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Hypokalemia, characterized by too low serum potassium levels, is a severe mineral disorder which can be life threatening. It is increasingly diagnosed in veterinarian healthcare and a topic of ongoing research. In this paper, we explore the different originating conditions of hypokalemia: reduced potassium intake, increased excretion, acid-base disturbances, or increased insulin, by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows.
Simulations are compared with literature. The results give insights into the network dynamics and point to scenarios on which experimental effort should be focused. Application of mathematical models can assist in experimental planning as well as the reduction, refinement and replacement of animal experiments.
Particle methods have become indispensible in conformation dynamics to
compute transition rates in protein folding, binding processes and
molecular design, to mention a few.
Conformation dynamics requires at a decomposition of a molecule's position
space into metastable conformations.
In this paper, we show how this decomposition
can be obtained via the design of either ``soft'' or ``hard''
molecular conformations.
We show, that the soft approach results in a larger metastabilitiy of
the decomposition and is thus more advantegous. This is illustrated
by a simulation of Alanine Dipeptide.
Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very
well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a
detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with
general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems.
To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1−40) peptide, periodically driven by an oscillating electric field.
The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.