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Biomathematics Research Unit (BIOMATH)

Mathematical modelling methods and computing have become increasingly important in almost all branches of biology. For example, the dynamical consequences of even quite simple ecological interactions or physiological mechanisms are impossible to understand without mathematical modelling and analysis. Evolutionary problems are often analysed in theoretical models for the prohibitively long time scales involved. Abundance of data also calls for mathematical modelling: The rapidly developing experimental techniques of molecular biology and genetics produce a large amount of data, which need efficient algorithms to be handled.

The biomathematics research unit does research in many diverse fields of Mathematical Biology. The projects lead by Kalle Parvinen are concentrated on modelling various phenomena occurring between individuals, covering topics such as mathematical ecology, especially metapopulation dynamics, and adaptive dynamics, mathematical evolutionary ecology. Projects lead by Tero Aittokallio model phenomena occurring within individuals, covering topics like modelling of physiological phenomena, analysis of biomedical signals, protein structure research, and computational systems biology. The projects led by Laura Elo develop and apply computational data analysis tools and mathematical modelling methods for biomedical research with a specific focus on high-dimensional molecular and clinical data.

Modelling and analysis in the above mentioned areas utilise the theory of dynamical systems, delayed differential equations, partial differential equations, functional analysis, graph theory, digital signal processing, statistical modelling and data mining methods, etc.

Research Unit Web Page: http://www.utu.fi/en/units/sci/units/math/Research/biomathematics/

Leader of the unit

Kalle Parvinen

Leaders of Research Groups

Kalle Parvinen Tero Aittokallio Laura Elo

Research Groups

Research Group of Kalle Parvinen

Members:       John D. Nagy
Tuomas Nurmi
Anne Seppänen

Research Group of Laura Elo

Members:       An Le Thi Thanh
Anna Pursiheimo
Maria Jaakkola
Teemu Daniel Laajala
Asta Laiho
Bishwa Ghimire
Deepankar Chakroborty
Fatemehsadat Seyednasrollah
Kalaimathy Singaravelu
Tomi Suomi
Rafael Alfredo Santos
Mehrad Mahmoudian


Theory of adaptive dynamics


In the last decades, the evolutionarily stable strategy (ESS) has become the main modeling tool for predicting the outcome of long-term evolution. The main disadvantage of the ESS is that it is a static concept, so that it always still remains to be seen whether an ESS can actually be reached. The Adaptive Dynamics framework developed by Metz et al. (1996) and Geritz et al. (1997, 1998) can be seen as the dynamic extension of ESS-theory and provides conceptual and mathematical tools for modeling long term evolution as a dynamic process in phenotype-space.

The theory of adaptive dynamics explicitly links population dynamics to long-term evolution by natural selection. A population is represented by the set of strategies present in positive numbers, and evolution is modelled as a sequence of such sets. The transition from one set to the next is caused by a new mutant strategy invading the population from initially small numbers, and possibly by the elimination of one or more strategies that were present in the population but are driven to extinction by the invading mutant. The approach is based on a number of simplifying assumptions, to wit clonal reproduction, small mutational steps and separate time scales for ecological and evolutionary dynamics. The combination of these assumptions allows to build tractable models for evolution also in complex ecological scenarios.

One of the most exciting phenomena uncovered by adaptive dynamics is evolutionary branching, whereby a single strategy splits into two diverging lineages. Evolutionary branching is possible near specific points in strategy space, where an invading mutant can coexist with the original strategy, and the two, initially very similar, strategies become increasingly distinct from one another while intermediate strategies are eliminated. Evolutionary branching is reminiscent of speciation and highlight the ecological conditions that favour the origin of new species.

The general framework of adaptive dynamics has been applied to many different ecological models in order to investigate evolution under specific ecological circumstances. Applications concern resource competition, interference competition, predation, host- parasite systems, cannibalism, mutualism, temporally stochastic and spatially heterogeneous environments, such as metapopulations, altruism, sexual selection, sex determination, mating systems, microbial ecology, etc.

There are many open questions in the general theory of adaptive dynamics. We are especially interested in the following topics:

Adaptive dynamics of function-valued traits
Presently, the theory of adaptive dynamics is best developed for one-dimensional strategies (i.e., the evolution of one continuous trait such as body size, etc.). In many situations it is more realistic to consider function-valued traits, which naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. We want to further develop methods for finding and analysing function-valued singular strategies.
Member involved: Kalle Parvinen
Collaborators: Ulf Dieckmann (IIASA, Austria), Mikko Heino (Bergen, Norway)

Evolutionary suicide
Many species that once lived on earth have gone extinct. A common explanation of such extinctions is that species have been unable to adapt to a rapid change in their environment. However, an alternative explanation exists: In some cases, even though the species in question could have persisted had it not changed its strategy, natural selection forces it to evolve, resulting in extinction. This phenomenon is known as evolutionary suicide. We want to understand better the theory and reasons behind this phenomenon, and to provide tools for management.
Member involved: Kalle Parvinen
Collaborator: Ulf Dieckmann (IIASA, Austria)

Adaptive dynamics in metapopulations


In " The Origin of Species " Darwin (1859) explained the unexpectedly wide geographical distribution of certain fresh-water species, by "...their having become fitted, in a manner highly useful to them, to short frequent migrations from pond to pond, or from stream to stream." It is clear from this quote that Darwin realized that dispersal is a life-history trait which is under selection and the change of which may have profound ecological implications. He also came very close to a verbal description of what is today known as a metapopulation. In general, a metapopulation is a population of local populations living in discrete habitat patches. By contrast, ordinary population models deal with homogeneous populations living in one habitat, and spatial structure has been neglected. As most natural populations have a hierarchical structure with several local populations, metapopulation models have a great potential of application to many types of biological systems.

Dispersal and local adaptation (specialization)
There are many ecological mechanisms which make dispersal advantageous. In a small local population, most individuals are related and therefore compete for resources among their own kin. By dispersing, an individual can avoid kin competition. Dispersal can also be seen as risk spreading. In case random catastrophes occur in the local populations, a non-dispersing species will eventually go extinct. A dispersing species can, however, be saved from such random extinction. Also if the local environment that individuals experience fluctuates in time, individuals may escape bad seasons by dispersing. There are also mechanisms making dispersal less advantageous. Dispersal often requires extra energy, which cannot be used for reproduction. Dispersal can also increases mortality risks. Also for an individual, which has specialized to the local environment, dispersing to a different environment is probably not beneficial, because by dispersing the individual may very well end up in a patch type to which it is not adapted. For a generalist individual, who performs reasonably well in all local environments, the benefit of dispersing is quite different.

As dispersal is a key trait in metapopulations, the evolution of dispersal has received a lot of interest, also among our group. Much of the literature is based on unstructured models without realistic local population growth and/or without catastrophes resulting in extinction of local populations. Including such phenomena is possible with structured metapopulation models, and therefore the group has studied them intensively. Also there is a lot of literature about the evolution of specialization. It is clear that these two life-history traits have a strong effect on the benefit of the other. However, there is only a very limited amount of research done about the co-evolution of dispersal and local adaptation, which is a target of the project. This work is needed in order to understand the dispersal and adaptation behaviour of different species observed in the nature.
Members involved:
Kalle Parvinen and Tuomas Nurmi

Modelling the American pika metapopulation
The American pika (Ochotona princeps) has become a model organism in the study of vertebrate population dynamics and life history evolution. Throughout their natural range in the Rocky Mountains and Sierra Nevada, pika populations are variously structured, from large, nearly contiguous talus habitats along portions of the Sierra Nevada crest, to almost perfect classical metapopulations, like that at Bodie, California. By using various metapopulation models, we want to understand how global climate change will affect the ecology and evolution of pikas.
Members involved: Kalle Parvinen and Anne Seppänen
Collaborator: John D. Nagy, Arizona, USA
Funding: Academy of Finland, project 128323

Computational Biomedicine


We develop computational data analysis tools and mathematical modelling methods for biomedical research. A specific focus is on analysing and interpreting data generated by modern high-throughput biotechnologies, such as microarrays, deep sequencing and mass-spectrometry-based proteomic assays. The eventual goal is to improve the diagnosis, prognosis and treatment of complex diseases, with a specific biomedical focus on Type 1 Diabetes.

While modern biotechnologies have enabled large-scale measurements of molecular events in health and disease, the experimental data alone are not sufficient for understanding the complex disease processes. Instead, computational methods and models are needed that can effectively integrate and analyse the experimental data so that meaningful interpretations can be made. Accordingly, mathematical modelling has become a central part of molecular biology and medicine as well as development of treatment and diagnosis strategies.

We have developed data integration and data-driven optimization approaches to improve the detection of reliable molecular markers and their interaction partners in global molecular networks. The eventual goal is to develop an integrative network-based modelling approach that can explain the observations as dynamic interaction networks and reveal the key molecular components and mechanisms underlying disease pathogenesis in a robust and unbiased manner.

Members involved:
Laura Elo, An Le Thi Thanh, Anna Pursiheimo, Maria Jaakkola, Teemu Daniel Laajala, Asta Laiho, Bishwa Ghimire, Deepankar Chakroborty, Fatemehsadat Seyednasrollah, Kalaimathy Singaravelu, Mehrad Mahmoudian, Rafael Alfredo Santos, Tomi Suomi

Selected collaborators:
Prof. Klaus Elenius, Prof. David Goodlett, Dr. Panu Jaakkola, Dr. Sirkku Jyrkkiö, Dr. Eija Korpelainen, Prof. Riitta Lahesmaa, Prof. Tarja Laitinen, Prof. Olli Nevalainen, Prof. Matti Poutanen, Prof. Olli Raitakari, Prof. Benno Schwikowski.

JDRF, Sigrid Juselius Foundation, Päivikki and Sakari Sohlberg Foundation, Diabetes Research Foundation, Academy of Finland, Yrjö Jahnsson Foundation, Otto A. Malm Foundation, K. Albin Johansson Foundation, CIMO, University of Turku Graduate School (UTUGS), Turku University Foundation

Multilevel modelling of cellular processes


The objective of the research is to develop a multilevel modelling framework for understanding the dynamic behaviour of cellular processes at systems-level, rather than investigating snapshots of individual genes, proteins or pathways separately. High-throughput experimental technologies are increasingly being used to illuminate the molecular mechanisms involved in the control of cellular systems in various conditions. However, interpretation of the resulting lists of genes or proteins remains a labour-intensive and error-prone task, because listing the individual elements alone can provide only a limited insight into the multitude of biological processes these elements participate in under different conditions and time-points. To facilitate distinguishing elements directly involved in a particular process from bystander elements, whose expression have been altered by secondary effects or technical artefacts, the experimental measurements can be mapped onto a global interaction networks that represent all the pertinent elements and their connections in the particular system. Due to the complexity of many biological processes, however, there is a great need for mathematical modelling and computational methods to integrate the system-level measurements and explain them as an interaction of key components and mechanisms regulating the system.

The appropriate description level of the models is strongly dependent on the experimental data and biological knowledge available as well as on the specific goals of the analysis. For instance, while detailed signalling models based e.g. on differential equations provide us a means of understanding the dynamic behaviour of the system and predicting its response to perturbations, extrapolating the standard kinetic models, which describe a single gene in one signalling pathway, to a larger system involving thousands of components and multitude of interacting pathways would render the model prohibitively complicated. Moreover, many cellular mechanisms and regulatory rules are still poorly understood, especially in higher organisms like humans, complicating such modeling work. Coarsegrained graph models, on the other hand, can efficiently provide us with valuable information about the global systems behaviour and modular organization by revealing dependence relationships among the experimental measurements and their contribution to the cellular processes of interest. Gradual focusing into the relevant and active sub-systems is an important prerequisite when eventually moving towards mechanistic modelling of the particular processes.

The multilevel modelling framework is organized through the following steps. After system manipulation (A), a set of high-throughput measurements, e.g. gene and/or protein expression patterns (B), are integrated and analysed together with global interaction networks connecting relevant components of the system. The next challenging problem concerns the dissection of the network into functional modules (C), i.e. groups of physically or functionally connected elements that work together to achieve the cellular functions of interest. These sub-systems can then be used as starting points for kinetic modelling and simulations studies (D), with the aim to define regulatory mechanisms most important for the particular process. The model predictions can finally be applied to distinguishing biomedical phenotypes or suggesting novel targets and their interactions (E), which are testable by subsequent experimentation. When applied to the system-level experimental data for human cell biology, that are becoming available at an increasing rate, such a predictive modelling approach can be used for identifying key players and their dynamic relationships responsible for multi-factorial behaviour in complex human disease networks, with the aim to provide systematic strategies to the identification of novel diagnostic and pharmaceutical targets for early detection and treatment of the diseases.

Members involved:
Tero Aittokallio, Marja Heiskanen, Teemu Daniel Laajala, Sebastian Okser, Johannes Tuikkala

Samuel Kaski (Department of Information and Computer Science, Helsinki University of Technology)
Eija Korpelainen (CSC – National IT Center for Science Ltd, Espoo)
Timo Koski (Department of Mathematics, Royal Institute of Technology, Stockholm)
Riitta Lahesmaa (Turku Centre for Biotechnology, University of Turku)
Olli Nevalainen (Department of Information Technology, University of Turku)
Tuula Nyman (Institute of Biotechnology, University of Helsinki)
Matej Orešic (Quantitative Biology and Bioinformatics, VTT Biotechnology)
Benno Schwikowski (Systems Biology Laboratory, Pasteur Institute, Paris)
Esa Tyystjärvi (Department of Biochemistry and Food Chemistry, University of Turku)
Esa Uusipaikka (Department of Statistics, University of Turku)
Mauno Vihinen (Institute of Medical Technology, University of Tampere)
Jan Westerholm (Department of Information Technologies, Åbo Akademi University)


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