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Mathematical Modeling of Abnormal Glutathione Metabolism in AutismCaley J. Burrus; Michael C. Reed, Ph.D.

Duke University Department of Mathematics

Abstract

Increased Oxidative Stress in Autism

Decreased Glutathione Peroxidase activity in Autism

Moving Forward: Future Research

References

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.

Introduction

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.

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.

Glutathione Metabolism Diagram

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 ApplicationAlthough 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.

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.

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).

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.

Increased Oxidative Stress in Autism: Graphs

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

X axis: time (hr)Y axis: concentration

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GSH

100*GSSG100*bGSSG

20*bGSH

X axis: time (hr) Y axis: concentration

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GSH

10*GSSGcGlut

90*bGlut