Applications of Optimal Control Theory to Immunology

When an animal is challenged by a foreign substance which promotes an immune response, certain cells within the animal begin dividing, secreting antibody molecules, and differentiating into more specialized cell types. Optimal control theory is applied to ascertain the best strategy available to the immune system in allocating its cells. A variety of mathematical models for cell populations and their antibody production are examined and in all cases it is found that the optimal strategy is one of bang-bang control. Experimental evidence which supports such strategies is also discussed.

[1]  P. Russell,et al.  The early antibody-forming response to Salmonella antigens. A study of morphology and kinetics in vivo and in vitro. , 1970, Immunology.

[2]  E. Wecker,et al.  AUTORADIOGRAPHIC STUDIES ON THE PROLIFERATION OF ANTIBODY-PRODUCING CELLS IN VITRO , 1974, The Journal of experimental medicine.

[3]  A. Coutinho,et al.  Continuous Growth of Mitogen‐Reactive B Lymphocytes , 1975 .

[4]  E. Sercarz,et al.  The asynchronous development of immunological memory in helper (T) and precursor (B) cell lines , 1971, European journal of immunology.

[5]  P. Baker,et al.  Characterization of the antibody response to type 3 pneumococcal polysaccharide at the cellular level. II. Studies on the relative rate of antibody synthesis and release by antibody-producing cells. , 1971, Immunology.

[6]  R. May,et al.  Bifurcations and Dynamic Complexity in Simple Ecological Models , 1976, The American Naturalist.

[7]  P. Baker,et al.  Characterization of the antibody response to type 3 pneumococcal polysaccharide at the cellular level. I. Dose-response studies and the effect of prior immunization on the magnitude of the antibody response. , 1971, Immunology.

[8]  P. Baker,et al.  Characterization of the antibody response to type 3 pneumococcal polysaccharide at the cellular level. 3. Studies on the average avidity of the antibody produced by specific plaque-forming cells. , 1971, Journal of immunology.

[9]  S. Avrameas,et al.  The relationship between storage and secretion of specific antibody by immune lymphoid cells: ultrastructural localization of anti‐peroxidase anti bodies in plaque‐forming cells of the rabbit popliteal lymph node , 1976, European journal of immunology.

[10]  H. Cottier,et al.  Cellular bases for relative radioresistance of the antibody-forming system at advanced stages of the secondary response to tetanus toxoid in mice. , 1974, Journal of immunology.

[11]  B MEMORY CELLS IN THE PROPOGATION OF STABLE CLONES OF ANTIBODY FORMING CELLS , 1974 .

[12]  G. Oster,et al.  Competition between phenotypes , 1976, Journal of mathematical biology.

[13]  M. Steward.  Staphylococci and Staphylococcal Infections: Recent Progress , 1975 .

[14]  J. Niederhuber,et al.  Antigenic markers on mouse lymphoid cells: origin of cells mediating immunologic memory. , 1973, Cellular immunology.

[15]  Michael Athans,et al.  Optimal Control , 1966 .

[16]  A. Perelson,et al.  Optimal strategies in immunology , 1978, Journal of mathematical biology.

[17]  A. Perelson,et al.  Optimal strategies in immunology , 1976, Journal of mathematical biology.

[18]  George Leitmann,et al.  A sufficiency theorem for optimal control , 1971 .

[19]  J. Humphrey.  The still unsolved germinal centre mystery (invited lecture). , 1976, Advances in experimental medicine and biology.