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Mathematical Modeling of Abnormal Glutathione Metabolism in Autism
Caley J. Burrus; Michael C. Reed, Ph.D.
Duke University Department of Mathematics
Abstract
Introduction
We have formulated a mathematical disease model for autism based
on the abnormalities commonly found in the metabolic profile for
glutathione in autism. Glutathione is the primary endogenous
antioxidant in the body and is responsible for removing oxygen
radicals in cells. Oxidative stress occurs when oxygen radicals are
present in too high quantities. Intriguingly, research has shown
glutathione to be too low in autism, while oxidative stress is too high
(1). Several other abnormal factors in glutathione metabolism have
been noted in autistic patients, including but not limited to abnormal
glutathione peroxidase activity, high GSSG (oxidized glutathione),
high homocysteine, and high glutamate (3,4). Using these clinically
observed patterns, we altered the model of glutathione metabolism
originally published by Reed and colleagues in 2008 to represent a
disease state of autism (2). There are some limitations of this model.
For instance, the model only looks at a small aspect of this larger
disease state. However, this model does present a reasonable
representation of abnormal glutathione metabolism as is present in a
number of autistic patients.
Autism is a disorder of social interaction which affects nearly 1 in 88
children in the United States. The rates of autism are increasing
dramatically for various reasons, and are up 25% since 2008 alone
(AutismSpeaks, 2012). However, the biological cause of autism is not
yet known. One hypothesis is that autism is a disorder of abnormal
amino acid metabolism. It has been shown that some autistic patients
have abnormal amino acid panels (3). Similarly, glutathione, the
primary endogenous antioxidant present in the body, appears to be
diminished in autism (4). Oxidative stress, the state which occurs
when too many oxygen radicals are present in the cells, occurs
commonly in autism as well (for review, see reference 1). Various
other aspects of glutathione metabolism, including glutathione
peroxidase activity, GSSG levels, and so forth have been shown to be
abnormal in autism. In summary, many of the metabolites in the
glutathione pathway have abnormal concentrations and some of the
enzymes have abnormal activity levels. Thus it is possible to
hypothesize that these abnormal metabolic variables could partly
underlie the biological mechanism of autism.
Glutathione Metabolism Diagram
Model of Glutathione Metabolism
The model was originally formulated by Michael Reed
and colleagues in 2008 to represent normal glutathione
metabolism in the liver. The model itself consists of a
sequence of ordinary differential equations (ODE). Each
equation expresses mass balance, in that the rate of
change of the metabolite is equal to the sum of the rates
by which it is manufactured minus the sum of the rates
by which it is being utilized. The model uses Michaelis
Menten kinetics to describe the velocities of the
enzymatic reactions.
Increased Oxidative Stress in Autism: Graphs
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GSH
10*GSSG
cGlut
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X axis: time (hr)
Y axis: concentration
Decreased Glutathione Peroxidase activity in Autism
Glutathione Peroxidase (GPx) is the enzyme which drives the conversion
of GSH to GSSG to remove oxidative stress in the cell. In this
experiment, we decreased the velocity with which GPx functions,
emulating the decreased GPx activity observed in autism (4). As
expected, GSH increases and GSSG decreases significantly in the cell.
Blood GSH doesn’t change significantly, nor does blood GSSG. Though
not shown here, a decreased activity level of GPx would imply that
oxidative stress is being reduced at a slower rate, meaning more
oxidative stress remains in the cell. This is also consistent with what has
been observed in autistic patients (1).
Decreased GPx activity in Autism: Graphs
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There are many ways in which a working model of errors in glutathione
metabolism in autism could be used. The authors are in the process of
using the model to try to better understand how the Ketogenic Diet (KD), a
controversial yet often effective treatment for epilepsy and autism, works to
improve autistic symptoms. The KD is a high-fat, low carbohydrate diet
used to induce ketosis. The method by which the KD works to reduce
seizures and autistic symptoms is unknown at this time. Since the KD
affects multiple aspects of glutathione metabolism, the model could be
helpful in gleaning new insights into the biological mechanisms underlying
the effects of the diet.
Likewise, a model similar to the one presented here could be useful in
creating a program for practitioners in clinical practice to use to predict
which treatments would be most successful for individual autistic patients.
References
1. Chauchan, A., & Chauchan, V. Review of oxidative stress in autism.
Pathophysiology, 2006, 13:171-181.
2. Reed, M., Thomas, R., Pavisic, J., James, J., Ulrich, C., & Nijhout, HF. A
mathematical model of glutathione metabolism. Theoretical Biology and
Medical Modeling, 2008, 5(8).
Increased Oxidative Stress in Autism
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Although this model represents a good start at creating a working disease
state model of glutathione metabolism in autism, it has some limitations
that must be properly accounted for. For instance, there were conflicting
conclusions in the literature not only regarding specific data values for the
concentrations and activities of the various reagents, but also regarding the
patterns and directions of changes for those reagents. The authors’ best
judgment was used to determine which values should be used, though this
is not a fool-proof method. Additionally, the model does not take into
account all the changes that have been observed in autistic patients. It only
includes those that relate directly to glutathione metabolism and those
found to be most common and replicable in the literature. Finally, it must be
made clear that this model does not represent all aspects of autism. It only
deals with one biochemical system that appears to correlate with the
disorder in some patients. Autism is not a single disorder, but rather a
spectrum of disorders that each likely has its own cause.
Moving Forward: Future Research
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In this experiment, we altered oxidative stress which has
been shown to be higher in autistic patients compared to
controls (1). The graphs on the top of the next column
show that GSH decreases and GSSG increases with
more oxidative stress present. Cellular glutamate also
decreases. However, glutamate in the blood increases
at first, as GSSG transported to the blood is broken
down into cysteine, glycine, and glutamate, the additive
components of glutathione.
Limitations of the Disease State Application
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GSH
100*GSSG
100*bGSSG
20*bGSH
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X axis: time (hr)
Y axis: concentration
3. Shinohe, A., Hashimoto, K., Nakamura, K., Tsujii, M., Iwata, Y., Tsuchiya,
K. et al. Increased serum levels of glutamate in adult patients with autism.
Progress in Neuro-Psychopharmacology & Biological Psychiatry, 2006,
30:1472-1477. doi: 10.1016/j.pnpbp.2006.06.013
4. Sogut, Z., Zorogul, S., Oxyurt, H., Yilmaz, H., Ozugurlu, F., & Silvasi, E.
Changes in nitric oxide levels and antioxidant enzyme activities may have
a role in the pathophysiological mechanisms involved in autism. Clinica
Chimica Acta, 2003, 331:111-117.