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Register a new userModeling polymerization of microtubules: a quantum mechanical approach
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In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion for the quantum fields are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. We find that the dynamics of a microtubule can be mathematically expressed via a cubic-quintic nonlinear Schr{o}dinger (NLS) equation. We show that a vortex filament, a generic solution of the NLS equation, exhibits linear growth/shrinkage in time as well as temporal fluctuations about some mean value which is qualitatively similar to the dynamic instability of microtubules.
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In this paper we propose a microscopic model to study the polymerization of microtubules (MTs). Starting from fundamental reactions during MTs assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in 3D. %coexistence with tubulin dimers in a solution. We found that the dynamics of a MT is mathematically expressed via a cubic-quintic nonlinear Schrodinger (NLS) equation. Interestingly, the generic 3D solution of the NLS equation exhibits linear growing and shortening in time as well as temporal fluctuations about a mean value which are qualitatively similar to the dynamic instability of MTs observed experimentally. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.
Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant patterns of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold.
In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. The latter equations are very similar to the phenomenological equations that describe dynamic instability of microtubules in a tubulin solution.
The complementary strands of DNA molecules can be separated when stretched apart by a force; the unzipping signal is correlated to the base content of the sequence but is affected by thermal and instrumental noise. We consider here the ideal case where opening events are known to a very good time resolution (very large bandwidth), and study how the sequence can be reconstructed from the unzipping data. Our approach relies on the use of statistical Bayesian inference and of Viterbi decoding algorithm. Performances are studied numerically on Monte Carlo generated data, and analytically. We show how multiple unzippings of the same molecule may be exploited to improve the quality of the prediction, and calculate analytically the number of required unzippings as a function of the bandwidth, the sequence content, the elasticity parameters of the unzipped strands.
Modeling the effects of mutations on the binding affinity plays a crucial role in protein engineering and drug design. In this study, we develop a novel deep learning based framework, named GraphPPI, to predict the binding affinity changes upon mutations based on the features provided by a graph neural network (GNN). In particular, GraphPPI first employs a well-designed pre-training scheme to enforce the GNN to capture the features that are predictive of the effects of mutations on binding affinity in an unsupervised manner and then integrates these graphical features with gradient-boosting trees to perform the prediction. Experiments showed that, without any annotated signals, GraphPPI can capture meaningful patterns of the protein structures. Also, GraphPPI achieved new state-of-the-art performance in predicting the binding affinity changes upon both single- and multi-point mutations on five benchmark datasets. In-depth analyses also showed GraphPPI can accurately estimate the effects of mutations on the binding affinity between SARS-CoV-2 and its neutralizing antibodies. These results have established GraphPPI as a powerful and useful computational tool in the studies of protein design.
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