Stochastic Modelling in the biomedical sciences

Physiological processes at several scales (subcellular, cellular, tissue, organ and even population) are inherently stochastic, due to a great variety of noisy factors affecting the phenomenon under investigation.

In fact, deterministic models (representing the vast majority of formalizations hitherto employed in biomedicine) are not realistic, unless the random fluctuations remain small. An incorrect representation, omitting substantial system noise where this is in fact present, leads to poor model identification, biased parameter estimations and inconsistent conclusions.

In recent years there has been an increased emphasis into modeling the randomness inherent in many physiological phenomena, and tools like Stochastic Differential Equations (SDE), or Equações Diferenciais Estocásticas , so far mainly utilized in finance, have found initial application. 

Connected with the use of these techniques in representing biomedical processes, are issues such as identifiability, stability or periodicity, which are typically more complicated to study then their deterministic counterparts.

==

Source: JG. Pires; P Palumbo; A De Gaetano; C. Manes. ‘Stochastic models in medicine and life sciences: mathematical analysis, model identification, validation and stability properties’. Proposal for PhD programme. 2014. Unpublished.

==
Jorge Pires

Think about it! Is it reality ‘deterministic’ or ‘stochastic’?

Maybe one of the most famous men in the battle against the “random world” as one of the truths was Einstein. He believed firmly until his death on a reality so deterministic that we could predict the future [1]. However, it is kind of fun that even his world played against him, with the famous work on Brownian Motion, one of his famous five papers [2]. Maybe if Julius Caeser had met Einstein, perhaps he would never had said that “his luck has been thrown to the dice.” This is irony maybe that the works on Brownian motion led to the current theory of stochastic differential equations, the “random” counterpart of the differential equations. 

What about the current state of the art?

“The message that keeps being repeated is that the kinetics of biological processes at the intra-cellular level are stochastic, and that cellular function cannot be properly understood without building that stochasticity into in silico models. ” [4]

 “I have reasons to expect that ‘quantum mechanics’ in ‘biological systems’ is not the only source of noise (randomness), and neither it is lack of knowledge. Those factors, mainly lack of knowledge, might be currently predominant, but it will perhaps be clear that biological systems are not so predictable as it is physical systems. It does not mean that they possess special set of laws. The matter might be boiled down to ‘flexibility’ and ‘variability’ in the cell level. The probability of finding true homogeneity in a cell population is almost zero, no matter the size. For instance, Brownian motion is significant in many real cases in biology, and it has nothing to do with quantum mechanics. “[5]

The problem of the observer in physics.

References:

[1] Clark, R. W. Einstein: the life and times. Públicado em acordos com World Publishing Company, 1971.

[2] Stachel, J (1998). Einstein’s miraculous year: five papers that changed the face of physics. Princeton University Press. New Jersey.

[3] Russell, Stuart; Norvig, Peter. Artificial Intelligence: A modern approach. Second edition. Prentice Hall Series in Artificial Intelligence: 2003.

[4] Wilkinson, DJ (2012). Stochastic modelling for systems biology. Second Edition. Chapman and Hall Book. CBC press. Online: http://www.staff.ncl.ac.uk/d.j.wilkinson/smfsb/2e/. last access: July 2014.

[5] Pires J G (2013). On the mathematical modelling in gene expression estimation. II Workshop and School on Dynamics, Transport and Control in Complex Networks  (ComplexNet), Ribeirão Preto, SP, Brazil. 21-26/October. Poster.

[6] Rome: The Rise and Fall of an Empire. Documentary.

[7] Ruffino, P R C. Uma iniciação aos sistemas dinâmicos estocásticos. Publicações Matemáticas.  IMPA, 2009.

===

Jorge Pires

NEWS

I have just created two new blogs: a counterpart for this one in Portuguese and a page for miscellaneous topics.

Jorge Pires

Upcoming Events (Summer Schools)

"Mathematical Models and Methods for Living Systems”
CIME-Foundation and CIRM
CIME
Levico Terme (Trento) from Sept. 1  to  Sept. 5, 2014

Status (Accepted, permission to travel given)

Mathematical Models and Methods for Living Systems

- Modelling the formation of vascular networks
Mark Chaplain (Univ. Dundee, Great Britain)
- Mathematical modeling of morphogenesis in living materials
Pasquale Ciarletta (CNRS, France)
- Cell movement in non-isotropic environments and the modeling of cancer spread
Thomas Hillen (Univ. Alberta, Canada)
- Cell-based, continuum and hybrid models of tissue dynamics
Hans G. Othmer (Univ. Minnesota, USA)
- Modelling cell migration in fiber networks
Luigi Preziosi (Politecnico Torino, Italy)
Il CIME ed il CIRM finanzieranno le spese di soggiorno per circa 30 partecipanti.
Per iscriversi collegatevi al sito
http://web.math.unifi.it/users/cime/

Summer School 2014 Participants (Levico Terme, Trento, Hotel Bellavista. Photo by  Augusto Micheletti)

“How To Understand Complex Biological Functions”

1st SyBSyM Como School

Lake Como School of Advanced Studies

September 21 to September 27,

Como, Italy.

School wesite

Status (Accepted, permission to travel given)

Poster accepted. 

Lectures

Sep 21, Sun

·                       Jens Nielsen (1), Lecture 1: Systems biology of yeast metabolism and evolution (Chalmers University of Technology, Göteborg)

Sep 22, Mon

·                       Jonathan Karr, Integrative computational models (Icahn School of Medicine at Mount Sinai, NYC)

·                       Lilia Alberghina, Systems biology of growth and the cell cycle, SYSBIO Italy (Univ. of Milano-Bicocca)

Sep 23, Tue

·                       Dina Petranovic, Yeast as a model for cell aging and death (Chalmers University of Technology, Göteborg)

·                       James Sharpe, Image-driven modelling of multicellular systems (CRG Barcelona)

Sep 24, Wed

·                       Jens Nielsen (2) Lecture 2: Systems biology of cancer metabolism (Chalmers University of Technology, Göteborg)

·                       Richard Kitney, ISBE: an infrastructure for systems biology and systems medicine ISBE Coordinator (Imperial College London)

·                       Walter Kolch CASyM, How to shape systems medicine? (CASyM Steering Committee, UCD Dublin)

Sep 25, Thu

·                       Marco Vanoni, Signaling and metabolism (SYSBIO Italy, Univ. of Milano-Bicocca)

·                       Matteo Barberis, Cell cycling and chromatin dynamics (University of Amsterdam)

Sep 26, Fri

·                       Damjana Rozman, From healthy to fatty liver: a systems approach (University of Ljubljana)

·                       Sampsa Hautaniemi, Analysis and Integration of Large-scale Molecular and Clinical Data in Cancers (University of Helsinki)

Sep 27, Sat

·                       Rudi Balling, Systems biology of Parkinson’s disease (Luxembourg Centre for Systems Biomedicine)

·                       Mikael Benson, Complex disease, omics maps and their clinical implementations (CASyM Steering Committee, University of Göteborg)

·                       Hans Westerhoff, Mapping the systems biology of multifactorial diseases (Univ. of Amsterdam, Univ. of Manchester)

Introduction (STOCHASTIC MODELS IN MEDICINE AND LIFE SCIENCES)

This blog intends to serve as a reference point for the project " STOCHASTIC MODELS IN MEDICINE AND LIFE SCIENCES: mathematical analysis, model identification, validation and stability properties".

It is intended to provide a place where anyone interested on the same can have important details, hopefully updated.

Unfortunately, with technologies, besides responsability, this is never ease to know what to post. Once said Einstein that the secret for the success is hard work, having fun, and keep your mouth shut down. But the same way that someone can purchase a car for myriad reasons such as catching the girls' eyes, a technology readily available can be used for several reasons such as to document an ongoing project, which presumably has its impact.

Regrettably Blogs are not considered references, whenever it is possible, references to published works will be done, hence the interested reader shall be endowed with formal manuscripts.

Involved Institutions

Department of Information Engineering, Computer Science and Mathematics
University of L'Aquila, Italy, Dews

Dews

Institute of Systems Analysis and Computer Science (IASI)
Cosiglio Nazionale  delle Ricerche (CNR) Rome, Italy

BioMatLab

Sponsorship

CAPES Foundation, Ministry of Education of Brazil (Science without Borders, CsF)

CAPES,Science without Borders

Contact

Jorge Pires