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The Wilson–Cowan model has been widely applied for the simulation of electroencephalography (EEG) waves associated with neural activities in the brain. The Runge–Kutta (RK) method is commonly used to numerically solve the Wilson–Cowan equations. In this paper, we focus on enhancing the accuracy of the numerical method by proposing a strategy to construct a class of fourth-order RK methods using a generalized iterated Crank–Nicolson procedure, where the RK coefficients depend on a free parameter c2. When c2 is set to 0.5, our method becomes a special case of the classical fourth-order RK method. We apply the proposed methods to solve the Wilson–Cowan equations with two and three neuron populations, modeling EEG epileptic dynamics. Our simulations demonstrate that when c2 is set to 0.4, the proposed RK4-04 method yields smaller errors compared to those obtained using the classical fourth-order RK method. This is particularly visible when the spectral radius of the connection matrix or the excitation-inhibition coupling coefficient is relatively large. 

The intracellular environment is crowded with diverse biomacrolecules (~80-400 mg/ml), likely affecting various biological processes such as protein folding, binding of small molecules, enzymatic activity, and pathological protein aggregation. As a model we have been using solutions of Ficoll, a highly branched polysaccharide, to mimic the environment. Besides its biomedical applications (e.g. blood separation), it has been used as a macromolecular crowder in studies of protein folding and stability, cell volume signaling, tissue engineering, and nanotransport. In this study, our goal is to identify and assess Raman spectral signatures associated with Ficoll molecules and Ficoll-Ficoll interactions for future investigations of crowding effects. In addition to the Raman peaks of water (~1640 cm-1 and ~3200 cm-1) and dissolved O2 (~1556 cm-1) and N2 (~2331 cm-1) we identified a distinct Raman peak (~2900 cm-1) in the 1500-3500 cm-1 wavenumber range, which is associated with Ficoll and CH and CH2 stretching modes. As the Ficoll concentration increases, the intensity of the Ficoll Raman peaks increases while the intensity of the water Raman peaks decreases, the latter likely due to reduction of water content. Further, we have applied the intensity correlation analysis (ICA) method to assess systematic changes of Raman spectra with Ficoll concentration (up to 1000 mg/ml). ICA indicates an overall linear trend over the full wavenumber range, but also shows closed loops that can be attributed to slight changes of the profiles of certain peaks. The results demonstrate ICA as a potential insightful tool for identifying Ficoll in chemical analysis of crowded biological samples. 

In this study, we used GROMACS, a versatile package for performing molecular dynamics to simulate the interactions between different nanoparticles and Dipalmitoyl Phosphatidyl Choline (DPPC) to understand the physical mechanisms that govern the interactions between nanoparticles and lipid membrane. Our simulations show the responses of the lipid bilayer to the nanoparticles, including the formation of an adsorbent layer on the nanoparticle surface, transmembrane ectopic movements, and inconspicuous endocytosis of the nanoparticle by the membrane. The effects of the size of the nanoparticles, structural shape, and charge state on the interaction and transport processes will be examined and summarized.