INFORMATION CONTENT OF TRACER DATA 

 WITH RESPECT TO STEADY-STATE SYSTEMS* 



MoNES Berman and Robert L. Schoenfeld 



Division of Biophysics, Sloan-Kettering Institute, New York 



Abstract — A method for the quantification of information in data from tracer experiments 

 on steady-state systems is presented. It is shown that if the system is represented by n com- 

 partments a point in an n^ dimensional space can serve to represent a specific model. Further- 

 more, uncertainty about the system due to statistical fluctuations and incomplete data can be 

 represented by regions in the n"^ dimensional hyperspace. A unit of information for such a 

 system is defined and serves as a measure of the amount of information necessary to determine 

 the system to within a desired accuracy. 



In order to express the data in terms of the generalized n^ dimensional space, a set of 

 invariants is defined for the data. A concise matrix relation is shown to exist between the 

 invariants of the data and the parameters that characterize the compartmental system. The 

 matrix relation allows mappings between the data and the system. 



The method presented is applicable to any compartmentalized system that shows linear 

 kinetics. 



I. INTRODUCTION 



This paper is concerned with the quantification of information contained 

 in data from tracer experiments performed on steady-state biological systems. 

 In general, the same set of data may be analysed in terms of different systems 

 of various degrees of complexity. To define the information content of the 

 data, therefore, it is necessary to specify the system in terms of which the data 

 are to be analysed. 



It can be assumed for many tracer experiments that the system! consists 

 of a discrete number of compartments (or pools) each representing a locali- 

 zation or chemical state of the labeled material, with exchange of molecules 

 between compartments. The rate of exchange of the unlabeled molecules 

 between compartments is in general a non-linear function of the amounts of 

 material in the compartments. If, however, the system is in a steady state and 

 the amount of the tracer is sufficiently small compared to its unlabeled isotope, 

 the rate of exchange of the tracer may be treated as a linear function of the 

 amounts of labeled material in the compartments (1). 



The problems that arise in treating the data of tracer experiments are: 

 first, to define the information content in the data, and second, to translate 

 the information in the data into values of the system parameters (the turn-over 

 rates of the compartments). In addition, it is desirable to have a measure of 



* This work was supported in part by the U.S. Atomic Energy Commission Grant 

 AT(30-1)-910. 



t For this paper, the word 'system' will be used to mean a specific number of compartments 

 independently of how they are interconnected. The word 'model' will refer to a specific 

 configuration of the system. 



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