding domains, in keeping with the possibility that acceptor stem recognition preceded anticodon recognition. Representing tRNA identity elements with two bits per base, we show that the anticodon encodes the hydrophobicity of each amino acid side-chain as represented by its water-to-cyclohexane distribution coefficient, and this relationship holds true over the entire temperature range of liquid water. The acceptor stem codes preferentially for the surface area or size of each side-chain, as represented by its vapor-to-cyclohexane distribution coefficient. These orthogonal experimental properties are both necessary to account satisfactorily for the exposed surface area of amino acids in folded proteins. Moreover, the acceptor stem codes correctly for ?-branched and carboxylic acid side-chains, whereas the anticodon codes for a wider range of such properties, but not for size or ?-branching. These and other results suggest that genetic coding of 3D protein structures evolved in distinct stages, based initially on the size of the amino acid and later on its compatibility with globular folding in water.
1000-01-01 | S-EPMC4475997 | BioStudies
Project description:This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zienau-Woolley hamiltonian. We question its validity and show that it is not equivalent to the minimal-coupling hamiltonian. In this article, we show that these two hamiltonians are not connected through a gauge transformation. We find that the gauge is not fixed in the Power-Zienau-Woolley hamiltonian. The interaction term is written in one gauge whereas the rest of the hamiltonian is written in another gauge. The Power-Zienau-Woolley hamiltonian and the minimal-coupling one are related through a unitary transformation that does not fulfill the gauge fixing constraints. Consequently, they predict different physical results. In this letter, we provide the correct quantum theory in the multipolar gauge with a hamiltonian involving only the physical fields.
1000-01-01 | S-EPMC5593841 | BioStudies
Project description:We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
2014-01-01 | S-EPMC4194464 | BioStudies