International audienceAnother conception that makes applications of mathematics quite different from applications of mathematics to sole biology resides in the interventionist nature of medicine ..

Clairambault, Jean

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Perspective on "New and Less New Opportunities For Mathematical Biology as Applied To Biological and Clinical Medicine"

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HAL Id: hal-01108995https://hal.inria.fr/hal-01108995Submitted on 27 Jan 2015HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Distributed under a Creative Commons Attribution| 4.0 International LicensePerspective on ”New and Less New Opportunities ForMathematical Biology as Applied To Biological andClinical Medicine”Jean ClairambaultTo cite this version:Jean Clairambault. Perspective on ”New and Less New Opportunities For Mathematical Biology asApplied To Biological and Clinical Medicine”. Society for Mathematical Biology Newsletter, Societyof Mathematical Biology, 2014, SMB Newsletter, 27 (2), pp.2. ￿hal-01108995￿Perspective on "New and Less New Opportunities For Mathematical Biologyas Applied To Biological and Clinical Medicine"by JEAN CLAIRAMBAULTAnother conception that makes applications of mathematics quite different from applications ofmathematics to sole biology resides in the interventionist nature of medicine ...This perspective, bouncing from Philip Maini’s"Perspective on The Changing Face of Mathematical Bi-ology" 1, focuses on the specific case of mathematicsas applied to medicine. Philip Maini acknowledgesthe pioneering work of James D. Murray in Oxford:for sure, this immense founding enterprise with noequivalent worldwide has led, through his stimulat-ing teaching and research, to the training of scoresof students, from pure to very applied mathemati-cians, many of whom have themselves become lead-ing scientists in different fields of mathematical bi-ology.In other parts of the world, such pioneers werescarce, but little by little, by the virtue of example,scientists coming either from the engineering worldor from pure and applied mathematics learnt toknow that non-trivial mathematics had been writtenby some of them, starting from open biology ques-tions, often by transposing methods from physicsor chemistry. For instance, reaction-diffusion equa-tions have been studied as providing a theoreticalbasis for traveling waves of physical phenomena byKolmogorov, Petrovsky and Piskunov and indepen-dently by Fisher (for the spread of a gene in a pop-ulation), all in 1937, and later a basis for morpho-genesis by Turing in 1952. However, James Murrayreports (Mathematical Biology 3rd ed., vol. 1, 13.2)that the first discovery of the so-called KPP-Fisherequation is due to the German chemist Luther in1906, but also that his publication soon sank intooblivion, to be rediscovered later, much later than1937. The scientific audience likely was not ripethen to catch the scope of this discovery and itspotential applications to biology, even though Fick(1855) in the same country had already presentedhis law of diffusion 50 years earlier. The now clas-sical examples of Hodgkin-Huxley (1952) and laterFitzHugh-Nagumo models of action potential prop-agation (1961, 1962) or Turing instability (1952)came later, on apparently more favorable ground.What had changed? Maybe the fact that biolog-ical phenomena that were until then considered asjust being there - the propagation of nerve impulseor the spots on a leopard - were investigated by ad-vanced scientists - physicists or mathematicians - ashaving in fact a physical basis and hence a mathe-matical expression. Maybe in about the same way asin the Greek antiquity, presocratic philosophers andthe mathematicians among them tried to organizea corpus of pre-existing observations (in particularfrom Babylon and Egypt) according to rules, someof which could be shown to be more than rules.The situation in which we are now is indeedsomewhat different. In a world where scientists ofdifferent disciplines regularly meet in conferencesand workshops, and publish jointly in journals inwhich attention is given to both mathematical mod-eling and experimental results, it is less likely thatbreakthrough discoveries may be lost. Furthermore,centers for mathematical biology, and as regardsoncology, centers for integrated research on can-cer (essentially in the US for the latter) now ex-ist and offer institutional opportunities to exchangeknowledge between disciplines, including mathe-matics and clinical medicine. In the UK, the Mathe-matics in Medicine Study Group (MMSG) organizesmeetings in different locations to model and tackleduring 2-3 days problems coming from requests bybiologists or physicians. Even in places where suchinstitutions are not yet present, grants coming frominternational and national calls more and more al-low constituting coherent teams of applied mathe-maticians working in close contact with teams of bi-ologists and - less frequently - physicians.As Philip Maini stresses, data coming from bi-ological experiments are most often static, i.e.,snapshot-like, when we need movie-like data toidentify the dynamics of the biological systems un-der study. Furthermore, a frequent and simplifyingunderlying assumption is that tissues are homoge-1http://www.smb.org/publications/newsletter/vol27no1.pdfSMB Newsletter, MAY 2014, Volume 27, No 2Page 14neous, genetically and phenotypically, when for in-stance multilocular samples in the same tumor showthat this is frequently not the case, at least in can-cer. In biological and medical research teams, peopleare keen on identifying intracellular signaling path-ways - or cell membrane targets upstream of them- searching for so-called “druggable targets" to blockor enhance them. But the dynamic viewpoint thatmathematicians are fond of "where does this lead to?i.e., what is the asymptotic behavior of the system,controlled or not?", is seldom present. However, sucha dynamic perspective has always been present inthe mind of biologists dealing with evolution, andrecently - remembering that, as stated by Theodo-sius Dobzhansky in 1973, “Nothing in biology makessense except in the light of evolution” - it has also be-come clear at least for some cancer biologists. Someindeed consider cancer as an evolutionary disease,in the sense that cell populations evolve, partly withprescribed rules, partly due to random events andpartly under the influence of tissue environmentalfactors, towards diseased states as populations ofmulticellular organisms do. In my opinion, this viewis about to deeply change our conception of diseases,and in particular of cancer.Another conception that makes applications ofmathematics quite different from applications ofmathematics to sole biology resides in the interven-tionist nature of medicine, that is absolutely irre-ducible to an applicative branch of biology. Whereasthe physicist describes the evolution with time ofnatural phenomena, and in particular of diseases,the physician is expected to correct them or preventthem, otherwise said to control them. This leads tothe idea, not only to apply optimization and opti-mal control principles to therapeutics, but also todesign models of health and disease in tissues andorganisms as dynamical systems under physiologi-cal control mechanisms that can be corrected whenthey fail. In this respect, firstly it is necessary to rein-troduce physiology at the era of genetics at all levelswhere physiological regulations occur: intracellulargene regulatory networks, equilibria between com-peting populations of cells, whole body hormonalregulations, and also between these levels; and sec-ondly, setting such physiological controls and thecorrection of their disruptions as optimization prob-lems (physiologically solved or to be solved by thera-peutic intervention) should foster much more workbetween physicians and mathematicians specialistsof optimal control. This is another opportunity thatI see for the future, and it will make all the moresense as the biological control mechanisms will bemore known. Even if they are not known in detail toperform quantitative predictions, qualitative resultsabout optimized therapeutic strategies to combinedrugs should prove helpful to clinicians.Of course, the continuous progress of imagerytechniques, at all possible biological levels of ob-servation, from intracellular signaling pathways towhole-body recordings, in a more and more dy-namic way, i.e. with space and time resolutions thatare driving us from a scenery of poorly defined snap-shots to another one of high precision movies, willnever exclude the fact that important variables ofthe dynamic systems under study will remain hid-den. This naturally calls for other new mathematicaldevelopments, which resort to statistical theory andto inverse problem methods.Such perspectives, some of them rather recent,together with a growing open-mindedness of biol-ogists and physicians towards mathematics opennew tracks to follow for the growing number ofmathematicians interested in doing "mathematics formedicine". There are hard problems - and less hardones - to solve, that will be a source of inspirationfor mathematicians and a help to physicians - be itonly to provide new ways to ask questions - providedthat the initial question is of biological and medicalnature, transposable in mathematical settings, andthat a collaborative work is performed interactivelybetween members of the two disciplines towardsadvances in solving them.About The Author:Dr. Jean Clairambault, PhD, MD,trained - in that order - in mathe-matics and medicine, is presentlya senior scientist (“directeur derecherche”) at INRIA and Labora-toire Jacques-Louis Lions, Pierreet Marie Curie University in Paris.His current research interests arethe emergence of drug resis-tance in cancer and the evolu-tion from premalignant cell populations to tu-mors, together with therapeutic optimization meth-ods using combined drug delivery strategies toovercome such evolutions at the cell populationlevel. Website: http://www.rocq.inria.fr/bang/JC/Jean_Clairambault_en.html.SMB Newsletter, MAY 2014, Volume 27, No 2Page 15

Hal-Diderot

Perspective on ”New and Less New Opportunities For
Mathematical Biology as Applied To Biological and
Clinical Medicine”
Jean Clairambault
To cite this version:
Jean Clairambault. Perspective on ”New and Less New Opportunities For Mathemati-
cal Biology as Applied To Biological and Clinical Medicine”. Society of Mathematical Bi-
ology Newsletter, Society of Mathematical Biology, 2014, SMB Newsletter, 27 (2), pp.2.
<http://www.smb.org/publications/newsletter.shtml>. <hal-01108995>
HAL Id: hal-01108995
https://hal.inria.fr/hal-01108995
Submitted on 27 Jan 2015
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destine´e au de´poˆt et a` la diffusion de documents
scientifiques de niveau recherche, publie´s ou non,
e´manant des e´tablissements d’enseignement et de
recherche franc¸ais ou e´trangers, des laboratoires
publics ou prive´s.
Distributed under a Creative Commons Attribution 4.0 International License
Perspective on "New and Less New Opportunities For Mathematical Biology
as Applied To Biological and Clinical Medicine"
by JEAN CLAIRAMBAULT
Another conception that makes applications of mathematics quite different from applications of
mathematics to sole biology resides in the interventionist nature of medicine ...
This perspective, bouncing from Philip Maini’s
"Perspective on The Changing Face of Mathematical Bi-
ology" 1, focuses on the specific case of mathematics
as applied to medicine. Philip Maini acknowledges
the pioneering work of James D. Murray in Oxford:
for sure, this immense founding enterprise with no
equivalent worldwide has led, through his stimulat-
ing teaching and research, to the training of scores
of students, from pure to very applied mathemati-
cians, many of whom have themselves become lead-
ing scientists in different fields of mathematical bi-
ology.
In other parts of the world, such pioneers were
scarce, but little by little, by the virtue of example,
scientists coming either from the engineering world
or from pure and applied mathematics learnt to
know that non-trivial mathematics had been written
by some of them, starting from open biology ques-
tions, often by transposing methods from physics
or chemistry. For instance, reaction-diffusion equa-
tions have been studied as providing a theoretical
basis for traveling waves of physical phenomena by
Kolmogorov, Petrovsky and Piskunov and indepen-
dently by Fisher (for the spread of a gene in a pop-
ulation), all in 1937, and later a basis for morpho-
genesis by Turing in 1952. However, James Murray
reports (Mathematical Biology 3rd ed., vol. 1, 13.2)
that the first discovery of the so-called KPP-Fisher
equation is due to the German chemist Luther in
1906, but also that his publication soon sank into
oblivion, to be rediscovered later, much later than
1937. The scientific audience likely was not ripe
then to catch the scope of this discovery and its
potential applications to biology, even though Fick
(1855) in the same country had already presented
his law of diffusion 50 years earlier. The now clas-
sical examples of Hodgkin-Huxley (1952) and later
FitzHugh-Nagumo models of action potential prop-
agation (1961, 1962) or Turing instability (1952)
came later, on apparently more favorable ground.
What had changed? Maybe the fact that biolog-
ical phenomena that were until then considered as
just being there - the propagation of nerve impulse
or the spots on a leopard - were investigated by ad-
vanced scientists - physicists or mathematicians - as
having in fact a physical basis and hence a mathe-
matical expression. Maybe in about the same way as
in the Greek antiquity, presocratic philosophers and
the mathematicians among them tried to organize
a corpus of pre-existing observations (in particular
from Babylon and Egypt) according to rules, some
of which could be shown to be more than rules.
The situation in which we are now is indeed
somewhat different. In a world where scientists of
different disciplines regularly meet in conferences
and workshops, and publish jointly in journals in
which attention is given to both mathematical mod-
eling and experimental results, it is less likely that
breakthrough discoveries may be lost. Furthermore,
centers for mathematical biology, and as regards
oncology, centers for integrated research on can-
cer (essentially in the US for the latter) now ex-
ist and offer institutional opportunities to exchange
knowledge between disciplines, including mathe-
matics and clinical medicine. In the UK, the Mathe-
matics in Medicine Study Group (MMSG) organizes
meetings in different locations to model and tackle
during 2-3 days problems coming from requests by
biologists or physicians. Even in places where such
institutions are not yet present, grants coming from
international and national calls more and more al-
low constituting coherent teams of applied mathe-
maticians working in close contact with teams of bi-
ologists and - less frequently - physicians.
As Philip Maini stresses, data coming from bi-
ological experiments are most often static, i.e.,
snapshot-like, when we need movie-like data to
identify the dynamics of the biological systems un-
der study. Furthermore, a frequent and simplifying
underlying assumption is that tissues are homoge-
1http://www.smb.org/publications/newsletter/vol27no1.pdf
SMB Newsletter, MAY 2014, Volume 27, No 2
Page 14
neous, genetically and phenotypically, when for in-
stance multilocular samples in the same tumor show
that this is frequently not the case, at least in can-
cer. In biological and medical research teams, people
are keen on identifying intracellular signaling path-
ways - or cell membrane targets upstream of them
- searching for so-called “druggable targets" to block
or enhance them. But the dynamic viewpoint that
mathematicians are fond of "where does this lead to?
i.e., what is the asymptotic behavior of the system,
controlled or not?", is seldom present. However, such
a dynamic perspective has always been present in
the mind of biologists dealing with evolution, and
recently - remembering that, as stated by Theodo-
sius Dobzhansky in 1973, “Nothing in biology makes
sense except in the light of evolution” - it has also be-
come clear at least for some cancer biologists. Some
indeed consider cancer as an evolutionary disease,
in the sense that cell populations evolve, partly with
prescribed rules, partly due to random events and
partly under the influence of tissue environmental
factors, towards diseased states as populations of
multicellular organisms do. In my opinion, this view
is about to deeply change our conception of diseases,
and in particular of cancer.
Another conception that makes applications of
mathematics quite different from applications of
mathematics to sole biology resides in the interven-
tionist nature of medicine, that is absolutely irre-
ducible to an applicative branch of biology. Whereas
the physicist describes the evolution with time of
natural phenomena, and in particular of diseases,
the physician is expected to correct them or prevent
them, otherwise said to control them. This leads to
the idea, not only to apply optimization and opti-
mal control principles to therapeutics, but also to
design models of health and disease in tissues and
organisms as dynamical systems under physiologi-
cal control mechanisms that can be corrected when
they fail. In this respect, firstly it is necessary to rein-
troduce physiology at the era of genetics at all levels
where physiological regulations occur: intracellular
gene regulatory networks, equilibria between com-
peting populations of cells, whole body hormonal
regulations, and also between these levels; and sec-
ondly, setting such physiological controls and the
correction of their disruptions as optimization prob-
lems (physiologically solved or to be solved by thera-
peutic intervention) should foster much more work
between physicians and mathematicians specialists
of optimal control. This is another opportunity that
I see for the future, and it will make all the more
sense as the biological control mechanisms will be
more known. Even if they are not known in detail to
perform quantitative predictions, qualitative results
about optimized therapeutic strategies to combine
drugs should prove helpful to clinicians.
Of course, the continuous progress of imagery
techniques, at all possible biological levels of ob-
servation, from intracellular signaling pathways to
whole-body recordings, in a more and more dy-
namic way, i.e. with space and time resolutions that
are driving us from a scenery of poorly defined snap-
shots to another one of high precision movies, will
never exclude the fact that important variables of
the dynamic systems under study will remain hid-
den. This naturally calls for other new mathematical
developments, which resort to statistical theory and
to inverse problem methods.
Such perspectives, some of them rather recent,
together with a growing open-mindedness of biol-
ogists and physicians towards mathematics open
new tracks to follow for the growing number of
mathematicians interested in doing "mathematics for
medicine". There are hard problems - and less hard
ones - to solve, that will be a source of inspiration
for mathematicians and a help to physicians - be it
only to provide new ways to ask questions - provided
that the initial question is of biological and medical
nature, transposable in mathematical settings, and
that a collaborative work is performed interactively
between members of the two disciplines towards
advances in solving them.
About The Author:
Dr. Jean Clairambault, PhD, MD,
trained - in that order - in mathe-
matics and medicine, is presently
a senior scientist (“directeur de
recherche”) at INRIA and Labora-
toire Jacques-Louis Lions, Pierre
et Marie Curie University in Paris.
His current research interests are
the emergence of drug resis-
tance in cancer and the evolu-
tion from premalignant cell populations to tu-
mors, together with therapeutic optimization meth-
ods using combined drug delivery strategies to
overcome such evolutions at the cell population
level. Website: http://www.rocq.inria.fr/bang/
JC/Jean_Clairambault_en.html.
SMB Newsletter, MAY 2014, Volume 27, No 2
Page 15


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