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WANG--CAN WE ACHIEVE A UNIFIED MODEL OF ALZHEIMER DISEASE?
1
Can We Achieve a Unified Model of
Alzheimer Disease?
Applications of Systems Biology
Rosalie H.L. Wang

Abstract—This paper discusses the current knowledge in
Alzheimer Disease (AD) research, and discusses the systems
biology approach applied in its study, with specific reference to
some of the mathematical models developed for specific aspects of
the disease process. The benefits of achieving a unified model of
AD and the potential challenges of such an endeavor are discussed
to demonstrate that systems biology is an ideal approach for
understanding the disease and finding means to prevent and
reverse the condition.
Index Terms—Alzheimer Disease, Amyloid, Mathematical
Model, Systems Biology
I. INTRODUCTION
I
t is projected that by 2011, 314 000 Canadians over the age
of 65 will have a diagnosis of Alzheimer Disease (AD) [1].
Because AD leads to a progressive decline in function, or
inability to care for oneself, it is a condition that affects not
only the individual, but also family, friends, and healthcare
resources due to the need for ongoing and increasing care and
support during the course of the disease. Although there is an
early onset form of the disease, the majority of those
diagnosed are over the age of 65. Since it is primarily a disease
of older adults, it is expected that the number of new cases will
rise significantly as the population of baby boomers age. As a
result, there is a strong impetus to find ways to prevent and
reverse the condition.
Much research has been done to date from a biological
perspective, looking at the components and molecular
pathways that lead to the onset and/or progression of the
disease. More recently, however, the need to integrate the
complex data on disease development, or pathogenesis, a
systems biology approach has been adopted by many
researchers. The systems biology approach aims to integrate
the knowledge acquired thus far on the components and
pathways related to the AD system, and incorporate this
knowledge into a workable mathematical model that can be
used to study the relationships of the components, further
refine the model, and make predictions and test hypotheses
about the disease system. Many models have already been
developed based on current knowledge of AD. These models,
however, are not complete by any means and depict only very
specific aspects of the disease process. To date, formation of a
comprehensive theory of disease onset and progression
summarized in one mathematical model, or a unified model of
AD, has not yet been possible. The benefits of such a model
and the inherent difficulties related to its development are
discussed with a view to answering the question – can we
achieve a unified model of AD?
II.
WHAT IS AD?
AD is a degenerative disorder of the brain that causes a
gradual decline in function. This functional decline manifests
as impairments in gross and fine movements, coordination,
balance, and changes in walking patterns; decreases in sensory
awareness, and registration and processing of information;
increases in forgetfulness and disorientation, difficulty with
learning, a loss of abstract thinking, personality changes; and a
decrease in the overall ability to care for oneself. The age of
onset is usually over 45 years, and the likelihood of having AD
increases after the age of 65. The onset is insidious, that is,
symptoms are subtle, slowly progressing, and do not come to
attention until clear clinical signs are evident. The duration of
the disease is typically 8 to 20 years [1]. The current treatment
for the disease is limited to temporarily decreasing symptoms
while maintaining function. Many novel treatments aimed at
the prevention and reversal of the disease are currently being
investigated [2]-[5].
III.
CHARACTERISTICS OF THE AD BRAIN
The primary disease markers of AD are extracellular amyloid (A) plaques, which are deposits composed of the A
protein; and intracellular neurofibrillary tangles (NFTs)
composed of tau, a cytoskeleton protein inside neurons [6].
The plaques and tangles are found primarily in the areas of the
brain involved in learning, memory, and emotions such as the
entorhinal cortex, hippocampus, basal forebrain and amygdala
[3]. These two markers have been studied extensively, and are
known to be present in other disease conditions; however, they
have a specific distribution and density in AD pathology [6].
Other characteristic changes associated with the AD brain
include: neuron and synapse loss, altered nutritional supply for
neuronal processes, formation of neuropil threads (densely
interwoven cytoplasmic processes of neurons and support
cells); other cytoskeleton changes (loss of microtubules in
affected neurons, and changes in normal microtubule
WANG--CAN WE ACHIEVE A UNIFIED MODEL OF ALZHEIMER DISEASE?
architecture) [6]. Typically, the sizes of the temporal and
frontal lobes of the brain are significantly reduced due to
neuron and synapse loss [3].
IV. RISK FACTORS
There are a few distinct known risk factors for AD. Genetic
risk factors include: family history of AD or other related
illness, mutations in the amyloid precursor protein (APP) on
chromosome 21, that may affect formation and breakdown of
A; mutations in Presenilin 1 (on chromosome 14) and
Presenilin 2 (on chromosome 1) that possibly form the secretase enzyme complex; carriage of the ε4 form of the
Apolipoprotein E gene (on chromosome 19), and Down’s
Syndrome [6]. Known environmental risk factors have also
been identified, one being a history of traumatic brain injury,
which is linked to a predisposition to AD [6].
There are also less well established risk factors currently
being investigated. Epidemiological studies and studies of
animal models have suggested increased risks with low
cognitively stimulating environments, lack of physical
exercise, and high calorie diets that contain cholesterol and
saturated fats [3]. There is also suggestion that a higher risk is
observed in individuals with abnormalities in glucose
regulation [3].
V.
CURRENT HYPOTHESES ON PATHOGENESIS
Although there was much debate concerning the
development of AD in regards to the roles of A plaques and
NFTs (i.e. which is the cause, which came first, are they
related and if so, how are they related), the dominating
hypothesis is that A is the primary causal agent in the onset
and/or progression of the disease [4]-[6]. It has been identified
that A, particularly the A42 form, is most likely to
spontaneously convert to an insoluble form and aggregate to
form plaques [6], and to be toxic to neurons [3]-[6]. A is
generated by the cleavage of APP by enzymes named  and secretases [4], [5]. But because -secretase is not specific, it
can produce proteins of varying lengths [4]. A toxicity has
been suggested to manifest in multiple ways, as shown in
Table 1.
TABLE I
POSTULATED TOXIC EFFECTS OF A ON NEURONS
Block of the response of one of the nicotinic acetylcholine receptors
[3]
Production of oxygen free radicals that lead to apoptosis of neurons via
oxidative stress [3]-[5]
Aggregation inherently toxic to cells, activating the inflammatory
response involving microglia and release of cytokines and more free
radicals [3]-[5]
Damage of neurons by disrupting membrane calcium pumps or by
forming channels in membranes leading to Ca2+ disregulation in cells
[3], [4]
Promotion of excess phosphorylation and oxidative changes in tau
protein leading to disassociation from microtubules and aggregation to
NFTs [3]
Aggregation of A protein may lead to dysfunction of ion and glucose
transporters at synapses, and impairs synaptic plasticity [3]
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Other contributors to the pathway to development of AD
include the Presenilins, likely parts of the -secretase enzyme
that form A. Evidence shows that mutations in Presenilins
increase the likelihood of producing toxic forms of A [4].
Apolipoprotein E appears to be involved although the pathway
is still unclear [4]. Changes in metabolism of cholesterol may
lead to changes in membrane fluidity and signal transduction
leading to neuronal degeneration [3].
VI.
REVIEW OF MODELS
Mathematical models have been developed depicting
specific pathways in the pathogenesis of AD. Many of these
models focus on the dynamics related to the production of A
fibrils, the solubility and folding of A fibrils, assembly or
aggregation of fibrils into plaques [2], possible mechanisms
related to neurotoxicity, and the inflammatory response to A.
Some models are aimed at monitoring changes in A levels
during treatment [2]. Studies showing the different areas of
mathematical modeling are described.
A. Model of A Aggregation
Reference [7] developed a quantitative model to describe the
kinetics of A fibril growth from the unfolded state. Their
model used differential and algebraic equations to describe the
A self-association kinetics pathway. The researchers used the
presumption that spontaneous A conversion from a soluble to
an insoluble folded form is related to the development of AD.
The parameters of the model were determined by experimental
data fitting. The strengths of this model included:
incorporation of physiological data (mass distribution and
fibril length changes, and multiple fibril forms–monomer,
dimer, and aggregated forms), and the comprehensiveness of
the description of A kinetics to include formation and
aggregation of amyloid fibrils. They suggested that their model
may help to develop compounds that discourage
Aaggregation, fibril growth, and toxicity.
B. Model of A Neurotoxicity
A study by [8] modeled one possible mechanism of the
neurotoxic effects of A. The researchers hypothesized that
A binds to closed ion channels and prevent them from
opening. They demonstrated using a mathematical model that
A blockage of the fast inactivating K+ channel can disrupt
intracellular Ca2+ homeostasis, causing a large influx, and
thereby increasing the excitability of the neuron membrane.
They modeled the dynamics of Ca2+ inside the hippocampal
neuron, looking specifically at the intracellular concentration
of Ca2+. Their mathematical model described the hippocampal
neuron in terms of elementary reactions and diffusions. The
modeled results matched those in the literature of in vitro
studies of neurons exposed to A. The researchers were able
to quantify the dependence of neuron response and level of
increase in intracellular Ca2+ on concentrations of Ca2+. Their
model included the features of normal neuronal function and
enabled them to examine the effects of A on Ca2+
concentration and neuron excitability.
WANG--CAN WE ACHIEVE A UNIFIED MODEL OF ALZHEIMER DISEASE?
C. Chemotaxis Model of Microglia
The basis of a mathematical model described by [9] related
to the nature and function of microglia. Microglia are nonneuronal cells in the brain that are part of the inflammatory
response in AD pathology. Microglia in the brain tend to
associate with A plaques, and show chemotaxis. Chemotaxis
is a property of some cells and describes the moving towards
or away in response to chemicals. Microglia respond to the
accumulation of A by multiplying and moving
chemotactically towards plaques and injured neurons, and
produce inflammatory chemicals such as cytokines. The study
described and modeled the chemotaxic response of microglia
and the signaling chemicals leading to local aggregation of
microglia and the buildup of chemicals detected in A
plaques. The results indicated that the model simulations of the
temporal formation of aggregates do not coincide with
observed data, although the predicted spatial (spacing)
formations compared with the data observed.
D. Model of A Burden
Reference [2] developed a mathematical model that can be
used to monitor the A total burden, or level, in the brain,
cerebrospinal fluid (CSF), and plasma of individuals with AD.
Their study was motivated by the need to find a biomarker to
enable ongoing monitoring of the effects of new treatments.
The model that was developed described A accumulation in
the brain, CSF, and plasma using “an infinite system of
nonlinear ordinary differential equations” that examined the
A kinetics in the three compartments [2]. They suggested that
the model may be used to derive parameter approximations for
transport, production and clearance of A. Formulae for the
steady state levels of A in the three compartments before and
after treatment were given. The authors found that CSF and
plasma levels of A gave reliable and indirect measures of the
A level in the brain, but not of the total A burden.
VII. WHY THE QUEST FOR A UNIFIED MODEL OF AD?
Research to date has demonstrated that the causes of AD are
complex and multi-factorial, involving genetic and
environmental factors. The onset and progression of the
disease result from interactions between multiple biological
components in numerous pathways. Therefore to adequately
study AD, a holistic systems biology approach is the only
foreseeable course. As mentioned, a systems biology approach
has already been applied by researchers, and models of very
specific aspects of the pathogenesis of AD have been
developed. However, researchers have not been able to
propose a unified model of AD. This is undoubtedly a
challenging endeavor, but there are many advantages to such a
model.
A. New Insights
A unified model of AD means having a complete account of
the pathogenesis. It will give an account of the causal links,
possible weak points in the system, and the temporal
progression of AD. A complete account of AD is necessary
because relationships and interacting components may not be
readily visible, and an integrated model system will help to
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expose unexpected relationships or reveal new insights [10].
As such, it will be possible to look at causal agents previously
lacking in recognized connection to the disease [11].
We will also be able to better understand why disease
presentation is different for different individuals, or why
disruption in the same pathway produces clinically different
disease manifestations. We will be able to identify and
understand individual responses to treatments and see why
some individuals respond well to one treatment and not others
[11].
Currently, the stimulus for cognitive decline is unknown [4],
but with a unified model, we will be able to identify the trigger
through model simulations. More and more genes are now
implicated in the pathogenesis of the disease [4], [5], and with
a unified model, we will be able to predict and simulate how
these genes interact with other factors to cause AD.
There is surmounting evidence that there are similarities in
the molecular pathways and events that cause many of the
chronic progressive neurodegenerative disorders including
AD, Parkinson’s Disease, and Amyotrophic Lateral Sclerosis
[12]. Therefore, any knowledge gained from the development
and application of a unified model of AD will help in the
understanding of other neurodegenerative conditions.
B. Hypothesis Generation and Testing
An integrated model using a systems biology approach will
allow for quick generation and testing of high quality
hypotheses [13]. With a complete mathematical model one
will envision a multitude of potential system perturbations that
can be evaluated at the simulation level and then tested in the
actual biological system [14].
C. Disease Prevention
It is becoming clear that AD pathogenesis occurs well before
symptoms are evident, and prevention of the development of
AD will be the ideal form of therapy [4], [5]. A unified model
will help predict and prevent dysfunction at the cellular level
and prevent disease from occurring through genetic testing and
examination of environmental risk factors. A complete model
will enable identification of the deficits leading to disease,
such as genetic mutations, and enable intervention early on to
prevent the onset of the disease. Currently with the
development of preventative drug therapies, complications
arise as we are unable to predict who will get the disease, and
hence, it is difficult to test the safety of drugs on humans [4]. If
humans are used, these studies are very difficult and costly due
to the number of subjects required [4]. Therefore, a complete
model where we are able to simulate the effects of drugs will
assist greatly in the prevention of the disease.
D. Disease Treatment
For individuals who already have the disease, a complete
model of the pathogenesis will enable us to understand the
underlying biological principles of the system during normal
and diseased states, and develop more effective and
efficacious treatment since we will be able to intervene at key
pathway nodes that will correct or modify the underlying
problems [10]. This offers a more rational approach to the
design of treatments and will enable more thorough and
WANG--CAN WE ACHIEVE A UNIFIED MODEL OF ALZHEIMER DISEASE?
comprehensive descriptions of the mechanisms of action. With
a unified model, it will be possible to foresee adverse effects
of treatments and allow problem solving using simulations
before testing on animal models or humans. The targeted
treatments developed using a unified model will eliminate the
possibility of interactions with normal biological function of
the components and pathways involved.
Increasingly evident is that AD therapy will involve
intervention at multiple nodes, or combination therapies [12].
Given this, to establish the most effective combinations of
therapies for different individuals, a unified model will be
essential. It is likely that treatment will involve combinations
of simultaneous treatments to: lower the A burden (e.g.
secretase inhibitors, cholesterol lowering drugs, aggregation
inhibitors, and A vaccines), decrease oxidative stress (e.g.
antioxidants and ion chelators), decrease the inflammatory
response (e.g. anti-inflammatory drugs), and block
excitotoxicity to regulate neurotransmission (e.g. Ca2+ channel
blockers), among other possibilities [4], [5], [12].
VIII. FUTURE DIRECTIONS
Information on the parts and pathways, and system models
describing the onset and/or progression of AD has increased
immensely, and many plausible hypotheses are being
investigated. However, there is still much to be done, such as
in the area of technology development. Currently, there are
limits in the availability of biomarkers to adequately monitor
disease onset, progression and treatment effects [2], [4]. There
is a deficit in the technology we have to measure events at the
cellular level both simultaneously and quantitatively [13].
There are difficulties with measurement of responses of cells
in 3D tissues and with the simultaneous measurement of
several parameters at one time [13]. There is still much work
to be done in the development of better systems models that
are more representative of the actual biological pathways and
interactions. Also, once we have all the mathematical models
to describe each module in the pathogenesis of AD, the
challenge of actually combining the models to form one
unified testable equation will have to be dealt with. Therefore,
adequate databases and computational tools to store, integrate
and process data are still required.
As already alluded to, many novel drugs and treatments are
currently being investigated. Because they at various stages of
pre-clinical trials, including computational and animal
modeling, and trials in humans a definitive treatment regime
remains to be established. Some treatments, such as
immunization with A-antibodies have been effective in
animal models but unsatisfactory in the early stages of human
clinical trials, indicating that the mechanisms of action in
hypothesized treatments are not yet fully understood [3], [13].
However, the process of finding a unified model is not
counterproductive, if anything, informs in the process of
finding a “cure”. With the more advanced application of
systems biology described here, one hopes that a more
comprehensive model with inherently logical properties will
lead to a better process to assist in the understanding of AD
through simulations and enable sound predictions to be made.
For some, finding a unified model will be a sincere quest, for
others it will serve as a reminder of the big picture in which
the numerous components and pathways of the disease are all a
part. In summary, achieving a unified model of AD is highly
possible as the motivation is high and benefits are numerous,
and in keeping with the momentum in which systems biology
is being applied to disease research and treatment, both a
unified model and a “cure” will eventually be found.
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IX. CONCLUSION
It is questionable whether we really need a unified model in
order to completely understand AD and prevent or reverse the
disease. The direction of research and drug and treatment trials
currently underway can arguably be sufficient. The quest for a
unified model can easily be dismissed as too abstract.
4
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