Mathematical modelling and numerical simulation of the morphological development of neurons

Background

The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.

Methods

A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.

Results

Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.

Conclusion

A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

     

Electronic structure of BaTiO3 using resonant X-ray emission spectroscopy at the Ba-L3 and Ti-K absorption edges

We have studied the electronic properties of the ferroelectric barium titanate BaTiO₃ using two complementary bulk-sensitive spectroscopic probes, resonant X-ray emission spectroscopy (RXES) and X-ray absorption spectroscopy in the partial fluorescence mode (PFY-XAS) at the Ba-L₃ and Ti-K absorption edges. Contrary to a previous study, we found no fine structure in the pre-edge area of the PFY-XAS spectrum at the Ba-L₃ edge, and no temperature-induced spectral change was observed between room temperature and 150 °C. This result is not supportive of the possible presence of the displacement around Ba²⁺ at the Curie temperature. RXES spectra were measured at the Ti-K edge for BaTiO₃, along with SrTiO₃ and La-doped metallic SrTiO₃. The photon energy of the emission peak is found to be nearly constant throughout the absorption edge for all three compounds. We deduce the Ti 3d states to have a delocalized character, in contrast with the Ba 5d states, a property which is consistent with the proposed scenario of the formation of electric dipoles in BaTiO₃.     

Thermodynamic non-additivity in disordered systems with extended phase space

Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.     

Electric field gradient in Mg and Zn detected by β-emitters,8Li and12x0392;x0392;x0392;

The quadrupole coupling constants of⁸Li and¹²B in hcp Mg and Zn are determined by use of a newly developed nuclear quadrupole resonance technique (NNQR) as ¦eqQ(⁸Li in Mg)/h¦=3.0±0.3 kHz, ¦eqQ(⁸Li in Zn)/h¦=33.5±2 kHz, and ¦eqQ(¹²B in Mg)/h¦=47.0±0.1 kHz. Correspondingly, the electric field gradients at room temperature are deduced: ¦q(⁸Li in Mg)¦=(3.81±0.39)×10¹⁸, ¦q(⁸Li in Zn)¦=(4.25±0.27)×10¹⁹, and ¦q(¹²B in Mg)¦=(1.47±0.03)×10²⁰, all in V/m². The experiments are compared with the results of first-principles super-cell band structure calculations which can treat local lattice relaxations around the impurity nuclei. The calculations show that the most favorable location of these light interstitials in hcp Mg is not the octahedral-like sites which have the biggest interstitial volume, but the basal trigonal sites with a local lattice expansion of as big as 30%. Calculated electric field gradients at the impurity nuclei reproduce the experimental values fairly well.     

Hyperfine quantum beat of short-lived beta-emitter8Li polarized by the tilted foil technique

To disclose the basic mechanisms of nuclear polarization creation realized by the tilted foil technique, hyperfine quantum beats of the nuclear polarization of the short-lived beta-emitter⁸Li(I =2⁺,T _1/2=840 ms) were measured as a function of the distance between two tilted foils. From the observed beats of the⁸Li nuclear polarization, it was found that the Fermi-contact interaction of the⁸Li nucleus with the ground 1s-electron in LiIII plays a main role in the final stage of polarization transfer from polarized orbital electrons to the⁸Li nucleus.     

Quadrupole moment of41Sc by use of new nuclear quadrupole resonance detection

Quadrupole effects in -NMR spectra of⁴¹Sc(I =7/2^–,T _1/2=0.596 s) implanted in a TiO₂ single crystal were detected by use of a modified -NMR technique. Using the field gradient in the crystal determined by the pulsed-Fourier-transformed NMR of⁴⁵Sc in TiO₂, the quadrupole moment of⁴¹Sc has been determined as |Q(⁴¹Sc; 7/2^–)|=166±8 mb.     

Nuclear spin dependence of polarization enhancement by multi-tilted foils studied by short-lived beta-emitters8B and12B

In order to study the basic mechanism of polarization enhancement realized by the multitilted foil technique, nuclear polarization of short-lived beta-emitter⁸B(T_1/2=769 ms,I =2⁺) was induced. Utilizing up to ten tilted foils, the polarization enhancement was measured as a function of the foil numbers. The observed enhancement for⁸B was combined with the previous results for¹²B(I =1⁺,T _1/2=20 ms) which has the same atomic configurations but different nuclear spin. Analyzing these results in the framework of the classical vector model, the essential features of the enhancement depending on the nuclear spin was disclosed.     

Turbulent flame visualization using direct numerical simulation

Combustion phenomena are of high scientific and technological interest, in particular for energy generation and transportation systems. Direct Numerical Simulations (DNS) have become an essential and well established research tool to investigate the structure of turbulent flames, since they do not rely on any approximate turbulence models. In this work two complementary DNS codes are employed to investigate different types of fuels and flame configurations. The code is π³ is a 3-dimensional DNS code using a low-Mach number approximation. Chemistry is described through a tabulation, using two coordinates to enter a database constructed for example with 29 species and 141 reactions for methane combustion. It is used here to investigate the growth of a turbulent premixed flame in a methane-air mixture (Case 1). The second code,Sider is an explicit three-dimensional DNS code solving the fully compressible reactive Navier-Stokes equations, where the chemical processes are computed using a complete reaction scheme, taking into account accurate diffusion properties. It is used here to compute a hydrogen/air turbulent diffusion flame (Case 2), considering 9 chemical species and 38 chemical reactions.     

Sensitization of spinal cord nociceptive neurons with a conjugate of substance P and cholera toxin

Background  

Several investigators have coupled toxins to neuropeptides for the purpose of lesioning specific neurons in the central nervous system. By producing deficits in function these toxin conjugates have yielded valuable information about the role of these cells. In an effort to specifically stimulate cells rather than kill them we have conjugated the neuropeptide substance P to the catalytic subunit of cholera toxin (SP-CTA). This conjugate should be taken up selectively by neurokinin receptor expressing neurons resulting in enhanced adenylate cyclase activity and neuronal firing.     

A 100 kHz Narrow-Pulse-Width Mid-Infrared Optical Parametric Oscillator Based on PPMgLN Crystal

We report a narrow pulse width optical parametric oscillator based on periodically poled MgO:LiNbO₃ (PPMgLN) with a high repetition rate under quasi-phase matched conditions. When the maximum pumping power of the 1,064-nm laser was 14.57 W, the acousto-optical (A-O) Q-switch repetition rate was 100 kHz, and the PPMgLN crystal grating period was 29.5 μm. A 1,474-nm signal light output power of 4.21 W and a 3,828 nm idler light output power of 1.547 W were obtained, corresponding to a pulse width of 9.52 ns and 9.65 ns, respectively. The overall optical–optical conversion efficiency was 39.5%. Additionally, by changing the temperature from 25°C to 150°C, a tunable signal wavelength of 1,474–1,499 nm and idler wavelength at 3,676–3,828 nm of the output laser were achieved.