Math 152 - Spring 2005

References Cited for Lectures

January 12, 2005 lecture: Intro to Calculus

A detailed predictive model of the mammalian circadian clock
by Daniel B. Forger and Charles S. Peskin
Full paper as a PDF file - December 9, 2003 PNAS 100: 14806-14811

Comments: The detailed mechanisms by which cells within mammals are coordinated to have the same 24 hour clock (the circadian clock) are quite complex. This involves a very large number of interacting enzymes and proteins. The authors develop a mathematical model that describes these complex interactions, using a collection of differential equations. These equations describe the rates at which different reactions occur as a function of the concentrations of the various proteins.

January 19, 2005 lecture: Continuity and Limits

Age-specific incidence of inherited versus sporadic cancers: A test of the multistage theory of carcinogenesis
by Steven A. Frank
Full paper as a PDF file - January 18, 2005 PNAS 102: 1071-1075

Comments: The author presents a simple mathematical model to compare the rate of onset of two different types of cancer - colon cancer which is quit prevalent, and a quite rare retinal cancer - as dependent upon age. Most common cancers have an incidence which increases as a function of age according to a 5-6 power of age, while childhood onset cancers decrease in incidence with age. The multistage theory of cancer assumes that there are stages that individuals go through in the progression to cancer. The author provides a an argument that simple mathematical models can provide more insight in analysis of complex problems such as cancer development than more elaborate models.

January 24, 2005 lecture: Intro to Derivatives

Human Population: The Next Half Century
by Joel E. Cohen
Full paper as a PDF file - 14 Nov 2003 Science 302:1172-1175

Comments: This paper reviews the history of human population on our planet focusing on the dynamics of the size of the population as well as its growth rates. The author points out how rapidly the human population has been growing, at an increasing rate. Thus the doubling time of the population has changed from 50 years in 1927 to 25 years in 1974. What is greatly significant is that the yearly population growth rate has declined over the past 3 decades from 2.1% to 1.2%, associated with a large reduction in the fertility rate (from over 5 to less than 3 children per woman per lifespan). The author uses mathematical models to project the changes in population structure (age) through the next 50 years.

January 26, 2005 lecture: Derivatives as Instantaneous rates of change

Ed Karrels Bike Races
Background on his races and A particular race with info on speed, heart rate, altitude and power used

January 31, 2005 lecture: Metabolic Rates, Obesity and Exercise

Interindividual Variation in Posture Allocation: Possible Role in Human Obesity
by James A. Levine, Lorraine M. Lanningham-Foster, Shelly K. McCrady, Alisa C. Krizan, Leslie R. Olson, Paul H. Kane, Michael D. Jensen, and Matthew M. Clark
Full paper as a PDF file - 28 Jan 2005 Science 307:584-586

Commentary and background on this is: PHYSIOLOGY: A NEAT Way to Control Weight?
by Eric Ravussin
as a PDF file - 28 Jan 2005 Science 307:530-531

Comments: This paper analyzes differences between lean and mildly obese "couch potato" individuals by following detailed aspects of their body movements over several days. The obese individuals were seated an average of 2 hours more per day than lean individuals. These observations were repeated by increasing food intake in some of the lean individuals and decreasing food intake in some of the obese individuals. These changes in diet had no effect on the individual's posture activity - e.g. NEAT (non-exercise activity theormogenesis) seems to be biologically determined. The Commentary by Ravussin considers these results relative to propensity to "fidget" and the impact on population health.

February2, 2005 lecture: Derivatives and epidemics

Host immunity and synchronized epidemics of syphilis across the United States
Full paper as a PDF file - Nature 433, 417 - 421 (27 January 2005)

Commentary and background on this is: Sexually transmitted diseases: Epidemic cycling and immunity
as a PDF file - Nature 433, 366 - 367 (27 January 2005)

Comments: This paper compares the dynamics of two STD's (syphilis and gonorrhoea) to evaluate the impact of environmental and behavioral factors in the transmission and growth of epidemics of the diseases as compared to factors inherent in the interactions between host and pa]thogen. Using mathematical models using derivatives for susceptibel and removed and infected individuals, they determine that syphilis does not depend as much on environmental factors in driving epidemics as gonorrhoea. They then go on to discuss spatial aspects of these diseases, pointing out that distance is not a good measure of mixing and therefore transmission rates.

February 7, 2005 lecture: Applications of derivatives

Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae
Full paper as a PDF file - Nature 433, 425 - 430 (27 January 2005)

Comments: This paper develops a model of the complex biochemical pathway for the metabolism of a lipid in yeast, using derivatives for the rates of change of the various chemical components of the pathway. The kinetics (that is the dynamics) of the various components of the pathway can now be experimentally evaluated, and the authors did this using Maple (the same software we are using in class) to estimate the parameters of the various kinetic pathways. The model is used to generate hypotheses about the system which offers potential new approaches to metabolomics (the study of metabolism as affected by biochemistry and genetics).

February 16, 2005 lecture: Rates of change

Abrupt rise in atmospheric CO2 overestimates community response in a model plant-soil system
Full paper as a PDF file - Nature 433, 621-624 (10 February 2005)

Comments: Derivatives are rates of change. This paper discusses the responses of an ecological system (a community of fungi) to an abrubt change in CO2 content of the air (as is done in many experiments) corresponding to a very high derivative of CO2 with respoect to time, to a very gradual increase in CO2 corresponding to a small positive derivative of CO2 with respect to time. They compare the sam overall increase by looking at change in species richness (how many species are present) and note that a gradual increase in CO2 leads to similar results to no change, as contrasted with an abrupt change in CO2. They caution against interpreting experiments with abrupt changes as representing true system response. For an example of experiments in large ecosystems with long-term CO2 increases having been kept for long periods, see ORNL FACE experiment

February 28, 2005 lecture: Optimization and evolution

Heritability and genetic constraints of life-history trait evolution in preindustrial humans
by Jenni E. Pettay, Loeske E. B. Kruuk, Jukka Jokela, and Virpi Lummaa
Full paper as a PDF file - Proc. Natl. Acad. Sci. USA. 2005; 102(8): p. 2838-2843 (22 February 2005)

Comments: This paper discusses the heritability and changes in certain life-history traits in a population of pre-industrial Finns (late 1700's to 1900). They point out the high heritability of certain life history traiots (fecundity, age at last reproduction, etc.) and certain fittness measures (lifetime reproductive success) for females. This does not occur for males. They found strong genetic correlations with certain life history traits (e.g. age a first reproduction and longevity). To do all this, they used a large geneological database from which they could compile pedigrees over 4 generations. They interpret their results in terms of the evolution of human life-history traits.

April 4, 2005 lecture: Work and Integrals

SYSTEMS BIOLOGY: Tracing Life's Circuitry
by Elizabeth Pennisi
Full paper as a PDF file - 5 Dec 2003 Science 302: 1646-1649

Comments: This news article described the new area of systems biology as an approach for linking mathematics, engineering and biology to address questions such as how networks of cells function. As I mentioned in class, one of the simplest models for cell cycling is similar in form to the mathematics of oscillations of the springs we discussed. Indeed, the simple harmonic oscillator (a spring without damping) is a basic model for much of rhythmic behavior in biology. The idea of systems biology is to link together models for biology at several hierarchical levels (within cells, cells, tissues, whole organisms) and attempt to determine the properties of the whole from the parts (a general goal in science from a reductionist perspective).

April 6, 2005 lecture: Density Functions and Oceanography

Two UT EEB Faculty manage large numbers of oceanography studies for the National Science Foundation in the Arctic Lee Cooper and Jacqueline Grebmeier and detailed information about their projects is at Arctic BIO UTK site
The types of data they organize expeditions (on ships) to collect are an expanded version of the type we discuss in this section of the course - distributions of the density of various marine organisms and chemical compounds as a function of depth and location in the ocean. For examples of these types of data, see Biological Atlas of the Arctic Seas and in particular for an example of the type of data similar to what we discuss in class, see Characteristics of Phytoplankton of the Barent's Sea

April 18, 2005 lecture: Differential equations for growth - tumor volume

Tumor Response to Radiotherapy Regulated by Endothelial Cell Apoptosis
by Monica Garcia-Barros, Francois Paris, Carlos Cordon-Cardo, David Lyden, Shahin Rafii, Adriana Haimovitz-Friedman, Zvi Fuks, and Richard Kolesnick
Full paper as a PDF file - 16 May 2003 Science 300:1155-1157

Comments: This article investigates the effect of radiation treatment, similar to that applied to treat many cancers, on various aspects of tumor growth. They particularly emphasize microvasculature and the effect of diffeernt cancer cell types on tumor growth.

Return to Math 152 Home Page

Return to L. Gross Home Page