Overview Topics

Interactions of Cells and Chemicals

        The simulation box represents a small region in the brain (roughly 400 by 400 microns in size). Time is scaled by the motion of microglia (green disks) with each time step equivalent to 0.5 minute. Chemical concentrations are calibrated in nM. (See conversions to other units).

        Where possible, rules governing interactions and values of parameters are based on experimental observations described in the scientific literature. (See References). The meanings of parameters is explained below. A simulation in which all these values can be varied is supplied on a separate page.

Summary of interactions

        Initially, small deposits of fibrillar Amyloid-Beta, microglia, and astrocytes are distributed randomly in the domain. An initial stimulus, e.g. a source of soluble Amyloid Beta (red) is located at the center of the region. (In the simulation, it is possible to remove the glial cells, and to reset the level of the stimulus by varying the appropriate parameters, see below. It is also possible to remove the initial stimulus after some period of time.) Microglia are attracted to the stimulus by a process of chemotaxis (motion towards higher concentration of a chemical, in this case, the amyloid). The microglia secrete a diffusible factor, the cytokine IL-1-Beta in response to ingestion of the stimulus. Buildup of IL-1-Beta triggers astrocytes (after some lag phase) which produce the inflammatory chemical, IL-6, which is toxic to neurons. Astrocytes also secrete TNF-Alpha which may protect or further injure the neurons, depending on a user-specified parameter value. The declining health of blocks of neurons (rather than individual cells) is shown by darkening regions. Further, IL-1-Beta uptake by neurons leads to new sources of Amyloid-Beta, and feeds the growth of fibrous deposits.



        Microglia (represented by green disks) sense the surrounding concentration of soluble Amyloid-B and move towards higher levels with sensitivity set by a chemotactic sensitivity parameter. A parameter adjusts their rate of motion ( motility time delay). Their initial number is determined by the (initial microglia count). Microglia stick to any site that has fiber with a probability determined by the half-sticking fiber level. However, this effect is mediated by the amount of soluble amyloid-beta present. The probability decreases so that there is a 50% probability of not sticking to fibers at the half-sticking sAB level. They cannot share a site with an astrocyte or with other microglia in excess of the maximum density.

        Microglia absorb soluble Beta Amyloid protein and degrade it. The maximum rate of uptake is ( maximum sAB microglia uptake rate), and the actual uptake depends on the amyloid concentration according to Michaelis-Menten kinetics with a half max amyloid binding conc. We also assume that the microglia neutralize the stored protein at the chemical breakdown rate. The fatal sol-AB dosage parameter governs the amount of amyloid that a microglia can store.

        Microglia secrete the cytokine IL-1-Beta (See details below) which triggers astrocytes in the region. In this demo, microglia do not reproduce or die. In the more detailed simulation, the option of including both effects is available, and both birth and death are assumed to depend on the chemical milieu.


        Astrocytes (represented by blue discs) are triggered to secrete IL-6 and TNF when the local concentration of IL-1B reaches the astrocyte trigger concentration. The initial astrocyte count determines the total number of astrocytes in the simulation. Birth and death of astrocytes is not included in this demo, but will be an option in the detailed simulation. Parameters affecting secretion include the signal detection level of IL-1-Beta. Currently, we have assumed that Astrocytes can not invade sites that contain fibrous amyloid deposits, microglia, or other astrocytes in excess of a maximum density parameter. Astrocytes remove, store, and eliminate IL-1-Beta with rates governed by adjustable parameters. astrocyte movement and its effects is another aspect of the simulation.


        Neurons are uniformly distributed in the region. This demo represent blocks of neurons, rather than individual cells (Neuron Health Background Display). Levels of grey represent stressed neuronal tissue, and black regions have died. While still alive, neurons absorb IL-1B ( IL-1B absorption rate up to the level maximum IL-1B absorbed). Beyond a threshold of IL-1B (source triggering level), the neuron begins to produce Amyloid Beta. This shows up as a new source of Amyloid (red square). Neurons also absorb IL-6 (IL-6 absorption rate) a toxic cytokine. Death of a neuronal block occurs when a fatal IL-6 concentration has accumulated in that block. Neurons also absorb TNFi (TNF absorption rate) up to the level maximum TNF absorbed. TNF protects neurons through positive values for the TNF efficacy for health parameter. When this parameter is zero, TNF does not affect neuron health. However, when the parameter is negative, TNF becomes a detriment to neuron health.

        Neuron health depends on the amount of IL-6 stored in a neuron and is modified by the amount of TNF in the same neuron. Overall neuron health, which is shown in the graph, is the percentage of neurons that are healthy. 100% overall neuron health means that all neurons are healthy, while 0% overall neuron health means that all neurons are dead. Thus, as neurons begin to absorb IL-6, the overall neuron health begins to decline.

        We currently formulate overall neuron health as follows. If s is the amount of IL-6 stored in a neuron and f is the amount of IL-6 fatal to a neuron, then neuron health due to IL-6 is c = [1 - (s/f)]. This is then modified by TNF. If p is the amount of TNF stored in a neuron, m is the maximum amount of TNF that a neuron can store, and e is the TNF efficacy for health, then TNF health factor is d = [1 + e(p/m)]. Neuron health is calculated by taking the product of the neuron health due to IL-6 and the TNF health factor so that h = (c)(d) = [1 - (s/f)][1 + e(p/m)] with bounds between 0 and 1. The overall neuron health is the average of all single neuron healths. Thus, if h(i) is the health of neuron i and there are n neurons, then the overall neuron health is calculated as

Birth and Death


        If Cell Death is turned on, then cells can either die because of old age or because they absorbed a lethal amount of amyloid protein. The lethal amount of protein can be adjusted with the fatal sol-AB dosage parameter. Old age is determined stochastically with the mean age defined by the typical cell duration parameter.


        If Cell Mitosis is turned on, then cells can split to produce a daughter cell. The daughter cell begins with half the absorbed protein of the parent cell and age equal to 0. Cell mitosis depends on four criteria:

  1. time to reproduce determined by the length of cell cycle parameter.
  2. they have not absorbed so much protein that they are sick determined by the poison effects on mitosis parameter.
  3. the chance of mitosis is great enough.
  4. there is room for another cell as defined by the maximum density and the maximum number of cells (which is set at 1000).
If all four criteria are satisfied, then mitosis occurs.


Amyloid Protein

Soluble Form

        Shades of magenta represent the level of soluble Amyloid-Beta. (Select Soluble Amyloid-B display option). The source concentration parameter represents the maximum level of amyloid produced at the sources (depicted as red squares), and amyloid diffusivity governs the rate of diffusion of amyloid.

Fibrillar Form

        Orange dots represent fibrous amyloid deposits. (Denser dots depict greater concentrations.) The number of initial "seed" deposits is adjusted by a parameter called the initial fiber occupancy.

        New fibers grow from the seeds at a rate that depends jointly on the local concentrations of the two forms by mass-action kinetics. Fibers may not grow until a critical level of soluble amyloid-beta (which we call the critical sol-AB for fibers) is present. The presence of an astrocyte currently prevents fibers from forming at a given site.


        Microglia secrete IL-1-Beta ( IL-1B secretion rate parameter) once their stored a level of Amyloid-B exceeds a triggering concentration. IL-1-Beta diffuses at a rate equal to the IL-1B diffusivity parameter. Selecting the IL-1B Background Display reveals the IL-1B concentration in shades of cyan.


        Astrocytes secrete IL-6 ( IL-6 secretion rate parameter) when they have stored a level of IL-1B that surpasses the triggering concentration. IL-6 diffuses at a rate equal to the IL-6 diffusivity parameter. Selecting the IL-6 Background Display reveals the IL-6 concentration in shades of yellow.


        Astrocytes secrete TNF ( TNF secretion rate parameter) when they have stored a level of IL-1B that surpasses the triggering concentration. TNF diffuses at a rate equal to the TNF diffusivity parameter. Selecting the TNF Background Display reveals the TNF concentration in shades of pink.

The above relations are similar to this Flow Chart.

Concluding Remarks

        The current demo and simulation is meant to describe some of the potential for simulations at the level of blocks of tens (to several hundreds) of cells, interacting chemicals, and neuronal death. The simulation is an ongoing project, in which assumptions, parameter values, and many other details are being explored, updated, and changed. We are currently in the stage of collecting further values of parameters from published biological literature.

Return to Simulation Description.