Temporal organization in cells; a dynamic theory of cellular control processes

Abstract

All Rights Reserved No part of this book may be reproduced in any form by photostat, microfilm, or any other means, without written permission from the pubhshers Library of Congress Catalog Number: 63-22091 PRINTED IN GREAT BRITAIN BY SPOTTISWOODE, BALLANTYNE AND CO. LTD LONDON AND COLCHESTER University as a post-doctoral fellow. It is a great pleasure for me to express my indebtedness to Professor C. H. Waddington for his encouragement in the pursuit of a theoretical study of biological processes, and for reading and suggesting improvements in the manuscript, I would like also to thank Dr. H. Kacser for discussions which clarified the groundwork of this analysis. In addition I owe a debt of gratitude to friends at the Massachusetts Institute of Technology who read and criticized various parts of the manuscript, especially Karl Kornacker. Finally it is to the National Research Council of Canada that I am deeply indebted for financial assitance in Edinburgh and in Montreal, without whose generosity this study could not have been undertaken.

Two-component feedback loops and deformed mechanics

“…By reviewing the relevant literature it can be confirmed that most (if not all) authors have adopted a model of this form when attempting to fit changes in molecular concentrations to experimental data (see, for example [12,13,14]). In particular, if x 1 is chosen to represent the concentration of an mRNA transcript of protein x 2 , then it is common to assume linear protein expression rates (f 2 (x 1 ) = γx 1 with constant γ) and take f 2 (x 1 ) to be monotonically increasing or decreasing depending on whether x 2 is an activator or repressor, respectively.…”

“…but since the coordinate change is a symmetry of the Hamiltonian 0 = ǫ{H, G} = ǫĠ (12) and therefore G is also conserved. The existence of conserved quantities is useful for qualitative study of complicated isolated systems, but these are rarely present in biological processes operating far from equilibrium.…”

Oscillations in the rate of hemoglobin synthesis in rabbit reticulocytes

“…A mathematical treatment of this model by the techniques of statistical mechanics as outlined by Goodwin [2], predicts oscillatory phenomena in the protein synthesizing system. However, relatively few examples of such a phenomenon have been reported.…”

Analysis of Gene Interactions Using Restricted Boolean Networks and Time-Series Data

“…Friedman introduced Bayesian networks [4] as a probabilistic tool for the identification of regulatory data and showed that they can reproduce certain known regulatory relationships. Among the continuous models we can cite the ordinary differential equations model which was suggested several decades ago [5]. For a more detailed review about models of gene regulatory networks see [6].…”