2014 Summer Undergraduate REU Program
The body regulates specific calcium levels in the blood since calcium plays an important role in many processes in the body. There are mechanisms in the body that maintains this specific level of calcium in the blood. If calcium is too low, then the parathyroid gland releases a parathyroid hormone (PTH) that acts to increase blood calcium level. It acts on the bone by causing resorption, the process by which the body breaks down bone so that calcium is released into the bloodstream. It also acts on the kidney by decreasing the amount of calcium loss in the urine as well as enhances the production of calcitriol which causes absorption of calcium from the intestine into the bloodstream. If the calcium levels are too high, calcitonin lowers blood calcium levels by counteracting PTH. In 2002, Raposo et al. developed a model of calcium homeostatis. This model, yet interesting, appears to have a plethora of underlying parameters which suggests that it could fit a variety of data. In 2010, Peterson et al. modified and expanded the model by including intracellular control mechanism to PTH and bone remodeling. Bone remodeling is the process that remedies cracks in the bone by first having bone removed by osteoclasts and then followed by the reformation of the bone matrix via osteoblasts.
A mathematical model can provide evidence of abnormal states such as the presence of cancer or renal disease. In a cancer state, tumors have shown to produce a parathyroid hormone-related protein (PTHrP) that acts like PTH but is not regulated by the calcium homeostasis system. In the renal disease state, there is a decrease in calcitriol production which leads to a decrease in the body's to absorb calcium. It is important to understand this system as well as disease states as bone health is vital to one's survival. This research project involves developing a mathematical model of calcium homeostasis with a minimal amount of differential equations that captures the qualitative features of the system. With this model, we will describe the effects of various disease states on the system and investigate how certain drugs can affect the system.
Schizophrenia is a chronic psychiatric disorder that has different origins and where different factors such as socio-environmental, developmental, neurophysiological, chemical (drugs), interact and participate in the onset of crises or "psychotic break". It is characterized by cognitive impairments like memory and attention correlated with a decrease of activity in the gamma band (in EEG and LFPs) and psychotic symptoms such as hallucinations and delusions (delusions are defined as "fixed false ideas about the world, often paranoid in content, but may also involve convictions of being controlled by a power outside of oneself".
These symptoms are notably correlated with high levels of dopamine in the striatum and the hippocampus and a reduced NMDA receptor function (N-methyl-D-aspartate acid) in cortical networks. The latter observations led to a computational model proposed by Edmund Rolls. This model is an integrate-and-fire attractor network; the key argument explaining abnormal activity of the network in schizophrenia is that the stability of his attractors is modified by reduced NMDA, and GABA neurotransmissions. These results thus mainly concern synaptic transmission. In addition to impaired synaptic neurotransmission, dysfunctional behavior of neocortical fast-spiking (FS) interneurons may also contribute to the etiology of schizophrenia. Dr. Kevin Jones' preliminary data suggests that the time it takes a fast-spiking interneuron to elicit an action potential after reaching threshold (known as the "spike latency") varies widely among FS interneurons of control mice. However, in his pharmacological model of schizophrenia, FS interneurons from experimental mice exhibited reduced average spike latency, and reduced variance in spike latency. Moreover, he discovered that FS interneurons from "schizophrenic" mice also were lacking a stimulus-insensitive latency period of approximately 2 ms, which was consistent in control mice. This abnormal spiking behavior appears to be intrinsic to the neurons (i.e., not due to synaptic inputs) and due to the presence of Kv1.1-containing potassium channels. These channels would lower the firing threshold, making the neurons fire earlier than expected in "normal" FS neurons. These specific dysfunctions in the cellular function of FS interneurons could interfere with the generation of gamma oscillations and other features of network synchronization that are known to be impaired in schizophrenia patients.
This research project examines the effect of alterations in spike latency of FS neurons in network dynamic models. Coupled with Dr. Jones' data and Dr. Washington's modeling expertise, a better model will be developed so that the details of the FS interneurons can be better understood.