Mathematical Biosciences 234 (2011) 154–155
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The Thirteenth Bellman Prize
In the 1940s and 1950s, Richard Bellman (1920–1984) developed the method of dynamic programming, which subdivides the task of optimizing a complex problem dynamically into solutions of smaller sub-problems that are easier to manage. At the time, dynamic programming offered an efﬁciency never seen before, and by now it has become a standard technique in applied mathematics and computer science. Bellman also coined the term curse of dimensionality, which continues to be a particular challenge for the mathematical analysis of many biological systems. Later, Bellman devoted his talents to mathematical analyses in biology and medicine and founded the journal Mathematical Biosciences. In his honor, the Bellman Prize was established shortly after Richard Bellman’s death (see Math. Biosc. 77, 1985). This prize is awarded by an independent selection committee to the authors of best paper published in Mathematical Biosciences over a two-year period. This year’s Thirteenth Bellman Prize recognizes the best paper published in 2008–2009. After intense review and discussions, the committee decided to award the Thirteenth Bellman Prize for the article Size distribution dependence of prion aggregates infectivity by Vincent Calvez, Natacha Lenuzza, Dietmar Oelz, Jean-Philippe Deslys, Pascal Laurent, Franck Mouthon, and Benoit Perthame (Mathematical Biosciences 217 (1), pp. 88–99, 2009). A synopsis of the article is presented below.
Fig. 1: Numerical size repartitioning of protein polymers for a normally distributed conversion factor. The x-coordinate indicates the polymer size and the vertical coordinate indicates the number density of polymers with this size. The arrow shows the location of the sharp maximum of the conversion factor. Such a bimodal polymer size distribution has also been reported from experiments in vivo.
Synopsis Abnormal growth and self-replication of protein polymers are processes involved in many neurodegenerative disorders. One such disorder, which constitutes the main focus for our research, is Creutzfeldt-Jakob disease in humans, a brain disorder that is caused by infectious proteins called prions. According to the socalled protein-only hypothesis, a prion may consist of a misfolded protein (called PrPsc for Prion Protein scrapie) that replicates in a self-propagating process, by converting the normal form of a protein into PrPsc. The precise mechanism of conversion is unclear because in vivo observations are very difﬁcult, and a critical challenge of prion biology remains to be the elucidation of this mechanism along with an explanation for the diversity of strains that may exist in the same host, although the same PrP molecule is expressed. Mathematical modeling provides a unique way to investigate possible mechanisms, because it allows us to study the effects of every elementary process during the conversion from PrP to PrPsc in a separate manner, which is difﬁcult to do experimentally. The models we propose are formulated as systems of differential equations for the concentration of normal protein, which are coupled to a Smoluchowski coagulation equation that describes the distribu-
tion of biopolymers according to their size x. In order to take into account recent biological observations, our study uses non-constant lengthening processes, fragmentation and degradation rates. This generality induces considerable difﬁculties for any further mathematical analysis, but we can circumvent them by using a result that is now completed  to show stability characteristics for the ‘infected steady state’. One might note that our theory in the Mathematical Biosciences article has by now also been expanded to include degenerate coefﬁcients , another realistic feature. Collectively, our results conﬁrm the potential inﬂuence of the production rate of amyloid precursor in promoting amyloidogenic diseases. We can now also investigate how the converting factor may depend upon the aggregate size. Besides the conﬁrmation that this size-dependence is important, our study suggests that the bimodal size repartitioning of PrPsc aggregates (Fig. 1) is among the most relevant pieces of experimental information for investigations of this dependence. In terms of prion strains, our results indicate that the PrPsc aggregate repartition could be a constraint during the adaptation to the disease.
Announcement / Mathematical Biosciences 234 (2011) 154–155
Benoit Perthame Laboratoire J.-L. Lions, Université Pierre et Marie Curie and CNRS, Institut Universitaire de France, INRIA Equipe BANG, BC187, 4, place Jussieu, F75252 Paris cedex 05, France
members independently chose papers, ranked them, chose among the top contenders, and ultimately decided on the award-winning article. Eberhard O. Voit Editor-in-Chief Mathematical Biosciences
This year’s Bellman Prize committee consisted of Professors Tatsuya Akutsu (Kyoto University), Helen Byrne (University of Nottingham), Edmund J. Crampin (University of Auckland), Juan B. Gutierrez (Ohio State University), Santiago Schnell (University of Michigan), and Ying Xu (University of Georgia). The committee
 V. Calvez, N. Lenuzza, M. Doumic, J-P. Deslys, F. Mouthon, B. Perthame, Prion dynamics with size dependency-strain phenomena, J. Dynam. Biol. 4 (1) (2010) 28–42.  M. Doumic, P. Gabriel, Eigenelements of a general aggregation-fragmentation model, Math. Models Methods Appl. Sci. 20 (5) (2010) 757–783.