Modeling of ThioS staining deposits and neuron interactions

To clarify the biophysical nature of the radial density function we obtained for ThiosS staining deposit (dependence on size, density, and $\beta$-pleated sheet conformation of $A\beta$), we investigate the effect of the growth of a dense object (ThioS positive $A\beta$ deposit) on adjacent neurons by using a molecular dynamics algorithm to simulate manu-body interactions. We explored two plausible physical mechanisms for the decreased neuronal density within ThioS staining deposit: (i) compact $A\beta$ behaves as a non-toxic space-occupying mass lesion, that simply pushes neurons away, or (ii) compact $A\beta$ kills neurons as it grows, engulfing surrounding neuronal cell bodies. We devised a numerical simulation that calculates the many-body interactions of $A\beta$ deposits as either non-toxic or toxic spherical objects, immersed in a sea of smaller spheres representing neurons. The simulation follows the standard Molecular Dynamics (MD) algorithm [34] typically used to simulate many-body interactions in physics. The MD algorithm consists of determining the speed and direction of motion of particles based on the total force that results on them. In our case we assume that the rate of growth of the $A\beta$ is so slow that we only need to consider the direction of motion of the surrounding model neurons. In Fig. 7 we show two typical configurations generated by a non-toxic (a) and non-toxic (b) mass lesion mechanisms.

In order to be able to compare simulations to the experimental data, we use for the simulations the same ThioS staining deposit size distribution as in Fig. 4. In Fig. 7(c) we show the radial density function for the model assuming a non-toxic mass lesion. Within $30\mu m$ of this type of $A\beta$ deposit, there are two peaks of increased neuronal density; corresponding to the nearest and next-nearest neurons that surround the $A\beta$ deposit. The increased value of this peak as compared to the average radial density beyond $30\mu m$ indicates the increased density of neurons that have been pushed and compressed together in the periphery of the deposit. In Fig 7(d) we show the radial density function for the model assuming a toxic mass lesion. The radial density function is entirely flat, indicating an undisturbed neuronal neighborhood just outside the periphery of the deposit. The radial density function in Fig 7(d) remarkably approximates the radial density function for ThioS staining deposit shown in Fig. 6, implying that ThioS staining deposits behave as toxic mass lesions without penumbra, rather than non-toxic mass lesions.