Neurons<title></head> <body bgcolor=#ffffff> <h2><font color=#118811>Neurons</font></h2> <p> Unlike microglia and astrocytes, neurons cannot move. The current formulation assumes that there is a neuron in every grid space. Earlier formulations assumed that multiple grid spaces lead to what was called a <i>neuron block</i> which is simply a population of neurons over some rectangular block of grid spaces. The computer code for this approach has not been deleted, but neither has it been updated. <p> The major functions of neurons in the simulation are to absorb IL-1B, IL-6 and TNF, secrete soluble amyloid, and change health. <p> At initialization, the neuron located in the grid space in the center of the <a href=index.html#space>environment</a> begins with a concentration of IL-1B equal to the average of the <b>maximum IL-1B absorbed</b> parameter and the <b>source triggering level</b> parameter. In this manner, the center grid space will always be a source of soluble protein. This allows the feedback loop to begin and result in a meaningful simulation. <br> <h3><a name=neurAbs><font color=#CC8811>Absorption of IL-1B, IL-6 and TNF</font></a></h3> <p> Absorption of IL-1B, IL-6 and TNF are all handled by the <a href=cells.html#reckin>receptor kinetics</a> described above. Therefore, for each chemical that is to be absorbed, there are corresponding user controlled parameters associated with them: the <b>chemical receptor equilibrium constant</b> is <i>k<sub>d</sub></i>, the <b>chemical receptor unbinding rate</b> is <i>k<sub>b</sub></i> and the number of <b>chemical receptors per neuron</b> is converted (<i>via</i> a programmer defined conversion constant and volume) into a concentration <i>r</i>. In order for absorption to occur, there must be sufficient concentration of chemical in the same grid space as the neuron. If <i>S</i> is the concentration of chemical (be it IL-1B, IL-6 or TNF) in the grid space, then <i>S/k<sub>d</sub></i> must be greater than one for absorption of the corresponding chemical to take place. If <i>S</i> is sufficiently large, then the change in concentration, <i>DS</i> can be calculated on the <a href=index.html#time>macro time scale</a> with time increment, <i>DT</i>, based on numerically solving the differential equation. Using a simple Euler method, we find that <br> <center><i>DS = DT*(k<sub>b</sub>*r/2)*(S/k<sub>d</sub> - 1).</i> </center> <i>DS</i> is calculated for each chemical (IL-1B, IL-6 and TNF). The concentrations for each chemical are then updated such that the concentrations of the chemicals in the grid space are reduced and the concentrations within the neuron are increased by the appropriate <i>DS</i>. <p> Special consideration is given when the chemical reaches the neuron's capacity to store it. The neuron will never absorb more chemical than it can hold. The limit for IL-1B is given by the <b>maximum IL-1B absorbed</b> parameter. The limit for IL-6 is given by the <b>fatal IL-6 concentration</b> parameter. The limit for TNF is given by the <b>maximum TNF absorbed</b> parameter. In the case where <i>DS</i> exceeds the room available to the chemical, <i>DS</i> is decreased to take the remaining room. <p> In the unlikely case that <i>DS</i> exceeds <i>S</i> (the concentration of chemical that is present in the grid space), <i>DS</i> is changed so that it equals <i>S</i>. This is just a check to make sure that no negative concentrations of chemicals result from the absorption process. This makes sense both biologically and mathematically. <br> <h3><a name=neurSec><font color=#CC8811>Secretion of Soluble Amyloid</font></a></h3> <p> Neurons act as sources for soluble amyloid protein based on the amount of IL-1B they have absorbed. In order for a neuron to become a source of soluble amyloid, the concentration of IL-1B that it has absorbed must exceed the <b>source triggering level</b> parameter. At the time at which this occurs, a final test is done to see if it actually becomes a source based on the <b>maximum proportion of neuron sources</b> parameter, <i>m</i>. This "test" is done in a Monte Carlo fashion where a uniformly distributed random variable between 0 and 1 is generated. If its value is less than <i>m</i>, the "test" is passed and the neuron becomes a source of soluble amyloid. Because, IL-1B is not reduced within the neuron, this "test" is only done once and will determine whether the neuron will be a source for the duration of the simulation. Of course, neuron death causes any sources of soluble amyloid to die with the neuron. <p> For details on the amounts of soluble amyloid secreted, see <a href=chemicals.html#amyloid>Amyloid Protein</a> under <a href=chemicals.html>Chemicals</a>. <br> <h3><a name=Health><font color=#CC8811>Health</font></a></h3> <p> Neuron health is computed as a function based on the concentration of chemicals within the neuron. Health varies between <i>0</i> and <i>1</i>. A value of <i>0</i> for health indicates death. A value of <i>1</i> indicates that the neuron is in perfect health. <p> The health, <i>H<sub>A</sub></i>, of a neuron due to a chemical, <i>A</i>, is based on the concentration of that chemical within the cell, <i>s<sub>A</sub></i>, <b>its effects on health</b>, <i>e<sub>A</sub></i>, and the neuron's capacity for the chemical, <i>c<sub>A</sub></i> such that <br> <center><i> H<sub>A</sub> = (1 + e<sub>A</sub> s<sub>A</sub>/c<sub>A</sub>). </i></center> The following table relates the user defined parameters with the appropriate chemicals and variables found in the formula above: <br><br> <center><table cellpadding=5 border=1> <tr> <td align=CENTER> <i>A</i> <td align=CENTER> <i>c<sub>A</sub></i> <td align=CENTER> <i>e<sub>A</sub></i> </tr> <tr> <td align=CENTER> IL-1B <td align=CENTER> <b>maximum IL-1B absorbed</b> <td align=CENTER> <b>IL-1B effects on health</b> </tr> <tr> <td align=CENTER> IL-6 <td align=CENTER> <b>fatal IL-6 concentration</b> <td align=CENTER> <b>IL-6 effects on health</b> </tr> <tr> <td align=CENTER> TNF <td align=CENTER> <b>maximum TNF absorbed</b> <td align=CENTER> <b>TNF effects on health</b> </tr> </table></center> <br> The <b>effects on health</b> parameter can vary between <i>-1</i> and <i>9</i>. It is easy to see that if <i>e<sub>A</sub></i> equals <i>-1</i>, then death can occur (it is the only situation that allows H to go to zero), while other negative values for <i>e<sub>A</sub></i> are detrimental to health. If <i>e<sub>A</sub></i> equals <i>0</i>, then the chemical does not affect health, while positive values indicate that the chemical is beneficial to health. <p> The health, <i>H</i>, of a neuron based on all the chemicals it can absorb is defined as the product of all the healths due to each chemical. Currently, <br> <center><i> H = (H<sub>IL-1B</sub>) (H<sub>IL-6</sub>) (H<sub>TNF</sub>). </i></center> <i>H</i> can never exceed <i>1</i> so that if the above calculation is greater than <i>1</i>, then <i>H</i> is automatically set to <i>1</i>. Averaging the healths of all the neurons gives one the <i>overall neuron health</i>. Thus, if <i>h(i)</i> is the health of neuron <i>i</i> and there are <i>n</i> neurons, then the overall neuron health is simply <br> <center><img src=summation.gif></center> <br><br> <hr><br> Return to <a href=../describe/index.html>flow chart</a> </body> </html>