Peter C. Greif

Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design

We define two levels of parameters. The basic parameters are associated with the model and experiment(s). However, the observations define a set of identifiable observational parameters that are functions of the basic parameters. Starting with this formulation, we show that an implicit function approach provides a common basis for examining local identifiability and estimability and gives a lead-in to the problem of optimal sampling design. A least squares approach based on a large but finite set of observations generated at initial parameter estimates then gives a uniform approach to local identifiability, estimability, and the generation of an optimal sampling schedule.

Balancing Needs, Efficiency, and Functionality in the Provision of Modeling Software: A Perspective of the NIH WinSAAM Project

The development of new software or the refinement of existing software for new operating environments each calls for judicious balancing. On the one hand, we strive for simplicity, predictability, and operational protection as it is well recognized that software with these attributes will attract an audience of satisfied users. But, on the other hand, these attributes do not conjure a sense of power, efficiency, or flexibility, and these other properties are also appreciated by users, albeit a somewhat different group of users. The goal is to achieve a blend which isolates critical functionality, flexible control, and user support while meeting the needs of the broadest collection of serious users. In this chapter, we discuss the issues impacting the migration of SAAM to the Windows environment, the NIH WinSAAM Project, and we outline the steps taken to ensure its feasibility. In addition, we describe a new paradigm for software development and use which ensures the durability of the software for modeling.

Computer analysis and structure prediction of nucleic acids and proteins.

We have developed an integrated computer system for analysis of nucleic acid and protein sequences, which consists of sequence and structure databases, a relational database, and software for structural analysis. The system is potentially applicable to a number of problems in structural biology including predictive classification of the function and location of oncogene products.

Cornerstones to Shape Modeling for the 21st Century: Introducing the AKA-Glucose Project

In this paper, we have reflected on the historical development during the twentieth century of several major cornerstones on which the edifice of mathematical modeling in nutrition and the health sciences was built. When we consider the scope and magnitude of problems in nutrition and the health sciences that have been addressed and solved by mathematical modeling, we as a group can justifiably feel a certain amount of satisfaction. But we should not be complacent. So much more remains to be done. The increasing pace of developments in biology (e.g., the human genome project) places a whole new range of challenges before us. We can also reflect on the mathematical basis of modeling and consider that we enter the twenty-first century with a solid foundation on which to build bigger and better models. At the same time, we have at our disposal computers of immense power. At the start of the twentieth century, no one could have foreseen where we are today. In our lifetimes, computers have been developed from lumbering behemoths with the calculating ability of an abacus to the present day machines with calculating capabilitie that we are only beginning to appreciate. There is general consensus that developments in the field of computing will continue far into the twenty-first century. Therefore, w can confidently assert that developments in modeling will not be greatly limited by our present mathematical foundation or by the capabilities of computers. In this paper, we have mainly dwelt on three cornerstones: the model development environment model dissemination and database technologies data exchange and post-fitting analysis. We have focused on SAAM, WinSAAM, and AKA-Glucose as illustrating these cornerstones, while acknowledging that there are many other modeling programs that also represent them. However, a building usually has four cornerstones. If one cornerstone is missing, then there may be a structural weakness in the entire building. We contend that, at the start of the twenty-first century, the edifice of modeling is missing the important fourth cornerstone: a modeling community. As modelers, we should cease to bowl alone. Now is the time to make a new beginning, to give modeling some formality, structure, and direction. We should form a community of modelers as we move into the 21st century.

Berman’s Simulation Analysis and Modeling

Dr. Mones Berman, whose photograph appears at the beginning of this section, had an enduring interest in the theoretical aspects of lipid, lipoprotein and apolipoprotein metabolism, which stemmed from a more general interest in the systematic analysis of the kinetics and dynamics of metabolic molecules in the biological system. When tracer molecules are used to observe and measure the kinetics of a substance of interest, the obser vations are frequently related to a specific biological models for complete analysis. Possible models should be restricted to those that are compatible with other information about the system. Dr. Berman spent his life developing a formalism for the systematic analysis of tracer data taken from dynamical biological systems in both the steady and changing state.

WinSAAM: application and explanation of use.

The WinSAAM modeling software is an integrated package of mathematical, simula-tion, and graphical tools for analysis of biokinetic data. WinSAAM is the Windows version of SAAM, the Simulation, Analysis, and Modeling computer program. SAAM, a collection of scientific subroutines, was created in the 1950s by Dr. Mones Berman to meet the mathematical needs of his research program. Over the decades, SAAM has been continually developed and enhanced (Berman and Weiss, 1978; Boston et al., 1981), and today, WinSAAM is an elegant and powerful tool for mathematical and compartmental modeling.

Nonrandom recurrence of consecutive repeats in noncoding mammalian sequences

Abstract Short, tandemly arranged repetitive sequences are a frequently encountered phenomenon in a variety of genomes. These sequences are thought to play an important role in regulation, genome organization, and recombination events. Analysis of GenBank sequences reveals that in noncoding mammalian sequences the numbers of tandem repeats are larger than statistical expectation. In contrast, noncoding bacterial sequences do not show this trend.