modeling in life sciences - congresstravel.hu filethe distinguished international journal acta...
TRANSCRIPT
Modeling in Life SciencesInterdisciplinary Conference
IPA Cross-border Co-operation Programme HU-SRB/0901/221/088
Teaching mathematics and statistics in sciences: modeling and computer-aided approach
University of Szeged – UNS Faculty of Sciences, Novi Sad
IPA Cross-border Co-operation Programme HU-SRB/0901/221/088A program a Magyarország – Szerbia IPA Határon Átnyúló Együttműködési Programban az Európai Unió társfinanszírozásával valósul meg.
www.model.u-szeged.hu | http://sites.dmi.rs/projects/ipa
3 November, 2011 SzegedUniversity of Szeged
PROGRAMMELectures
Department of Medical Physics and Informatics, University of Szeged
http://www3.szote.u-szeged.hu/dmi/
The Department of Medical Physics and Informatics was established on the 1st July 2010 from
the earlier Institute of Medical Physics and Biophysics and from the Institute of Informat-
ics. Our department is the place of interdisciplinary activities. Medical Informatics serves
the needs of medical and life sciences; but, at the same time, is an independent discipline
in its own right. Hence the most important call is to promote the expansion of the informa-
tion technological approach and practice in all the activities of the Faculty of Medicine; to
promote health care and research more effective and productive; interdisciplinary education
and research in medical and other life sciences, such as Medical Physics, Medical Informatics,
Biostatistics, Mathematics and Computer-aided Modeling, and Cerebrovascular and Respira-
tory Physiology.
Bolyai Institute, University of Szeged
http://www.math.u-szeged.hu
Bolyai Institute – the mathematical institute of the University of Szeged – was founded in
1921 by the two world-famed professors of mathematical analysis, Frigyes Riesz and Alfréd
Haar. Since then, the institute has become one of the most important centers for mathemat-
ics in Hungary, where several internationally renowned researchers have been working. More
than 50 mathematicians – including four members of the Hungarian Academy of Sciences –
work in the six departments: Algebra and Number Theory, Applied and Numerical Mathematics,
Analysis, Geometry, Set Theory and Mathematical Logic, and Stochastics. The institute has a
mathematical library with about 50000 volumes. The distinguished international journal Acta
Scientiarum Mathematicarum founded by Riesz and Haar, and several mathematical textbooks
are published by the institute.
The Organizer Institutes
Venue: University of Szeged, Lecture Hall of Department of Ophthalmology Szeged, Korányi fasor 10–11.
10 00 – 10 10 Prof. Béla Rácz, Vice Rector of University of Szeged opens the conference
10 10 – 10 20 János Karsai (SZTE): TEACHING MATHEMATICS AND STATISTICS IN SCIENCES (SUMMARY OF THE IPA PROJECT)
10 20 – 10 50 Beáta Oborny*, Péter Englert (ELTE, Budapest): ADAPTATION BY “FALLING APART?” – GROWTH STRATEGIES IN MODULAR ORGANISMS
10 50 – 11 20 Géza Meszéna (ELTE, Budapest): DARWINIAN SPECIATION ON A REGULATED ADAPTIVE LANDSCAPE
11 20 – 11 45 COFFEE BREAK
11 45 – 12 00 Ágnes Méri (SZTE): SPATIAL MODELLING OF THE DISPERSION AND HOST FINDING BEHAVIOUR OF CUSCUTA CAMPESTRIS
12 00 – 12 15 Diána H. Knipl (SZTE, Szeged): THE EFFECT OF GLOBAL AIR TRANSPORTATION ON THE INVASION OF PANDEMICS
12 15 – 12 30 Kyeongah Nah (SZTE, Szeged): THE DILUTION EFFECT OF THE DOMESTIC ANIMAL POPULATION ON THE TRANSMISSION OF P. VIVAX MALARIA AND FMD
12 30 – 12 45 Jelena Piperac*, Jadranka Luković, Lana Zorić and Nevena Nagl (Univ. Novi Sad): STEREOLOGICAL ANALYSIS OF SUGAR BEET PETIOLE
12 45 – 14 15 LUNCH BREAK
14 15 – 14 45 George Mihalas (Univ. of Medicine and Pharmacy, Timisoara): PRINCIPLES OF MODELING IN MOLECULAR BIOLOGY. APPLICATION FOR P53-MDM2 PROTEIN INTERACTION
14 45 – 15 15 András Málnási-Csizmadia (ELTE, Budapest): NON-TARGET BASED DRUG DESIGN
15 15 – 15 45 Viktória Lázár (SZBK, Szeged): AUTOMATED MAPPING OF ANTIBIOTIC INTERACTIONS IN ESCHERICHIA COLI
15 45 – 16 10 COFFEE BREAK
16 10 – 16 40 Szilárd Fejér (SZTE, Szeged): VIRUS CAPSID MODELING: COMPLEX SELF-ASSEMBLY FROM SIMPLE BUILDING BLOCKS
16 40 – 17 10 Yukihiko Nakata (Basque Center of Appl. Math., Bilbao): GLOBAL DYNAMICS OF TWO COMPARTMENT MODELS FOR CELL PRODUCTION SYSTEMS WITH REGULATORY MECHANISMS
17 10 – 17 40 Henggui Zhang (The University of Manchester): DEVELOPMENT OF A MATHEMATICAL MODEL FOR WHOLE RABBIT HEART
17 40 – 18 00 CLOSING AND DISCUSSIONS
Programme – November 3, 2011 3
4 Lectures
TEACHING MATHEMATICS AND STATISTICS IN SCIENCES (SUMMARY OF THE IPA PROJECT)János Karsai
Institution: University of Szeged, Department of Medical Physics and InformaticsPosition: Associate ProfessorContact: E-mail: [email protected] Web: www.math.u-szeged.hu/~knipl
It is known that phenomena in the Nature can often be described by quite complicated mathemati-cal models which cannot be studied using only classical theoretical methods. In addition, students, researchers in applied fields would like to take most benefit with minimal effort. For them, the experi-ments are more convincing than the theoretical study. These methods now are organic parts of the sci-entific research, but became possible only by the appearance of high powered desktop computers with realistic real-time graphical capabilities.
Consequently, is not easy to teach math and doing mathematical research for applied fields. Not only the curricula of the courses must be specified very precisely, special didactic methods and tools fit-ting the specialties of the given field are also needed. Even more, mathematicians involved must have knowledge in the given field. In addition, sometimes the teacher must resolve the problems of negative preconceptions which often comes from the society.
In our talk, we deal with our efforts in the frame of our IPA HU-SRB/0901/221/088 project to improve the computer-aided and modeling-based teaching of Mathematics and Statistics at University of Szeged and University of Novi Sad. We summarize our results, and show some examples of the teaching materi-als developed.
ADAPTATION BY “FALLING APART?” – GROWTH STRATEGIES IN MODULAR ORGANISMSBeáta Oborny and Péter Englert
Institution: Loránd Eötvös University, Department of Plant Taxonomy, Ecology, and Theoretical Biology
Position: B.O.: Associate Professor, P.E.: BSc studentContact: E-mail: [email protected] Web: http://beata.web.elte.hu
Modular organization of the body is widespread in many taxa of plants and animals. We modelled the growth process - the production of modules and branching - of a modular organism in space. Growth pro-ceeded in a heterogeneous environment, in which an essential resource, required for growth, was distrib-uted in patches. We varied the number, size, and permanence of patches, to simulate different habitats. The model was based on stochastic cellular automata, extended with some specific features of the organisms. Two basic strategies were compared. In the Integrator, the modules remained interconnected throughout
Lectures 5
their lives, and shared the resource. In the Splitter, the modules were independent (“selfish”). We let the strategies compete for the resource, and we recorded their developing spatial patterns over time. The results show that each strategy has a characteristic parameter range (habitat type) in which it is adaptive. Coexistence of the strategies is possible in a broad parameter range, where the Integrator fills the gaps left open by the Splitter. We review some results from percolation theory to explain exclusion vs. coexistence, and consider their implications for the diversity of species in ecological communities.
DARWINIAN SPECIATION ON A REGULATED ADAPTIVE LANDSCAPEGéza Meszéna
Institution: Eötvös University, Department of Biological PhysicsPosition: Associate ProfessorContact: E-mail: [email protected] Web: http://evol.elte.hu/~geza/
Darwin envisioned speciation as a gradual transformation from within-species diversity to between spe-cies one, driven by the fitness-advantage of reduced competition via niche-segregation. However, this suggestion has been considered problematic since the New Evolutionary Synthesis and replaced by the theory of allopatric speciation by Ernst Mayr.
The underlying mathematical issue is that the notions of niche and reduced competition have no meaning in the context of a rigid adaptive landscape. Instead, one has to consider the landscape (i.e. the fitness function) as a function of the phenotype-distribution in a functional analytic context. The functional de-rivative of this map is the competition function with the correct biological meaning. The adaptive dynamics phenomenology, including evolutionary branching, can be derived from this setup. In this way, develop-ment of the mathematical theory recreates the original, Darwinian intuition on speciation in a precise form.
SPATIAL MODELLING OF THE DISPERSION AND HOST FINDING BEHAVIOUR OF CUSCUTA CAMPESTRISÁgnes Méri
Institution: University of Szeged, Department of Medical Physics and Informatics, Depart-ment of Ecology
Position: PhD studentContact: E-mail: [email protected] Web: www.model.u-szeged.hu
Cuscuta species are fast growing plant parasites of different communities. Their role in the maintenance of equilibrium states of the communities is partly still undiscovered. Under warmer climate conditions, some of them are treated as dangerous pests, since they can cause great losses in agricultural sites. On
the other hand, in countries like Scandinavia they are protected species, since their growth is inhibited by the cold weather. Moreover, these plants have a special strategy to find their host, it is called forag-ing. In addition to land study we investigate their behaviour by using mathematical models. Planar, spa-tially explicit models may be one of the appropriate tools, but some other types of modelling techniques are also being considered. Computer simulations with Mathematica on these models will certainly give a lot of information on cuscuta species. In the talk we give an overview on the behaviour and known results of cuscutas. Then, we present the possible issues and the first results of our research.
THE EFFECT OF GLOBAL AIR TRANSPORTATION ON THE INVASION OF PANDEMICSDiána Hulmán-Knipl
Institution: University of Szeged, Bolyai Institute, Department of Applied and Numerical Mathematics
Position: Ph.D. StudentContact: E-mail: [email protected] Web: www.math.u-szeged.hu/~knipl
National boundaries never hindered infectious diseases to reach distant territories; however, the speed at which an infectious agent can now spread around the world is significantly increased in the last 50 years. We introduce an SEAIR-based model for large distance travel networks, which describes the dynamics of a pandemic on regions connected by air transportation. Due to the high connectedness of several distant places, we include the possibility of transmission of the disease during travel. We detail the method of the calculation of the reproduction number, and parametrize the model with influenza and real air traffic data.
THE DILUTION EFFECT OF THE DOMESTIC ANIMAL POPULATION ON THE TRANSMISSION OF P. VIVAX MALARIA AND FMDNah Kyeongah
Institution: University of Szeged, Bolyai InstitutePosition: Ph.D. studentContact: E-mail: [email protected]
The diversion of mosquitoes from humans to animals may reduce transmission of malaria. A system of differential equations model is introduced to study the dilution effect of animals on the transmission of P.vivax malaria. With sensitivity analysis, we showed that increasing the relative animal population size works better in P. vivax malaria control than decreasing the mosquito population when the relative animal population size is larger than a threshold value.
6 Lectures
In the meanwhile, mosquito biting rate on human is expected to increase when animal population is re-duced. During Foot-and-Mouth Disease(FMD) epidemic in Korea, more then 350 millions of animal were culled. We simulate the change of malaria incidence before and after FMD spread in Kyunggi Province, which is one of the malaria endemic area.
STEREOLOGICAL ANALYSIS OF SUGAR BEET PETIOLEJelena Piperac 1, Jadranka Luković 1, Lana Zorić 1 and Nevena Nagl 2
Institution: 1 University of Novi Sad, Faculty of Science, Department of Biology and Ecology; 2 Institute of Field and Vegetable Crops, Novi Sad
Position: JP: MSC student; JL: Assoc. Professor; LZ: Assist. Professor; NL: Sen. Res. FellowContact: E-mail: [email protected] Web: http://www.pmf.uns.ac.rs/o_fakultetu/departmani/biologija_i_ekologija
Stereology is an interdisciplinary field that enables three-dimensional interpretation of planar sections of diverse materials. Based on mathematical principles, stereological methods are useful tools for quantitative evaluation of structural characteristics of plant organs. Water is becoming more and more limiting factor of sugar beet production. Consequently, the productivity of the crop can be significantly improved by increased drought tolerance. Assessment of the degree of variability of anatomical and morphological traits of breeding material with respect to water use efficiency and drought can be used as potential markers for selection of sugar beet genotypes with better tolerance to water deficiency. Petioles, as a plant organ which have the main function in transportation of organic and inorganic mol-ecules between leaves and fleshy beet root, also gives mechanical support to leaf blades. Therefore, we performed a stereological analysis of the sugar beet (Beta vulgaris L.) petiole in ten genotypes of variable drought tolerance. Emphasis has been laid on the relationship between morphoanatomical characteristics and the capacity of sugar beet to overcome drought.
PRINCIPLES OF MODELING IN MOLECULAR BIOLOGY. APPLICATION FOR P53-MDM2 PROTEIN INTERACTIONGheorghe Ioan Mihalas
Institution: University of Medicine and Pharmacy “Victor Babes” Timisoara, Department of Biophysics and Medical Informatics
Position: ProfessorContact: E-mail: [email protected] Web: www.medinfo.umft.ro
Mathematical modeling of molecular processes in biological system can reveal interesting features about time evolution of various molecular species. The introduction referes to the principles of model construction in molecular biology, mainly the first step - building the kinetic scheme of all molecular in-
Lectures 7
teractions to be traced. Second step is creating the corresponding computer simulation program which can produce both qualitative and quantitative results. A reliable interpretation can be given only to the results obtained with trustful parameters describing the system. Such an example is be presented; it re-fers to the well known P53-MDM2 loop of protein-protein interaction, which has an oscillatory behavior. Both time evolution graphs and phase diagrams are discussed. A comparison between two activation functions (continuous versus step-wise) is finally presented.
NON-TARGET BASED DRUG DESIGNAndrás Málnási-Csizmadia
Institution: Department of Biochemistry, Eötvös University Budapest (ELTE)Position: Associate ProfessorContact: E-mail: [email protected] Web: http://www.malnalab.hu/
Most drugs exert their effects via multi-target interactions, as hypothesized by polypharmacology1. While these multi-target interactions are responsible for the clinical effect profiles of drugs, current methods have failed to uncover the complex relationships between them. Here we introduce an approach which is able to relate complex drug-protein interaction profiles with effect profiles. Structural data and registered effect profiles of all small-molecule drugs were collected and interactions to a series of non-target pro-tein sites of each drug were calculated. Statistical analyses confirmed a close relationship between the effect and interaction profiles. Based on this relationship, the effect profiles of drugs can be revealed in their entirety, and hitherto uncovered effects can be predicted in a systematic manner.
AUTOMATED MAPPING OF ANTIBIOTIC INTERACTIONS IN ESCHERICHIA COLI
Viktória Lázár
Institution: Evolutionary Systems Biology Group, Biological Research Center, Szeged, HungaryPosition: Research AssociateContact: E-mail: [email protected] Web: http://group.szbk.u-szeged.hu/sysbiol/
The rapid evolution of bacterial drug resistance has motivated the use of drug combinations to combat resistance and maintain clinical efficiency. There is an increasing need to develop reliable systematic methods to map synergistic and antagonistic interactions between pairs of antibiotics (i.e. when two compounds enhances or diminishes each other’s effect, respectively). Large-scale antibiotic interac-tion maps would be useful for i) exploring the mechanisms behind drug interactions, and ii) for the development of new combination therapies. We developed a high-throughput, automated screening
8 Lectures
and a robust statistical analysis methodology for identifying antibiotic interactions using a robotic liquid handling system. We systematically measured interactions between 24 antibiotics to experimentally construct a complete, high resolution antibiotic interaction map of E. coli. Using a data-mining approach, we searched for predictors of interactions based on chemical and biological features of antibiotics.
VIRUS CAPSID MODELING: COMPLEX SELF-ASSEMBLY FROM SIMPLE BUILDING BLOCKSSzilárd Fejér
Institution: University of Szeged, Faculty of Education, Department of Chemistry and Chemical Informatics
Position: postdoctoral researcherContact: E-mail: [email protected] Web: www.szilard.ro
We present what we believe is the simplest and most versatile virus capsid model to date. Clusters of rigid building blocks composed of one ellipsoid and two ‘polarised’ repulsive sites can self-assemble not only into shells of icosahedral or octahedral symmetries, but into elongated, ‘squashed’ shells and double-shell structures as well. The parameter space of the model is very large, with large sections of it favouring particular morphologies (shells, tubes, spirals). For example, when increasing the side-by-side interaction strength between the oblate ellipsoids, we observe the formation of kinetic traps corresponding to competing tubular structures with different radii, analogous to carbon nanotubes with different chirality. Similar structures have been observed in vitro for HIV CA proteins. We find single tran-sition state rearrangements during which more strained tubes can relax into less strained morphologies (sliding mechanisms). Other morphologies that self-assemble by simply changing the building block parameters are: capped rods, spirals analogous to tobacco mosaic virus, and even head-tail structures.
GLOBAL DYNAMICS OF TWO COMPARTMENT MODELS FOR CELL PRODUCTION SYSTEMS WITH REGULATORY MECHANISMSYukihiko Nakata
Institution: BCAM-Basque Center for Applied MathematicsPosition: Postdoctoral FellowContact: E-mail: [email protected] Web: http://www.bcamath.org/
We analyze two-compartment models of a hierarchical cell production system under three different mechanisms of regulation by the level of mature cells. In the first model the stem cell’s division rate is regulated whereas in the second model the stem cell’s fraction of self-renewal is regulated. For these
Lectures 9
two models we prove that respective reproduction numbers exceed one if and only if a positive equi-librium exists and that it is globally asymptotically stable. This shows that the regulation mechanisms control the cell production system properly and that homeostatic conditions of stem and mature cells are reached. For the mathematical proof we employ a method of Lyapunov function exploiting nonlin-earity of the model. We show that the amount of stem cell population that keep the balance of mature cell population influences on the dynamical behavior of cell populations and compare the amount of stem and mature cells at equilibrium. Additionally, we formulate a third model, in which the stem cell’s fraction of differentiation is regulated. We prove that a positive equilibrium, if it exists, is unstable and the numbers of stem and mature cells always tend to infinity if the reproduction number exceeds one.
DEVELOPMENT OF A MATHEMATICAL MODEL FOR WHOLE RABBIT HEARTHenggui Zhang
Institution: School of Physics & Astronomy, The University of ManchesterPosition: Professor of Biological PhysicsContact: E-mail: [email protected] Web: www.biological.physics.manchester.ac.uk/people/drhengguizhang/
In this talk, I shall report the progress of our long-lasting effort to develop a mathematical model for simulating the electro-physiology of whole heart for the rabbit. The anatomical structure of the heart was reconstructed by DT-MRI scan with a spatial resolution of 200 micro-meter. A novel family of single cell models have been developed for simulating the electrical action potentials for 16 distinctive cell types from regions of the sinoatrial node, the atria, the AV node, Purkinje fibre, left and right ventricles. These single cell models were incorporated into the 3D anatomical structure of the heart to simulate the initiation and conduction of excitation waves across the whole heart, from which EEC was extracted. The model was validated by quantitatively compare the characteristics of simulated ECG with experimental recordings.
10 Lectures
Interesting Mathematical Problems in Sciences and Everyday Life – 2011
Electronic book containing 19 papersUniversity of Szeged, University of Novi Sad, 2011
As you have not seen before
Pictures of the ExhibitionUniversity of Szeged, 2011
Mathematics and Computer-aided Modeling in Sciences
The complete CD of the spring School, 2011University of Szeged, University of Novi Sad
Collected Electronic Teaching Materials
for Various Fields in Mathematics (available in December, 2011)University of Szeged, University of Novi Sad, 2011
NEW ELECTRONIC MATERIALSavailable on
www.model.u-szeged.hu
C & T Hungary Kft.6720 Szeged, Dugonics tér 12. Tel./fax: +36 62 548 485E-mail: [email protected]
Modeling in Life Sciences Interdisciplinary Conference
November 3, 2011
Organized by Department of Medical Physics and Informatics, Bolyai Institute of University of Szeged, Department of Mathematics and Informatics of University of Novi Sad
www.model.u-szeged.huhttp://sites.dmi.rs/projects/ipa
HU-SRB/0901/221/088