Mathematics and Statistics beta

Mathematical analysis is crucial to the data-rich science of biology

Biology has become a data rich science. The amount and complexity of data produced in biology now exceeds that of any other scientific field. As a consequence, statistical analysis and mathematical modeling are becoming ever more crucial ingredients in many areas of biology, including genetics, cell biology, structural biology, development and evolution.

EMBL units researching Mathematics and Statistics

Many groups at EMBL include researchers with a focus on mathematics and statistics, and several groups specialise in these fields:


Gerstung Group

Computational cancer biology

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We have developed statistical models for relating different layers of genomic, molecular and clinical data to extract the precise connections among variables to understand the connection of genotype and phenotype. Moreover we have been working on biostatistical models and informatics tools for predicting outcome based on comprehensive high-dimensional data sets.

Another area of our research are the evolutionary dynamics of cancer. The process of developing cancer is driven by mutation and selection; hence the language to quantify that process is that of evolutionary dynamics. Deep sequencing unmasks the clonal composition of a cancer, which sheds some light on its evolutionary history. Accurate detection of subclonal mutations and reconstruction of phylogenies requires, however, accurate bioinformatics tools that we are actively developing.

Selected publications

Cancer evolution: mathematical models and computational inference

Beerenwinkel N, Schwarz RF, Gerstung M, Markowetz F.

Systematic Biology 2015

64:e1-e25 Europe PMC

Subclonal variant calling with multiple samples and prior knowledge

Gerstung M, Papaemmanuil E, Campbell PJ.

Bioinformatics 2014

30:1198-1204 Europe PMC

Clinical and biological implications of driver mutations in myelodysplastic syndromes

Papaemmanuil E, Gerstung M, Malcovati L, et al.

Blood 2013

122:3616-27 Europe PMC


Goldman Group

Evolutionary analysis of DNA and amino acid sequences

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We develop and use mathematical probabilistic models that describe DNA sequence evolution, DNA sequencing, and storage of digital information in DNA. The main focus of the group has traditionally been the development of models that describe how DNA changes through time during the course of evolution.

Our aim is to improve inference of evolutionary histories (phylogenies), and ancient genomes (ancestral sequence reconstruction), as well as to improve our capabilities at detecting the footprint of natural selection from genomic data.

More recently, the group has expanded its focus over computational and mathematical methods to improve the storage of digital information in DNA ─ a technology that promises to revolutionize how we store data in the long term. We are also developing probabilistic and information theoretical models to improve the efficiency of DNA sequencing ─ in particular nanopore sequencing.

Selected publications

Modeling structural constraints on protein evolution via side-chain conformational states

Perron, U., Kozlov, A. M., Stamatakis, A., Goldman, N., & Moal, I. H.

Molecular Biology and Evolution 2019

36, 2086-2103

More on the best evolutionary rate for phylogenetic analysis

Klopfstein, S., Massingham, T., & Goldman, N.

Systematic Biology 2017

66, 769-785

Maximum likelihood phylogenetic inference is consistent on multiple sequence alignments, with or without gaps

Truszkowski, J., & Goldman, N.

Systematic Biology 2016

65, 328-333


Huber Group

Statistical Computing and Mathematical Modeling

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Progress in biology is driven by technology. High throughput sequencing and microscopy require sophisticated statistical and computational operations in order to exploit their potential. To understand (and, eventually, manipulate) biological systems, all available data about them need to be integrated into computable maps and mathematical models. Ideas and techniques from physics, mathematics, statistics, computer science and engineering are the crucial drivers for our research.

Modern Statistics for Modern Biology

Selected publications

Covariate powered cross-weighted multiple testing

Nikolaos Ignatiadis, Wolfgang Huber

2017

arXiv

Adaptive penalization in high-dimensional regression and classification with external covariates using variational Bayes

Britta Velten and Wolfgang Huber

Biostatistics 2019

DOI
More publications

Marioni Group

Computational and evolutionary genomics

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High-throughput sequencing is allowing the genome, transcriptome and epigenome of an enormous range of species, including model and non-model organisms, to be studied in exquisite detail.

Moreover, as technology develops further, we will move from studying populations of cells to studying regulatory processes at the single-cell level ─ this will enable numerous insights into developmental processes (e.g. embryogenesis and early-development), neurological processes (e.g., a fine-grained map of gene expression within specific brain regions), and the way in which tumours develop.

However, to make the most of these opportunities, appropriate computational tools for managing, analyzing, visualizing and downloading the data are essential. With this in mind, our work focuses on the development of statistical methods that will exploit these data to the fullest extent.

Selected publications

RNA-seq: An assessment of technical reproducibility and comparison with gene expression arrays

Marioni J.C., Mason C.E., Mane S.M., Stephens M., Gilad Y.

Genome Res. 2008

Sep; 18(9):1509-17 PDF

Understanding mechanisms underlying human gene expression variation with RNA sequencing

Pickrell J.K., Marioni J.C., Pai A.A., Degner K.F., Engelhardt E.B., Nkadori E., Veyrieras J-B., Stephens M., Gilad Y., Pritchard J.K.

Nature 2010

Apr; 464(7289):768-72 PDF

Genomic-scale capture and sequencing of endogenous DNA from feces

Perry G.H.*, Marioni J.C.*, Melsted P., Gilad Y.

Molecular Ecology 2010

(in press) (* joint first authors)


Patil Group

Architecture and regulation of metabolic networks

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Mathematical and statistical tools provide essential theoretical basis to our quest to uncover basic principles underlying operation of cellular metabolic networks. To this end, we are developing new model formulations and algorithms that are motivated by the underlying biological questions.

Holistic understanding of the functioning and regulation of complex metabolic networks requires identifying biologically meaningful operating points in a high-dimensional space. We use linear and mixed-integer linear programming (MILP) tools to tackle the resulting modeling challenges.

We have developed several in silico models for quantitatively predicting metabolic phenotypes from a defined genotype. To enhance the predictive power of metabolic models, we are also developing methods to integrate genomic, transcriptomic, proteomic and metabolomic information.

Selected publications

Uncovering transcriptional regulation of metabolism by using metabolic network topology

Patil, K.R. & Nielsen, J.

Proc Natl Acad Sci USA 2005

Feb 22;102(8):2685-9. Epub 2005 Feb 14 PubMed

Metabolic network topology reveals transcriptional regulatory signatures of type 2 diabetes

Zelezniak, A., Pers, T.H., Soares, S., Patti, M.E. & Patil, K.R.

PLoS Comput Biol. 2010

Apr 1;6(4):e1000729 PubMed

Improved vanillin production in baker's yeast through in silico design

Brochado, A.R., Matos, C., Moller, B.L., Hansen, J., Mortensen, U.H. & Patil, K.R

Microb Cell Fact. 2010

2010 Nov 8;9(1):84 PubMed


Stegle Group

Statistical genomics and systems genetics

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Our interest lies in computational approaches to unravel the genotype– phenotype map on a genome-wide scale. How do genetic background and environment jointly shape phenotypic traits or causes diseases? How are genetic and external factors integrated at different molecular layers, and how variable are these molecular readouts between individual cells?

We use statistics as our main tool to answer these questions. To make accurate inferences from high-dimensional ‘omics datasets, it is essential to account for biological and technical noise and to propagate evidence strength between different steps in the analysis. To address these needs, we develop statistical analysis methods in the areas of gene regulation, genome wide association studies (GWAS) and causal reasoning in molecular systems.

Our methodological work ties in with experimental collaborations and we are actively developing methods to fully exploit large-scale datasets that are obtained using the most recent technologies. In doing so, we derive computational methods to dissect phenotypic variability at the level of the transcriptome and the proteome and we derive new tools for single-cell biology.

Selected publications

Computational analysis of cell-to-cell heterogeneity in single-cell RNA-sequencing data reveals hidden subpopulations of cells

Buttner, F. et al.

Nat Biotech 2015

33, 155-160 DOI

Warped linear mixed models for the genetic analysis of transformed phenotypes

Fusi, N. et al.

Nat Comm 2014

5, 5890 DOI

Single-cell genome-wide bisulfite sequencing for assessing epigenetic heterogeneity

Smallwood, S. et al.

Nat Meth 2014

11, 817-820 DOI

Other Research Topics

From microscopy to mycology, from development to disease modelling, EMBL researchers cover a wide range of topics in the biological sciences.