GIVE GRAPHICAL MODEL BASED ON GIVEN INFORMATION:   There are three elements in this specific model: Alpha Secretase: This node represents the variable or concept of Alpha Secretase, a proteolytic enzyme that cleaves Beta-Amyloid molecules. Beta-Amyloid Formation: This node represents the variable or concept of Beta-Amyloid Formation, which describes the process of the formation and accumulation of Beta-Amyloid protein in the brain. It is regarded as toxic and contributes to the onset of Alzheimer's disease. Calcium signaling: This node represents the variable or concept of Calcium Signaling, which refers to the cellular process involving the regulation and influx of calcium ions. Alzheimer's disease is known to influence calcium signaling pathways.

GIVE GRAPHICAL MODEL BASED ON GIVEN INFORMATION:  

There are three elements in this specific model:

• Alpha Secretase: This node represents the variable or concept of Alpha Secretase, a proteolytic enzyme that cleaves Beta-Amyloid molecules.
• Beta-Amyloid Formation: This node represents the variable or concept of Beta-Amyloid Formation, which describes the process of the formation and accumulation of Beta-Amyloid protein in the brain. It is regarded as toxic and contributes to the onset of Alzheimer's disease.

• Calcium signaling: This node represents the variable or concept of Calcium Signaling, which refers to the cellular process involving the regulation and influx of calcium ions. Alzheimer's disease is known to influence calcium signaling pathways.

The directed edges in the graph indicate the causal relationships between the variables. The situation:

1. There is a directed edge between Alpha Secretase and Beta-Amyloid Formation, indicating that Alpha Secretase has a direct influence on the formation of beta-amyloid protein. It suggests that the presence and activity of Alpha Secretase may inhibit the development of Beta-Amyloid plaques in the brain.
2. There is a directed edge between Calcium Signaling and Beta-Amyloid Formation, indicating that alterations in Calcium Signaling pathways can impact the formation of beta-amyloid protein. This indicates that calcium signaling dysfunction may contribute to the formation of more beta-amyloid in Alzheimer's disease.

The graphical model gives insight into the relationships between the variables and acquires a better understanding of the potential effects of Alpha Secretase and Calcium Signaling on the progression of Alzheimer's disease. Specifically, this will analyze behaviors that occur during early onset AD. 

Background on Alzhiemer’s Disease 

Alzheimer's Disease (AD) is the most common cause of dementia, as it accounts for 60-80% of all dementia cases [1]. Patients with AD will often undergo memory loss and suffer from impaired cognitive abilities required for daily life  [1]. Over time, this disease will increase in severity. Patients with early stage AD will have mild memory loss but those with late stage AD often lose the ability to communicate and complete daily tasks [1]. AD has no cure and thus it is imperative to find treatments to slow the development of the disease. 

AD is typically characterized by an alteration in the calcium signaling pathways and  increased calcium influx. One of the developments this can cause is the formation and release of ?-amyloid, a protein that is considered toxic as it can disrupt cell function and communication between neurons [2]. ?-amyloid is thought to be toxic as it is chemically “sticky” and when clumped together creates plaques [3]. When groups of ?-amyloid pieces combine, they can block cell-to-cell signalining and lead to problems with brain functions. 

One way to decrease the amount of ?-amyloid in the brain is through ⍺-secretase. ⍺-secretases are proteolytic enzymes that have the ability to cleave ?-amyloid molecules preventing further growth of plaque [3]. Currently, it is known that ⍺-secretase has the ability to prevent ?-amyloid growth however, the molecular mechanisms that regulate ⍺-secretase is only partially known [3]. Currently, there are not many drugs available that can directly impact the growth of ⍺-secretase. For this reason, there is not much research available on this molecule or the relationship between ?-amyloid and ⍺-secretase. 

Problem Statement

It is important to note that this is not the only chemical and neurological change AD patients undergo. However, for the purpose of this model, the focus will be on exploring the varying effect ⍺-secretase has on ?-amyloid. The goal of this model will be to analyze the ?-amyloid pathology and see how change ?-amyloid values will affect alpha secretase production. The model will look at three different variables: Amyloid beta pathology, Neuronal degeneration and cognitive impairment. These variables will be represented via mathematical modeling however will be modified to add in a variable for ⍺-secretase. We can then determine quantitatively how ⍺-secretase will impact  ?-amyloid and the trajectory of neuronal degeneration and cognitive impairment.