Fetching marked items from an unsorted database in NMR ensemble computing

Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.Comment: 4 pages and 1 figur

Non-Ergodic Nuclear Depolarization in Nano-Cavities

Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin,$P_1(0)= 1$ then the exact spin dynamics of the model is shown to exhibit a periodical short pulses of the polarization of the first spin, the effect being typical of the systems having a large number, $N$, of spins. If $N \gg 1$, then within the period $4\pi/g$ ($2\pi/g$) for odd (even) $N$-spin clusters, with $g$ standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time independent value, 1/3, over the time interval about $(g\sqrt{N})^{-1}$, thus, almost all the time, the spin 1 spends in the time independent condition $P_1(t)= 1/3$. The period and the width of the pulses determine the volume and the form-factor of the ellipsoidal cavity. The formalism is adopted to the case of time varying nano-fluctuations of the volume of the cavitation nano-bubbles. If the volume $V(t)$ is varied by the Gaussian-in-time random noise then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits the Gaussian (or exponential) time dependence when the correlation time of the fluctuations of the nano-volume is larger (or smaller) than the $<(\delta g)^2 >^{-1/2}$, where the $$ is the variance of the $g(V(t))$ coupling. Finally, we report the exact calculations of the NMR line shape for the $N$-spin gaseous aggregate.Comment: 26 pages, 3 figure

Conformational Control of the Binding of the Transactivation Domain of the MLL Protein and c-Myb to the KIX Domain of CREB

The KIX domain of CBP is a transcriptional coactivator. Concomitant binding to the activation domain of proto-oncogene protein c-Myb and the transactivation domain of the trithorax group protein mixed lineage leukemia (MLL) transcription factor lead to the biologically active ternary MLL∶KIX∶c-Myb complex which plays a role in Pol II-mediated transcription. The binding of the activation domain of MLL to KIX enhances c-Myb binding. Here we carried out molecular dynamics (MD) simulations for the MLL∶KIX∶c-Myb ternary complex, its binary components and KIX with the goal of providing a mechanistic explanation for the experimental observations. The dynamic behavior revealed that the MLL binding site is allosterically coupled to the c-Myb binding site. MLL binding redistributes the conformational ensemble of KIX, leading to higher populations of states which favor c-Myb binding. The key element in the allosteric communication pathways is the KIX loop, which acts as a control mechanism to enhance subsequent binding events. We tested this conclusion by in silico mutations of loop residues in the KIX∶MLL complex and by comparing wild type and mutant dynamics through MD simulations. The loop assumed MLL binding conformation similar to that observed in the KIX∶c-Myb state which disfavors the allosteric network. The coupling with c-Myb binding site faded, abolishing the positive cooperativity observed in the presence of MLL. Our major conclusion is that by eliciting a loop-mediated allosteric switch between the different states following the binding events, transcriptional activation can be regulated. The KIX system presents an example how nature makes use of conformational control in higher level regulation of transcriptional activity and thus cellular events

In Silico Elucidation of the Recognition Dynamics of Ubiquitin

Elucidation of the mechanism of biomacromolecular recognition events has been a topic of intense interest over the past century. The inherent dynamic nature of both protein and ligand molecules along with the continuous reshaping of the energy landscape during the binding process renders it difficult to characterize this process at atomic detail. Here, we investigate the recognition dynamics of ubiquitin via microsecond all-atom molecular dynamics simulation providing both thermodynamic and kinetic information. The high-level of consistency found with respect to experimental NMR data lends support to the accuracy of the in silico representation of the conformational substates and their interconversions of free ubiquitin. Using an energy-based reweighting approach, the statistical distribution of conformational states of ubiquitin is monitored as a function of the distance between ubiquitin and its binding partner Hrs-UIM. It is found that extensive and dense sampling of conformational space afforded by the µs MD trajectory is essential for the elucidation of the binding mechanism as is Boltzmann sampling, overcoming inherent limitations of sparsely sampled empirical ensembles. The results reveal a population redistribution mechanism that takes effect when the ligand is at intermediate range of 1–2 nm from ubiquitin. This mechanism, which may be depicted as a superposition of the conformational selection and induced fit mechanisms, also applies to other binding partners of ubiquitin, such as the GGA3 GAT domain

A Major Determinant of Cyclophilin Dependence and Cyclosporine Susceptibility of Hepatitis C Virus Identified by a Genetic Approach

Since the advent of genome-wide small interfering RNA screening, large numbers of cellular cofactors important for viral infection have been discovered at a rapid pace, but the viral targets and the mechanism of action for many of these cofactors remain undefined. One such cofactor is cyclophilin A (CyPA), upon which hepatitis C virus (HCV) replication critically depends. Here we report a new genetic selection scheme that identified a major viral determinant of HCV's dependence on CyPA and susceptibility to cyclosporine A. We selected mutant viruses that were able to infect CyPA-knockdown cells which were refractory to infection by wild-type HCV produced in cell culture. Five independent selections revealed related mutations in a single dipeptide motif (D316 and Y317) located in a proline-rich region of NS5A domain II, which has been implicated in CyPA binding. Engineering the mutations into wild-type HCV fully recapitulated the CyPA-independent and CsA-resistant phenotype and four putative proline substrates of CyPA were mapped to the vicinity of the DY motif. Circular dichroism analysis of wild-type and mutant NS5A peptides indicated that the D316E/Y317N mutations (DEYN) induced a conformational change at a major CyPA-binding site. Furthermore, nuclear magnetic resonance experiments suggested that NS5A with DEYN mutations adopts a more extended, functional conformation in the putative CyPA substrate site in domain II. Finally, the importance of this major CsA-sensitivity determinant was confirmed in additional genotypes (GT) other than GT 2a. This study describes a new genetic approach to identifying viral targets of cellular cofactors and identifies a major regulator of HCV's susceptibility to CsA and its derivatives that are currently in clinical trials