Submitted Papers

In West Nile Virus Survival Curve Models with N. King and A. Kesson Submitted to Epidemics. In this work, a model of the cross-reactive adaptive immune response seen in flavivirus infections is developed. The model specifically addresses flavivirus pathogen virulence in G_0 vs. G_1 cell states. The MHC-I up-regulation of resting cells (G_0 state) allows the {T-cells} generated for flavivirus peptide antigens to attack healthy cells also. The cells in G_1 state are not up-regulated as much and so virus hides in them and hence is propagated upon rupture. Hence, this type of model is referred to as a decoy model because the immune system is decoyed into paying attention to the up-regulated cells while the virus actively propagates in another small, but important, cell population. We show that the generic assumption of up-regulation via a model which includes the G_0/ G_1 differential activation leads to the host survival curve results that have been observed in laboratory data. We achieve this in two ways: first, through a simple back of the envelope calculation that implies the existence of oscillations in the survival curve and second, through a more detailed simulation model. We also derive a first step towards a nonlinear relationship between long term antigen levels and various probabilities of immune and viral interaction that seems promising.

In Theory and Implementation Of Small Brain Models Submitted to IEEE Transactions on Autonomous Mental Development An outline of mechanisms that will allow the creation of small brain models is discussed. We believe from these models, we can derive mixed software and hardware devices to subserve computational cognition devices for field use. Implementation and simulation results will be discussed in later works. This paper addresses several aspects of the challenge of building a small brain model capable of being useful in autonomous mental development. Such a fusion of algorithm development, biological abstraction and software development would have to be fieldable in possibly adverse environments and learn from environmental input in an unsupervised manner. We will argue it is possible to build such a small brain model with useful functionality by abstracting, from the messiness of biological complexity, the essential connection and structural information needed to assemble graphs of computational objects. This is done by developing

a neural object model of the relevant signal transductions

a low dimensional biological feature vector model of the information contained in the action potential of an excitable neuron

modular directed graphs of fundamental information processing blocks such as cortex and thalamus

a graph Laplacian plus hebbian link weight update strategy for associating the high level precepts formed by sensor fusion in the upper columns of cortex with sensor data

novel training data which is emotionally tagged in both the visual and auditory modalities to build emotional attributes into the model

decision architectures

Published Papers

In Abstract Action Potential Models For Toxin Recognition
2006, Journal Of Theoretical Medicine, Vol. 6, No. 4, pp 199 - 234 , coauthored with T. Khan, a robust methodology is presented using mathematical pattern recognition schemes to detect and classify events in action potentials for recognizing toxins in biological cells. The focus is on event detection in action potential via abstraction of information content into a low dimensional feature vector within the constrained computational environment of a biosensor. Generated families of action potentials from a classic Hodgkin - Huxley model are used to verify our methodology and build toxin recognition engines. Good recognition rates are shown to be achievable with our methodology.

In Neural Computational Elements That Subserve Decision Making
2005, Smart Engineering System Design: Neural Networks, Fuzzy Logic, Evolutionary Computation, Swarm Intelligence: Volume 15, Proceedings of the Artificial Neural Networks in Engineering (ANNIE 2005) Conference, November, 2005, ed. C. Dagli, A. Buczak, D. Enke, M. Embrechts, and O. Ersoy, ASME Press, 33 - 42.
In this paper, a very short version of the ideas in the reports Biological Feature Vector Modulation By First and Second Messenger Pathways and Abstract Second Messenger Objects and Excitable Cell Input Integration is presented. A model of bioinformation processing was discussed which consists of three critical components: first, a model of dendritic and soma processing that requires an abstract view of second messenger pathways; second, a detailed algorithm which determines what voltage is presented to the axon hillock of the neuron based upon the first and second messenger influences presented in the inputs and third; a suite of mechanisms which determine the shape of the resulting action potential which the neuron emits. These abstractions have been carefully designed to permit the neuron model to be plastic at both the hardware and software levels.

This had to be formatted into 10 pages with wide margins, so it was very difficult for this exposition to be very complete.

Current Reports

Most of the following reports are being used to write our long document on building cognitive models. This is now in four volumes (delusions of grandeur I am afraid!) which are available at A Primer On Cognitive Modeling.

In Abstract Second Messenger Objects and Excitable Cell Input Integration an abstract view of second messenger signaling is presented for use in models of bioinformation processing. This allows us to develop efficient algorithms to integrate time and spatially tagged information arriving in the dendritic arbor of a neuron. The second messenger information algorithms are part of a larger model which consists of three critical components: first, a model of dendritic processing and soma processing that requires an abstract view of second messenger processing; second, a detailed algorithm which determines what voltage is presented to the axon hillock of the neuron based upon the first and second messenger influences presented in the inputs and third; a suite of mechanisms which determine the shape of the resulting action potential which the neuron emits. These abstractions have been carefully designed to permit the neuron model to be plastic at both the hardware and software levels.

In Biological Feature Vector Modulation By First and Second Messenger Pathways an abstract model of the output of an excitable cell is presented in which a generic Hodgkin - Huxley class action potential is replaced by a low dimensional biologically based feature vector or BFV. The voltage pulse that arrives at the axon hillock of the neuron model must then modulate the BFV output in accordance to first and second messenger effects seen in the neural element's input and cell body regions. Algorithms are derived from first principles for the combination of two BFV's, in a useful biological manner, which are used in input side computations. It is also shown how how first and second messenger inputs can modulate the components of the BFV in efficient manner. These algorithms are therefore part of a model which consists of three critical components: first, a model of dendritic processing and soma processing that requires an abstract view of second messenger processing; second, a detailed algorithm which determines what voltage is presented to the axon hillock of the neuron based upon the first and second messenger influences presented in the inputs and third; a suite of mechanisms which determine the shape of the resulting action potential which the neuron emits. These abstractions have been carefully designed to permit the neuron model to be plastic at both the hardware and software levels. Hence, the design details of their implementation within an asynchronous programming protocol on a variety of computer networks have always been part of the development process.

In An Implementation Of The King - Kesson Flavivirus Decoy Model written with the students of my Spring 2005 MTHSC 974 Modeling Course, Steven Crawford, Alexander Engau, Joseph Johnson, Andreas Tsolakis, Zachary Voller and Leonard Wilkins Jr., a model of the broadly tuned adaptive immune response seen in flavivirus infections is developed. The model specifically addresses flavivirus pathogen virulence based on differential $NF - \kappa B$ mediated MHC-I up-regulation in $G_0$ vs. $G_1$ cell states. The model is agent based, although a mathematical description is also given. The MHC-I up-regulation appears to lead to the development of broadly tuned T-Cells for flavivirus peptide antigens. This broad tuning leads to immune system attacks on healthy cells. Hence, this type of model is referred to as a {\em decoy} model. The up-regulation mechanism may be based on changes in antigen processing within the cytoplasm prior to endoplasmic reticulum assembly of the antigen to the MHC-I molecule. It may also arise from specificity issues due to the way that Langerhans cells process antigen or it may come from other mechanisms. In this paper, it is shown that the generic assumption of up-regulation via a model which includes the $G_0$/ $G_1$ differential activation leads to collateral damage to healthy uninfected cells. However, this paper does not model the specific mechanism by which the up-regulation occurs. The model choices used are discussed very carefully so that the model can be modified as needed by other researchers.

In Spring 2005, I taught a M974 course on advanced mathematical modeling to a small group of 7 students. I covered immunology and west-nile virus infections and agent based modeling. The only output of the class was a paper we all wrote and then submitted for professional feedback. This paper was the one we are discussing here.

The most interesting model of flavivirus infection in my opinion ( one type of flavivirus is the west nile virus) is due to Alison Kesson and Nicholas King. It is a surprising thing that upon infection, flavivirus stimulates a ten fold increase in immune response yet even so, infected young and old people can still die. So there has been great interest in understanding how the increased immune response could somehow hide a potentially fatal overall outcome.

We studied the King - Kesson decoy model to see if we could develop a simulation in MatLab using principles from agent based modeling that would shed insight into this process. I chose this type of modeling effort because it was very cutting edge and used many ideas and tools from disparate fields. I wanted our paper to stimulate the interest of King and Kesson themselves to the point where a door would open to further collaboration. That appears to have happened as detailed below. So I worked very hard with the students in the class to help them learn how to write for an audience of cell biologists and immunologists. We wanted to be clear about our logic but we had to be very careful about how much math we used and how we used it.

In A Primer On West Nile Virus Infection Simulations many of the details on how to build a Qt4.x simulation of a West Nile Virus simulation are discussed in this document. Here, the focus is on survival curves.

In Extension Report: Cognitive Modeling Design for Mixed Decision Making we laid out our first implementation of a general C++ software architecture for modeling with computational objects. We want this to support cognitive modeling research.

In Cognitive Models for Compositional Design in Genetic Algorithms: Data Abstraction with M. Kurz, we present some ideas on how to model absract decision processes using FeedForward network and Genetic Algorithm modeling as examples.

In Data Abstraction In Cognitive Models for Compositional Design in Music with L. Dzuris, we attempt to design abstract data models for emotionally neutral music.

In Data Abstraction In Emotionally Tagged Models for Compositional Design in Music with L. Dzuris, we attempt to design abstract data models for music which has emotional content.

In Data Abstraction In Cognitive Models for Compositional Design in Painting with L. Dzuris, we design abtract data models for paintings which have neutral emotional content. The painting data was developed by my son Quinn.

In Data Abstraction In Emotionally Tagged Models for Compositional Design in Painting with L. Dzuris, we design abstract data models for paintings with emotional labelings. The painting data was developed by my son Quinn.

In Neutral Cognitive Models of Compositional Design we tie the three data models for neutral emotional content into a unified framework and suggest simple neural architectures that might be able to create emotional art and music.

In Cognitive Models of Emotionally Labeled Compositional Design we tie the three data models for emotionally labeled content into one framework and suggest simple neural architectures that might be able to create emotional art and music.

Author: Dr. Peterson, Mathematical and Biological Sciences, Clemson University
Last Updated: December 10, 2008
petersj@clemson.edu