Length control of microtubules by depolymerizing motor proteins

In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.Comment: Added section with figures and significantly expanded text, current version to appear in Europhys. Let

Dicke quantum spin glass of atoms and photons

Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin glass phase can appear, with a random linear combination of the cavity modes superradiant. We compute atomic and photon spectral response functions across this quantum phase transition, both of which should be accessible in experiment.Comment: 4 pages, 3 figures, v2: described quantum optics set-up in more detail; extended discussion on photon correlation functions and experimental signatures; added reference

Computing Anti-Derivatives using Deep Neural Networks

This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of definite integrals, but primitives or indefinite integrals are often non-elementary. Anti-derivatives are necessarily required when there are several parameters in an integrand and the integral obtained is a function of those parameters. There is no theoretical method that can do this for any given function. Some existing ways to get around this are primarily based on either curve fitting or infinite series approximation of the integrand, which is then integrated theoretically. Curve fitting approximations are inaccurate for highly non-linear functions and require a different approach for every problem. On the other hand, the infinite series approach does not give a closed-form solution, and their truncated forms are often inaccurate. We claim that using a single method for all integrals, our algorithm can approximate anti-derivatives to any required accuracy. We have used this algorithm to obtain the anti-derivatives of several functions, including non-elementary and oscillatory integrals. This paper also shows the applications of our method to get the closed-form expressions of elliptic integrals, Fermi-Dirac integrals, and cumulative distribution functions and decrease the computation time of the Galerkin method for differential equations

Adiabatic Quantum Search in Open Systems

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size, their robustness in open systems remains unresolved. We study the dynamics in the proximity of such an avoided level crossing associated with the adiabatic quantum search algorithm in a quantum system that is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. At finite temperature, however, scattering processes render the algorithm inefficient and no quantum speedup can be achieved. Owing to the generic nature of our model, we expect our results to be widely applicable to other adiabatic quantum algorithms.Comment: Accepted version. 6 pages, 2 figures, 10 pages supplemental material

Noise-Induced Subdiffusion in Strongly Localized Quantum Systems

We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. Our qualitative conclusions are also valid for interacting systems in the many-body localized phase

Genome-scale mapping models and algorithms for stationary and instationary MFA-based metabolic flux elucidation

Metabolic models used in 13C metabolic flux analysis (13C-MFA) generally include a limited number of reactions primarily from central metabolism, neglecting degradation pathways and atom transition contributions for reactions outside central metabolism. This study addresses the impact on prediction fidelity of scaling-up core bacterial and cyanobacterial mapping models to a genome-scale carbon mapping (GSCM) models, imEco726 (668 reaction and 566 metabolites) and imSyn711 (731 reactions, 679 metabolites) for E. coli and Synechocystis PCC 6803, respectively, representing a ten-fold increase in model size. The GSCM models are constructed using the CLCA algorithm following reduction of the corresponding metabolic models, iAF1260 and iSyn731, using experimentally measured biomass and product yield during growth on glucose and CO2, respectively. The mapping models are then deployed for flux elucidation using isotopic steady-state MFA for E. coli to recapitulate experimentally observed labeling distributions of 12 measured amino acids, and isotopic instationary MFA for Synechocystis, to recapitulate labeling dynamics of 15 central metabolites. In both models, 80% of all fluxes varies less than onetenth of the basis carbon substrate uptake rate primarily due to the flux coupling with biomass production. Overall, we find that both the topology and estimated values of the metabolic fluxes remain largely consistent between the core and GSMM models for E. coli. Stepping up to a genome-scale mapping model leads to wider flux inference ranges for 20 key reactions present in the core model. The glycolysis flux range doubles due to the possibility of active gluconeogenesis, the TCA flux range expanded by 80% due to the availability of a bypass through arginine consistent with labeling data, and the transhydrogenase reaction flux was essentially unresolved due to the presence of as many as five routes for the inter-conversion of NADPH to NADH afforded by the genome-scale model. By globally accounting for ATP demands in the GSMM model the unused ATP decreased drastically with the lower bound matching the maintenance ATP requirement. A non-zero flux for the arginine degradation pathway was identified to meet biomass precursor demands as detailed in the iAF1260 model. Significant flux range shifts were observed using a GSCM model compared to a core model in Synechocystis arising from the inclusion of 18 novel carbon paths in the GSCM model. In particular, no flux is channeled through the oxidative pentose phosphate pathway, resulting in a reduced carbon fixation flux. In addition, a higher flux is seen through the Transaldolase reaction, serving as a bypass route to Fructose bisphosphatase. Serine and glycine are found to be synthesized from 3-phosphoglycerate and the photorespiratory pathway, respectively. Pyruvate is synthesized exclusively via the malate bypass with trace contributions from pyruvate kinase. Furthermore, trace flux is predicted through the lower TCA cycle indicating either pathway incompleteness or dispensability during photoautotrophic growth. Despite these differences, 80% of all reactions in both genome-scale models are resolved to within 10% of the respective substrate uptake rate due to the presence of 411 and 407 growth-coupled reactions in E. coli and Synechocystis, respectively. Flux ranges obtained with GSCM models are compared with those obtained upon projecting core model ranges on to a genome-scale metabolic model to elucidate the loss of information and erroneous biological inferences about pathway usage arising from assumptions contained within core models, reaffirming the importance of using mapping models with global carbon path coverage in 13C metabolic flux analysis