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QUASAR: A Flexible QM-MM Method for Biomolecular Systems based on Restraining Spheres
No full textQuantum mechanical models of molecules theoretically offer unprecedented accuracy in predicting values associated with these systems, including the free energy of interaction between two molecules. However, high-accuracy quantum mechanical methods are computationally too expensive to be applied to larger systems, including most biomolecular systems such as proteins. To circumvent this challenge, the hybrid quantum mechanics/molecular mechanics (QM/MM) method was developed, allowing one to treat only the most important part of the system on the quantum mechanical level and the remaining part on the classical level. To date, QM/MM simulations for biomolecular systems have been carried out almost exclusively on the electronic structure level, neglecting nuclear quantum effects (NQEs). Yet NQEs can play a major role in biomolecular systems [1]. Here, we present i-QI, a QM/MM client for the path integral molecular dynamics (PIMD) software i-PI [2, 3, 4]. i-QI allows for carrying out QM/MM simulations simultaneously, allowing for the inclusion of electronic as well as nuclear quantum effects. i-QI implements a new QM/MM scheme based on constraining potentials called QUASAR, which allows handling diffusive systems, such as biomolecules solvated in water solvent. The QUASAR method is suitable in particular when the properties of interest are equilibrium properties, such as the free energy of binding. i-QI is freely available and open source, and we demonstrate it on a test system
CoDA: Interactive Segmentation and Morphological Analysis of Dendroid Structures Exemplified on Stony Cold-Water Corals
No full textSource code and simulation results: Resonance modes in microstructured photonic waveguides - Efficient and accurate computation based on AAA rational approximation
No full textDissecting origins of wiring specificity in dense cortical connectomes
No full textWiring specificity in the cortex is observed across scales from the subcellular to the network level. It describes the deviations of connectivity patterns from those expected in randomly connected networks. Understanding the origins of wiring specificity in neural networks remains difficult as a variety of generative mechanisms could have contributed to the observed connectome. To take a step forward, we propose a generative modeling framework that operates directly on dense connectome data as provided by saturated reconstructions of neural tissue. The computational framework allows testing different assumptions of synaptic specificity while accounting for anatomical constraints posed by neuron morphology, which is a known confounding source of wiring specificity. We evaluated the framework on dense reconstructions of the mouse visual and the human temporal cortex. Our template model incorporates assumptions of synaptic specificity based on cell type, single-cell identity, and subcellular compartment. Combinations of these assumptions were sufficient to model various connectivity patterns that are indicative of wiring specificity. Moreover, the identified synaptic specificity parameters showed interesting similarities between both datasets, motivating further analysis of wiring specificity across species
Synchronization and random attractors in reaction jump processes
No full textThis work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie’s stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems
Partial mean-field model for neurotransmission dynamics
No full textThis article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios
Learning interpretable collective variables for spreading processes on networks
No full textCollective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically
Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization
No full textThis article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: the speed of LP iterative refinement, in particular in the majority of cases when a double-precision floating-point solver is able to compute approximate solutions with small errors, and the robustness of precision boosting whenever extended levels of precision become necessary.
We compare the practical performance of the resulting algorithm with both puremethods on a large set of LPs and mixed-integer programs (MIPs). The results show that the combined algorithm solves more instances than a pure LP iterative refinement approach, while being faster than pure precision boosting. When embedded in an exact branch-and-cut framework for MIPs, the combined algorithm is able to reduce the number of failed calls to the exact LP solver to zero, while maintaining the speed of the pure LP iterative refinement approach
The Kramers turnover in terms of a macro-state projection on phase space
No full textWe have investigated how Langevin dynamics is affected by the friction
coefficient using the novel algorithm ISOKANN, which combines the transfer
operator approach with modern machine learning techniques. ISOKANN describes
the dynamics in terms of an invariant subspace projection of the Koopman
operator defined in the entire state space, avoiding approximations due to
dimensionality reduction and discretization. Our results are consistent with
the Kramers turnover and show that in the low and moderate friction regimes,
metastable macro-states and transition rates are defined in phase space, not
only in position space