Social dilemmas ... and how bacteria and humans solve them (2012-2013)
We will try to understand how individual decision-making can contribute
to the resolution of social dilemmas. We will first discuss some basic
ideas by introducing the language of game theory to then identify a
fundamental principle of social behavior, i.e., conditional
cooperation, that will then be further illustrated with examples in
systems as different as bacteria and ... humans! Lectures: day 1, day 2, day 3.
The mathematics of Biology (2011-2012)
Can we compute with biological systems? If so, how? And how can
different systems exhibiting complex behaviours, such as clocks, work
together? Moreover, if we want systems to work together, why not
designing them to cooperate? We will discuss these issues using
mathematics and biology by means of three topic lectures by Matteo
Cavaliere (Engineering automata in biological systems), Saúl Ares (The rise and fall of synchrony in biological clocks) and myself (How to design cooperative communities).
Conflict and cooperation in microorganisms II (2010-2011)
How do altruistic traits evolve? Which are the main theories linked to
the evolution of cooperation? How are they related? And to what extent
microbial systems could help us to understand these issues? We
discussed these topics in class with some introductory lectures (based
on last year notes) and the discussion of recently published works.
Conflict and cooperation in microorganisms (2009-2010)
These are the notes for the lectures of the Master in Biophysics
at Autónoma University, Madrid, Spain. We discussed the problem of
cooperation (and conflict) in biological systems. I first introduced
the theoretical background, e.g., frequency-dependent selection, game
theory, prisoner's dilemma, kin selection, Price's theorem, etc. Then,
I discussed several recent experimental works on the evolution of
cooperation in microbial systems. Lectures: day 1, day 2, day 3. Exercises: Ex.
Noise in Gene Expression (2008-2009)
These are the notes for the lectures of the Master in Biophysics and Master in Biosciences
at Autónoma University, Madrid, Spain. I first asked why gene
expression is noisy. Second, I introduced some mathematics to
understand the current models describing noisy genes -Master equations,
Gillespie's algorithm, etc- to then discuss about the implications of
noisy genes in prokaryotic and eukaryotic Biology. Lectures: day 1, day 2, day 3, day 4, day 5, summary. Matlab codes: code1.m, code1equations.m, code2.m, code2equations.m.
Introduction to SYSTEMS BIOLOGY and SYNTHETIC BIOLOGY(2006-2007)
(Curso de doctorado en Biología de Sistemas y Biología Sintética)
research is in the midst of a radical transformation. Within the last
few years, experimental advances derived from genome sequence projects
are transforming Biology in a data rich discipline where complex
mechanisms of cellular evolution and function can be deciphered. This
has promoted the emergence of two new research areas: Systems Biology
and Synthetic Biology, a combination of disciplines such as
Mathematical Biology, Genetic Engineering or Bioinformatics.
Course goals. The
aim of this course is to introduce some aspects of this new
interdisciplinary areas with special emphasis on showing how the
integration of experimental and theoretical approaches my help us to
address fundamental biological questions. A very important goal of this
course is to promote the interaction among students with very different
backgrounds, e.g., Biology or Physics, and to make them aware of the
existing research opportunities and the rapidly accumulating
information in this new field.
course will consist of several instructor lectures introducing each
week's topic, a journal club and a personal project. One of the papers
will be explained and discussed on class at the end of the week. A
"course project" related to these topics should be done by each
student. The goal of these projects is to investigate some biological
question in a more quantitative way, either with mathematics or
Time & Place. This PhD course will be held next fall (academic year 2006-2007). Three lectures per week. Schedule to be arranged. (see course 2005-2006)
If you have some questions, please e-mail me
COURSE BRIEF OUTLINE (see also info course 05-06)
1. Recurrent units of cellular information processing: Networks motifs.
2. Cellular decision making: Positive feedback loops, ultrasensitivity, bistability, epigenetic differentiation.
3. Molecular oscillations: Negative feedback loops, relaxation-based clocks.
4. Spatial and Temporal organization: Just-in-time kinetics, principles of cellular patterning.
5. Robustness in cellular networks.
V Master in Biophysics course
genes noisy? What do we mean by that? How can noisy genes enable robust
function? We will address these questions by first introducing the
required mathematical framework to then discuss some recent
experimental results. Lectures: day 1, day 2, day 3, day 4.
IV Master in Biophysics course
lectures are a (very) brief introduction to deterministic and
stochastic dynamics in biological systems. The course is part of the IV
Master in Biophysics (2006 - 2007) at Universidad Autónoma, Madrid, and
it will be taught in collaboration with Raúl Guantes who is teaching
deterministic biodynamics. I will be discussing recent experimental
reports on stochastic gene expression and also introducing some
theoretical and computational approaches to analyse them. Lectures: day 1, day 2, day 3, day 4.
III Master in Biophysics course
course is a (very) brief introduction to dynamics in biological systems
(genetic switches, cellular clocks, molecular motors, noisy dynamics
and population dynamics). The course is part of the III Master in
Biophysics (2005 - 2006) at Universidad Autónoma, Madrid and it will be
taught in collaboration with Raúl Guantes. We will be discussing recent
experimental results and also introducing some theoretical and
computational approaches to analyse them. Lectures not yet available.
II Master in Biophysics course
course is a (very) brief introduction to the study of noise in gene
expression. The course is part of the II Master in Biophysics (2004 -
2005) at Universidad Autónoma, Madrid. We will be discussing recent
experimental results and also introducing some theoretical and
computational approaches to analyse them. These are the lectures: [alldays].
I Master in Biophysics course
course is a (very) brief introduction to Biodynamics. The course is
part of the I Master in Biophysics (2003 - 2004) at Universidad
Autónoma, Madrid. We will be discussing multistability, bifurcations
and oscillations in cellular systems, focused in particular on the
lambda phage and the cell cycle cases.These are the lectures (in