Classes: Duration of the school is two weeks, including 11 days of classes, Monday through Friday, plus the intervening Saturday morning. Each day there will be 8 or 9 lecture units of 40 min by the staff and by invited speakers. Afternoon practice and exercise sessions will be conducted three times a week. Participants will also have the opportunity to deliver their own presentations. Two afternoon sessions per week will be conducted at the Mario Negri Pharmacological Research Institute (Consorzio Mario Negri Sud, Santa Maria Imbaro, Chieti), the purpose being to expose the participants of the school to real-life biological problems voiced in discussions with the Mario Negri researchers, as well as to show actual laboratory experiments from which data arise.

The language of the school is English. Most school activities will take place in the same hotel where rooms and meals are provided. Most of the lecture sequences will be completed in a single week, biological subjects being treated in the first week and more mathematical subjects being treated in the second week.

Calendar:

September  1998: First announcement, topics covered
February   1999: Second announcement, program and logistics
April 15   1999: Deadline for submission of financial support form
April 20   1999: Communication of admissions and financial support 
                 to participants. Pre-registration opens.
May 1      1999: Deadline for submission of contributed presentations
May 20     1999: Pre-registration closes. Final announcement.


June 1999
Sunday     6  Welcome and registration.
Monday     7  School starts
Friday    18  School ends
Saturday  19  Farewell breakfast, instructors' meeting

Instructors and invited lecturers

Zvia Agur, Saverio Alberti, William Amos, Ovide Arino, Jacques Belair, Edoardo Beretta, Alessandro Bertuzzi, Ranajit Chakraborty, William Coleman, Andrea DeGaetano, Luigi Del Vecchio, Alberto Gandolfi, Raffaella Giavazzi, Kristian Helin, Thomas Hoefer, Mimmo Iannelli, Marek Kimmel, Tanya Kostova, Sophie Lelievre, Michael Mackey, Daniela Morale Luigi Preziosi, Eva Sanchez, Damien Schoevaert, Andrzej Swierniak, Ziad Taib, Paolo Ubezio, Jany Vassy, Giancarlo Vecchio, Glenn Webb.

FIRST WEEK

TUMOR CELL BIOLOGY

(S. Alberti, R. Giavazzi, K. Helin and G. Vecchio)

- Introduction: cell structure and function.
- Molecular mechanisms of cell cycle progression.
- Deregulation of cell cycle control in cancer.
- Cell membrane molecules that regulate tumor growth rates and
  patterns of tumor growth.
- Trop-regulated cell-cell adhesion in normal and tumorigenic cells.
- Angiogenesis in tumors.
- Mechanisms of activation of oncogenes and tumor suppressor genes in human neoplasia.

CONTROL OF HAEMOPOIESIS

(M. Mackey and J. Belair)

- Periodic Hematological Diseases: Pathology, Modeling, and Treatment 
(two units).
- Peripheral Control of Red Blood Cell Production (two units).
- Peripheral Control of White Blood Cell Production (two units).
- Stem Cell Dynamics:  Understanding Cyclical Neutropenia and Periodic 
Leukemia (two units).
- Regulation of Platelet Production by Thrombopoietin (two units).

CYTOMETRY AND PARAMETER ESTIMATION

(A. Bertuzzi, A. De Gaetano, L. Del Vecchio and P. Ubezio)

- Basic flow cytometry.
- Characterization of asynchronous exponential growth.
- Models for the analysis of data from asynchronous growth. 
- Evaluation of cell cycle effects of drugs.
- Proliferation markers and detection of cell death.
- Gene expression analysis by flow cytometry and confocal microscopy.
- CD45-driven identification of normal and leukemic cells in human   
bone marrow.
- Basic geometry of parameter estimation for nonlinear models.
- Fundamental results for least-squares and maximum likelihood 
estimators.
- Curvature, confidence intervals and model choice.
- Population parameter estimation for nonlinear models.

CYTOSKELETON AND REGULATION OF CELL FUNCTION

(Jany Vassy, Sophie Lelièvre, Damien Schoevaert, Michael Beil and Stéphanie Portet)

- Tissue architecture and gene expression, study of tissue matrix in 
three-dimensional models of cell culture. 
- Cytoplasmic cytoskeleton as a link between cell environment and 
nucleus. 
- Non-chromatin structure of the nucleus or nuclear matrix, its 
interaction with chromatin structure and its role in the regulation of 
gene expression. 
- Automated image analysis of the cytoskeleton architecture. Methods
and applications.
- Image analysis of the cytoskeleton in cell movement.
- Modelisation of the architecture of cytokeratin networks.

ROUND-TABLE

The role of biomathematics in large biological research institutions and corresponding career openings for young biomathematicians (Chair: M.B.Donati).

SECOND WEEK

STRUCTURED CELL POPULATIONS

(E. Sanchez, O. Arino, T. Kostova and G. Webb)

- Asynchronous exponential growth and semigroup theory. Existence of 
steady-state distributions. Generalities on semigroup theory. Positive 
semigroups.
- Size-density models.Syngle type models. Models with two 
compartments. Size-age density models.
- Time continuous daughter cell models. Model with deterministic 
lifelength. Model with stochastic lifelength.
- A short review of other linear structured cell population models. 
Comparison of approaches to modeling of cell population dynamics.
- Introduction to nonlinear models. Unequal division. Selective 
regulation of cell population growth.
- Structured population models of the blood cell production system. 
Chaotic behavior in maturity structured models.
- Structured population models of limited proliferative capacity in 
dividing cell lines. Telomere fragment shortening on the ends of 
chromosomes.
- Structured population models of tumor cord cell migration. Cell 
kinetics in the vascularized steady state.
- Examples  of Age- and Size- Structured Models in Cellular Biology. 
What does Numerical Solving mean? The Grid and the Step.
- Interpolation, Quadratutures, Order of Approximation, the Error,
Runge-Kutta Methods. Outline of Several Numerical Methods to Solve 
Age- and Size- Structured Models. First, second, high accuracy 
methods.

MODELLING CANCER CHEMOTHERAPY

(Z. Agur and A. Swierniak)

- The use of mathematical models for understanding the cell cycle 
clock in mammalian cells and its crackdown in cancer.
- Optimizing cell-cycle specific chemotherapy: insights gained from   
mathematics (two units).
- Introduction to optimal control, controllability, observability.   
The Bellman principle of optimality.
- Dynamic programming, application of dynamic programming to discrete-
time systems, the discrete LQ problem.
- Pontryagin maximum principle, application of the maximum principle   
to continuous LQ problems and bang-bang control.
- Introduction to stochastic optimization (dynamic programming   
approach), LQG problem, problem with Markovian jumps JLQ.
- Examples of applications in optimization of cancer therapy.

Two additional units are to be announced.

POPULATION GENETICS OF ORGANISMS AND CELLS

(M. Kimmel, R. Chakraborty and W. Amos)

- Basic principles of genetics of diploid organisms: chromosomes, 
genes, alleles, DNA, segregation, and recombination.
- Genetics of populations: mutation, genetic drift, selection.
- Important loci systems: autosomal and sex-linked loci, mitochondrial    
DNA, repeat-DNA.
- Genetics of unicellular organisms, somatic cells and organelles.
- Estimation of relatedness of individuals.
- Models of mutational processes: Markov Chain models, Infinite Allele    
and Infinite Site Model and Stepwise Mutation Model.
- Wright-Fisher-Moran model of genetic drift.
- Coalescence: the backward look at population genetics processes. 
Ancestral stochastic processes. Connection with branching processes.
- Coalescence with mutations and demographic change. Relationship to 
dynamical systems. Population dynamic coded in DNA
- Evolution of microsatellite loci: inference from data and connection 
with mathematical models (two units).
- Dynamic mutations and trinucleotide-related diseases: Data and 
models.
- Infinite Sites Model and mitochondria as molecular clocks.
- Evolution of mitochondria in somatic cells: origins of heteroplasmy, 
mitochondrial diseases.

One additional unit is to be announced.

INVITED TALKS

- Sufficient conditions for non-existence of periodic solutions in some classes of delay differential equations (E. Beretta)

- From a stochastic system of interacting individuals to a non linear diffusion continuous aggregation model. (V. Capasso, D. Morale)

- The Conditional Neyman-Pearson Lemma and model choice (W.P. Coleman)

- Chemotaxis and aggregation in the cellular slime mould (T. Hoefer)

- Modelling age-structured populations (M. Iannelli)

- Free boundary problems for solid tumor evolution (L. Preziosi)

- Modelling Cell Populations Using Branching processes: Theory And Specific Applications (Z. Taib)

LABORATORIES

- Experimental techniques in oncology and molecular biology: transfection (S. Alberti).

- Cancer and chemotherapy in animal models (S. Caltagirone, A. Di Castelnuovo).

- Electrophysiology and microdialysis in the study of the CNS (M. Di Mascio).

- Production of transgenic mice by pronuclear microinjection of foreign DNA (C. Dossi).

- Potassium channels studied in Xenopus Laevis oocytes (M.Pessia).

- Regulation of cell-cycle, oncogenes and anti-oncogenes (A. Sala).

- Measurement of cellular DNA content by flow citometry (P. Ubezio, N. Martelli).

- Electron microscopy in cell biology (R. Weigert).