For my current activities, please see my lab page.


I'm intrigued by the idea of networked tools for biology. Science will benefit from powerful scientific research instruments deployed through the web and the opportunities for the collaborative organization of real-time knowledge these instruments enable. Our contribution in this direction is the Kappa platform.


I believe there is a substantial overlap between the core subject matters of computer science and biology. Both disciplines reason about behaviors (such as operating systems and cells) by means of linguistic structures (such as programs and chemical expressions). Both are concerned with resources (computational complexity and thermodynamics, for example). As Wojciech Zurek once remarked, "there is no information without representation". I take this to mean that information is processed by manipulating its representation. This representation is of logical nature in computer science and of material nature in biology. Once unified, the core overlap between these two disciplines will yield a science of organization. If you have patience for a piece of computational philosophy of biology, try this.

Among the past pursuits that I'm most fond of, I would emphasize the following two.

The formalization and emergence of functional organization

The formal structure of evolutionary theory is based upon the dynamics of (populations of) “individuals.” It therefore assumes the entities whose existence it is supposed to explain. At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. The research theme Leo Buss and I called Algorithmic Chemistry (AlChemy) was an attempt at constructing a formal framework for thinking about molecular organization through a minimal abstract chemistry.  Our stance was to view molecules as rules of transformation and to exploit a mathematical theory of functions (lambda-calculus) to represent abstract “molecules” that act upon one another generating new molecules, that is, rules of transformation. Under suitable boundary conditions this model generates self-maintaining collectives of rules whose mutual transformations permit the continuous regeneration of these same rules.  The “organization” of such a system is specified by the relationships of transformation that enable self-maintenance, i.e. the algebraic structure of the system.  This framework permits to address the robustness of organizations with respect to the elimination of components (self-repair), the addition of components not belonging to the organization (constrained extension) and the merger of autonomous organizations into higher-order structures (integration).

Although this particular model has slipped into the background, its basic vision remains intact. I keep gravitating back to the question of how the theoretical foundations of computation can help us represent biological processes and reason about them. Computation is organization and the classical theories of computation (sequential or concurrent) are but theories of very specific forms of organization. Others will be discovered.

Key collaborator:  Leo Buss (Yale)

selected papers:

  • W. Fontana and L. W. Buss, The Barrier of Objects: From Dynamical Systems to Bounded Organizations, in: Boundaries and Barriers, J. Casti and A. Karlqvist (eds.), pp.56–116, Addison-Wesley, 1996 [pdf]
  • W. Fontana and L. W. Buss, 'The Arrival of the Fittest': Toward a Theory of Biological Organization, Bull. Math. Biol., 56, 1-64 (1994) [pdf]
  • W. Fontana and L. W. Buss , What would be conserved if ‘the tape were played twice’?, Proc. Natl. Acad. Sci. USA, 91, 757–761 (1994) [pdf]
Genotype-phenotype mappings

The heritable modification of biological phenotypes occurs by mutation of the genotype. Accessing one phenotype from another is therefore an indirect process mediated by the mapping from genotype to phenotype (development). Evolutionary dynamics and innovation depend on the statistical features of this mapping. I studied this mapping at the level of a single type of molecule: RNA. An RNA molecule is a sequence (genotype) that folds into a shape (phenotype). The statistical analysis of RNA folding has produced insights that may generalize to more complex systems. The most consequential feature is the notion of a neutral network: a mutationally connected set of sequences folding into the same shape and spanning a web through sequence space. Neutral networks allow populations to drift across genotype space without losing their current phenotype. In this way, populations can access many more novel phenotypes than if they were confined to a small region of genetic space. Neutral networks dispel the dichotomy of robustness versus evolvability by demonstrating that robustness enables change. Prompted by this line of work, researchers at MIT’s Whitehead Institute discovered neutral networks in RNA test tube experiments (Schultes and Bartel, Science, 289, 448-452, 2000). The adjacency of neutral networks can be used to define a notion of phenotype space based on the accessibility of phenotypes through genetic mutation rather than phenotypic similarity. Other concepts that emerged from this line of research are shape space covering (that all frequent shapes occur within a relatively small neighborhood of any random sequence) and plasto-genetic congruence (that the genetic variability of a shape on a given sequence correlates with the alternative structures accessible by thermal fluctuations). Plasto-genetic congruence suggests a trade-off between genetic robustness and phenotypic plasticity.

Key collaborators: Peter Schuster (Vienna), Peter Stadler (Vienna), Lauren Ancel-Meyers (Austin)

selected papers:

  • W.Fontana, Modelling ‘Evo-Devo’ with RNA, BioEssays, 24, 1164–1177 (2002) [pdf]
  • L.W.Ancel and W.Fontana , Plasticity, Evolvability and Modularity in RNA, J.Exp.Zool. (Mol.Dev.Evol.), 288, 242–283 (2000) [pdf]
  • W.Fontana and P.Schuster, Continuity in Evolution: On the Nature of Transitions, Science, 280, 1451–1455 (1998) [pdf]
  • P.Schuster, W.Fontana, P.F.Stadler and I.Hofacker, From Sequences to Shapes and Back: A Case Study in RNA Secondary Structures, Proc. Roy. Soc. (London) B, 255, 279–284 (1994) [pdf]