Math Biology: Looking at the Future

(September 19,2012 - September 21,2012 )

MBI's 10th Anniversary Meeting The meeting will feature talks about areas in which exciting progress has been made in recent years and in which future advances can be expected. Speakers: Reka Albert (Penn State) Bill Bialek (Princeton) Emery Brown (MIT/ Mass General) Jim Collins (BU) Nicholas Jewell (Berkeley) Nancy Kopell (BU) Simon Levin (Princeton) Philip Maini (Oxford) Martin Nowak (Harvard - Keynote Speaker) Lior Pachter (Berkeley)

Accepted Speakers

Reka Albert
Department of Physics, Pennsylvania State University
William Bialek
Physics, Princeton University
Emery Brown
Department of Anesthesia, Massachusetts General Hospital
James Collins
HHMI and Department of Biomedical Engineering, Boston University
Ingrid Daubechies
Dept. of Mathematics, Duke University
Nick Jewell
Biostatistics and Statistics, University of California, Berkeley
Nancy Kopell
Department of Mathematics and Statistics, Boston University
Simon Levin
Department of Ecology & Evolutionary Biology, Princeton University
Philip Maini
Centre for Mathematical Biology, Mathematical Institute
Martin Nowak
Program for Evolutionary Dynamics, Harvard University
Lior Pachter
Department of Mathematics, University of California, Berkeley
Wednesday, September 19, 2012
Time Session
11:00 AM

Shuttle to MBI

12:45 PM
01:00 PM

Welcome and introductions

01:00 PM
02:00 PM
James Collins - Life Redesigned: The Emergence of Synthetic Biology
Synthetic biology is bringing together engineers, mathematicians and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, "green" means to fuel our car and clean our environment, and targeted therapies to attack "superbugs" and diseases such as cancer. In this talk, we highlight recent efforts to model and create synthetic gene networks and programmable cells, and discuss a variety of synthetic biology applications in biocomputing, biotechnology and biomedicine.
02:00 PM
02:30 PM

Break

02:30 PM
03:30 PM
Nick Jewell - The Missing Step: Statistical Inference from Big Data
The 20th century revolution in statistics focused on measurement, experimental design, modeling and computational issues in a world of "small" data where the number of observations and/or variables were typically limited and information available in single sources. Scientists face very different challenges in the current age where data is often streamed in real time, and the number of inputs, outputs or confounders are often massive. This presents challenges for reliable inference about "old" questions, while providing opportunities to investigate much more subtle issues about mechanisms of action, while reducing our reliance on unnecessary assumptions. We describe briefly some recent advances in data measurement, cleaning, and analysis that reflect these ideas, focusing finally on two applications (i) determining gene expression signatures of benzene exposure, and (ii) examining the influence of bisphenol A (BPA) in utero on patterns of weight gain in children.
03:30 PM
04:30 PM

Break

04:30 PM
05:30 PM
Martin Nowak - Evolution of eusociality
Eusociality is an advanced form of social organization, where some individuals reduce their reproductive potential to raise the offspring of others. Eusociality is rare but hugely successful: only about 2% of insects are eusocial but they represent 50% of the insect biomass. The biomass of ants alone exceeds that of all terrestrial non-human vertebrates combined. I will present a simple model for the origin of eusociality. In the solitary life style all offspring leave to reproduce. In the primitively eusocial life style some offspring stay and help raise further offspring. A standard natural selection equation determines which of those two reproductive strategies wins for a given ecology. The model makes simple and testable predictions without any need to evoke inclusive fitness theory. More generally, I will discuss the limitations of inclusive fitness theory. I will argue: once fitness is calculated in a standard model of natural selection every aspect of relatedness is included.

Further reading:

Nowak MA, CE Tarnita, EO Wilson (2010). The evolution of eusociality. Nature 466: 1057-1062. (see also: http://www.ped.fas.harvard.edu/IF_Statement.pdf)
Nowak MA, Highfield R (2011). SuperCooperators: Why We Need Each Other to Succeed. Free Press.
05:30 PM
06:30 PM

Reception (Jennings 001 Atrium) Hosted by the College of Arts and Sciences

06:30 PM

Shuttle pick-up from MBI

Thursday, September 20, 2012
Time Session
08:30 AM

Shuttle to MBI

09:00 AM
09:30 AM

Breakfast

09:30 AM
10:30 AM
Emery Brown - The Mathematics of the Unconscious Brain Under General Anesthesia
General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest mysteries of modern medicine. We have been using three experimental paradigms to study general anesthesia-induced loss of consciousness in humans: combined fMRI/EEG recordings, high-density EEG recordings and intracranial recordings. By using a wide array of signal processing techniques, these studies are allowing us to establish precise neurophysiological, neuroanatomical and behavioral correlates of unconsciousness under general anesthesia. Combined with our mathematical modeling work on how anesthetics act on neural circuits to produce the state of general anesthesia we are able to offer specific hypotheses as to how changes in level of activity in specific circuits lead to the unconscious state. We will discuss the relation between our findings and two other important altered states of arousal: sleep and coma. Our findings suggest that the state of general anesthesia is not as mysterious as currently believed. Statistical and mathematical analyses have played a key role in deciphering this mystery.
10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM
Nancy Kopell - Brain Rhythms in Health and Disease
The brain produces electrical activity whose spectral structure is highly correlated with cognitive state. Yet how rhythms participate in cognition, and how changes in rhythms in pathological states affect cognition, is just beginning to be explored. This talk will address several case studies comparing dynamics in normal and altered states, giving insight into the loss of consciousness, pathological rhythms in Parkinson's disease, and mechanisms for selective attention with implications for diseased states. It places these phenomena in the larger context of the multiple interactions of experimental neuroscience and mathematics, interactions that are certain to grow in the future.
12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Philip Maini - Modelling invasive processes in biology
The collective movement of cells in tissue is vital for normal development but also occurs in abnormal development, such as in cancer. We will review three different models: (i) A vertex-based model to describe cell motion in the early mouse embryo; (ii) A individual-based model for neural crest cell invasion; (iii) A model for acid-mediated tumour invasion.

In each case we shall use the model to answer important issues concerning biology. For example, in (i) we shall propose a role for rosette formation, in (ii) we propose that two cell types are necessary for successful invasion, and in (iii) we shall show how the model suggests possible therapeutic strategies for tumour control.
03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Reka Albert - The mathematics of biological regulatory networks
Interaction between gene products forms the basis of essential biological processes like signal transduction, cell metabolism or embryonic development. The variety of interactions between genes, proteins and molecules are well captured by network (graph) representations. Experimental advances in the last decade helped uncover the structure of many molecular-to-cellular level networks, such as protein interaction or metabolic networks. For other types of interaction and regulation inference methods based on indirect measurements have been used to considerable success. These advances mark the first steps toward a major goal of contemporary biology: to map out, understand and model in quantifiable terms the topological and dynamic properties of the various networks that control the behavior of the cell.

This talk will sample recent progress in two directions: intracellular network discovery and integration of different types of regulation (e.g. integration of metabolic and transcriptional networks), and connecting intra-cellular network structure, network dynamics and cellular behavior. A significant trust of the current research is to reveal or predict the topological or dynamic changes in the network responsible for abnormal behavior. This line of research will strenghten in time, and can be a fertile ground for mathematical biologists interested in adapting graph theory or nonlinear dynamical systems theory to biological systems.
04:30 PM
07:00 PM

Poster session/reception (Jennings 3rd floor)

07:00 PM

Shuttle pick-up from MBI

Friday, September 21, 2012
Time Session
08:30 AM

Shuttle to MBI

09:00 AM
09:30 AM

Breakfast

09:30 AM
10:30 AM
William Bialek - Birds, brains, and B-cells: Statistical mechanics for real biological networks
Most of the phenomena of life that attract our attention result from interactions among many components in a network. Examples include the interactions among neurons in the brain, among birds in a flock or fish in a school, and even the interactions among amino acids in a single protein. In all these cases there are "emergent" or collective behaviors that are properties of the network but not the individual components. In the physics of systems at thermal equilibrium, we have many examples of such emergent phenomena (some mundane, like the rigidity of solids, others more spectacular, such as superconductivity), and we have a language for describing such phenomena, statistical mechanics. There is a long standing intuition that this same language should be useful in thinking about collective phenomena in biological systems, an idea which is best developed in the context of neural networks, but one has to admit that much of what is done theoretically is not terribly well connected to experiment. I will review the argument that the maximum entropy construction gives us a way of going directly from real data to the more abstract statistical mechanics models, emphasizing the opportunities created by new, larger scale experiments. I'll start with flocks of birds, where the simplest version of these ideas seems remarkably successful. I'll then say a few words about proteins, using recent data on complete antibody repertoires in zebrafish as motivation. Finally, I'll discuss neurons, focusing on the response of the vertebrate retina to natural movies. Along the way I hope to make clear the connections between things that seem natural and interesting in the statistical mechanics context and things that seem relevant for the organism. Most startlingly, in all of these systems we find that the particular models which describe the real systems sit close to critical surfaces in the space of all possible models. I'll explain several different ways of seeing that this is true, why it is surprising, and speculate on why it is important. It certainly suggests that there is something deeper going on here, which we don't yet understand.
10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM
Lior Pachter - The human genome: 10 years later
The modern era of human genomics began ten years ago with the launch of the HapMap project following the publication of the first draft of the human genome. Although the sequencing of the genome was a major scientific achievement, it has become clear that naive analysis of sequence will not be sufficient to address the fundamental challenge in genomics: determination of the function of genes and the prediction of their regulatory dynamics.

We will discuss modern "Star-Seq" technologies that leverage cheap sequencing technology to enable high-throughput molecular biology and that are revealing, for the first time, the complexities of the genome and its dynamics at full resolution. The development, analysis and interpretation of the assays is based on a number of computational, statistical and mathematical primitives that we will survey.

The sequencing of the first vertebrate genomes coincided with the founding of the Mathematical Biosciences Institute, and we will highlight the huge impact that the marriage of mathematics and genomics has had on biology, with a view towards the exciting possibilities in the decade ahead.
12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Ingrid Daubechies - Dissimilarity distances between surfaces
We describe new distances between pairs of two-dimensional surfaces (embedded in three-dimensional space) that use both local structures and global information in the surfaces.

These are motivated by the need of biological morphologists to compare different phenotypical structures. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This necessity renders these studies inaccessible to nonmorphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns.

Unlike other algorithms presented for morphological correspondences, our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces.

We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.
03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Simon Levin - Challenges In Mathematical Ecology: Scaling And Collective Phenomena
The subject of mathematical ecology is one of the oldest in mathematical biology, having its formal roots a century ago in the work of the great mathematician Vito Volterra, with links, some long before, to demography, epidemiology and genetics. Classical challenges remain in understanding the dynamics of populations and connections to the structure of ecological communities. However, the scales of integration and scope for interdisciplinary work have increased dramatically in recent years. Metagenomic studies have provided vast stores of information on the microscopic level, which cry out for methods to allow scaling to the macroscopic level of ecosystems, and for understanding biogeochemical cycles and broad ecosystem patterns as emergent phenomena; indeed, global change has pushed that mandate well beyond the ecosystem to the level of the biosphere. Secondly, the recognition of the importance of collective phenomena, from the formation of biofilms to the dynamics of vertebrate flocks and schools to collective decision-making in human populations poses important and exciting opportunities for mathematicians and physicists to shed light. Finally, from behavioral and evolutionary perspectives, these collectives display conflict of purpose or fitness across levels, leading to game-theoretic problems in understanding how cooperation emerges in Nature, and how it might be realized in dealing with problems of the Global Commons. This lecture will attempt to weave these topics together and both survey recent work, and offer challenges for how mathematics can contribute to open problems.
04:30 PM
05:30 PM

Break

05:30 PM
06:30 PM

Cocktails at Faculty Club

06:30 PM
09:00 PM

Banquet at Faculty Club

09:00 PM

Shuttle from Faculty Club to hotel

Name Email Affiliation
Albert, Reka ralbert@phys.psu.edu Department of Physics, Pennsylvania State University
Altrock, Philipp altrock@evolbio.mpg.de Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology
Bayleyegn, Yibeltal 211543822@ukzn.ac.za Mathematical Sciences, University of KwaZulu-Natal
Beckman, Noelle nbeckman2@unl.edu Mathematical Biosciences Institute, The Ohio State University
Bergelson, Vitaly vitaly@math.ohio-state.edu Mathematics, The Ohio State University
Beri, Arjun beri.3@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Best, Janet jbest@math.ohio-state.edu Mathematics, The Ohio State University
Bialek, William wbialek@princeton.edu Physics, Princeton University
Brown, Emery enb@neurostat.mit.edu Department of Anesthesia, Massachusetts General Hospital
Brown, Patrick patrickjonbrown@gmail.com Food, Agricultural, and Biological Engineering, The Ohio State University
Cardona, Jorge jcardona@math.miami.edu Mathematics, University of Miami
Chen, Duan chen.906@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Cherif, Alhaji cherif@maths.ox.ac.uk Mathematical Institute, University of Oxford
Chifman, Julia jchifman@wakehealth.edu Cancer Biology, Wake Forest School of Medicine
Cipra, Barry bcipra@rconnect.com Freelance Mathematics Writer
Cogdell, James cogdell@math.ohio-state.edu Mathematics, The Ohio State University
Collins, James jcollins@bu.edu HHMI and Department of Biomedical Engineering, Boston University
Coskun, Huseyin hcoskun@math.ohio-state.edu Department of Mathematics, The Ohio State University
Cracium, Gheorghe craciun@math.wisc.edu Dept. of Mathematics, University of Wisconsin-Madison
Curtis, Peter curtis.7@osu.edu EEOB, The Ohio State University
Dabaghian, Yuri dabaghia@bcm.edu CAAM, Rice University
Daubechies, Ingrid ingrid@math.duke.edu Dept. of Mathematics, Duke University
Dawes, Adriana dawes.33@osu.edu Department of Mathematics / Department of Molecular Genetics, The Ohio State University
Day, Judy judyday@gmail.com Department of Mathematics, University of Tennessee
Diekman, Casey cdiekman@mbi.osu.edu MBI, The Ohio State University
Dougherty, Daniel doughe57@msu.edu Lyman Briggs School of Science, Michigan State University
Eisenberg, Marisa meisenberg@mbi.osu.edu MBI - Postdoc, The Ohio State University
Enciso, German enciso@uci.edu Mathematics, University of California, Irvine
Epstein, Irving epstein@brandeis.edu Chemistry, Brandeis University
Federico, Paula pfederic@capital.edu Mathematical Biosciences Institute, The Ohio State University
Feinberg, Martin feinberg.14@osu.edu Chemical Engineering & Mathematics, The Ohio State University
Friedman, Avner afriedman@math.ohio-state.edu Department of Mathematics, The Ohio State University
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Grajdeanu, Paula paulabudu@gmail.com Mathematics, Shenandoah University
Gross, Louis gross@tiem.utk.edu Mathematics/Ecology & Evolutionary Biology, University of Tennessee
Gulenko, Maria maria.gulenko@gmail.com Mathematics, University of Miami
Guo, Yixin yixin@math.drexel.edu Department of Mathematics, Drexel University
Hamilton, Ian hamilton.598@osu.edu EEOB/Mathematics, The Ohio State University
Handelman, Sam shandelman@mbi.osu.edu Pharmacology, The Ohio State University
Herbers, Joan herbers.4@osu.edu Biology, The Ohio State University
Hinkelmann, Franziska hinkelmann.1@mbi.osu.edu MBI, The Ohio State University
Holmes, William holmes@ohio.edu Biological Sciences, Ohio University
Horn, Mary Ann mhorn@nsf.gov Division of Mathematical Sciences, National Science Foundation
Hurtado, Paul hurtado.10@mbi.osu.edu Mathematical Biosciences Institute & Aquatic Ecology Laboratory, The Ohio State University
Jain, Harsh hjain@mbi.osu.edu Department of Mathematics, Florida State University
Jewell, Nicholas jewell@uclink.berkeley.edu Biostatistics and Statistics, University of California, Berkeley
Just, Winfried mathjust@gmail.com Mathematics, Ohio University
Kang, Hye-Won kang.235@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Kaper, Hans kaper@mcs.anl.gov n/a, Mathematics and Climate Research Network
Kopell, Nancy nk@bu.edu Department of Mathematics and Statistics, Boston University
Koslicki, David koslicki@math.psu.edu Mathematics, Drexel University
Lam, Adrian lam.184@math.ohio-state.edu Mathematical Biosciences Institute, The Ohio State University
Leander, Rachel rleander@mbi.osu.edu Mathematics, Middle Tennessee State University
Lee, Shernita shernita@vbi.vt.edu Genetics, Bioinformatics, and Computational Biology, Virginia Polytechnic Institute and State University
Levin, Simon slevin@princeton.edu Department of Ecology & Evolutionary Biology, Princeton University
Liao, Kang-Ling kangling.am95g@nctu.edu.tw Mathematical Biosciences Institute, The Ohio State University
Lim, Sookkyung limsk@math.uc.edu Department of Mathematical Sciences, University of Cincinnati
Lin, Shili shili@stat.osu.edu Statistics, The Ohio State University
Lo, Wing Cheong (Jon) lo.75@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Lockhart, Deborah dlockhar@nsf.gov Division of Information and Intelligent Systems, National Science Foundation
Luo, Shishi szl@math.duke.edu Mathematics, Duke University
Maini, Philip maini@maths.ox.ac.uk Centre for Mathematical Biology, Mathematical Institute
Makrides, Elizabeth elizabeth_makrides@brown.edu Division of Applied Mathematics, Brown University
Marschall, Elizabeth marschall.2@osu.edu Evolution, Ecology, and Organismal Biology, The Ohio State University
Matamba Messi, Leopold lemat@uga.edu Mathematical Biosciences Institute, The Ohio State University
Miura, Robert miura@njit.edu Department of Mathematical Sciences, New Jersey Institute of Technology
Murrugarra, David davidmur@vbi.vt.edu Mathematics, Georgia Tech
Nevai, Andrew anevai@math.ucf.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Newby, Jay newby@maths.ox.ac.uk Mathematical Biosciences Institute, The Ohio State University
Nikitin, Vyacheslav nikitin.4@osu.edu Mathematical Psychology, The Ohio State University
Nowak, Martin martin_nowak@harvard.edu Program for Evolutionary Dynamics, Harvard University
Pachter, Lior lpachter@math.berkeley.edu Department of Mathematics, University of California, Berkeley
Park, Jincheol park.jincheol@gmail.com MBI, The Ohio State University
Reed, Michael reed@math.duke.edu Mathematics, Duke University
Rejniak, Katarzyna Kasia.Rejniak@moffitt.org H. Lee Moffitt Cancer Center & Research Institute, H. Lee Moffitt Cancer Center & Research Institute
Rempe, Michael mrempe@whitworth.edu Mathematics and Computer Science, Whitworth University
Robertson, Suzanne srobertson@mbi.osu.edu Department of Mathematics and Applied Mathematics, Virginia Commonwealth University
Rubin, Jonathan rubin@math.pitt.edu Department of Mathematics, University of Pittsburgh
Santosa, Fadil santosa@ima.umn.edu Insitute for Mathematics and its Applications, University of Minnesota
Schmidt, Deena dschmidt@case.edu Department of Biology & Department of Mathematics, Case Western Reserve University
Schugart, Richard richard.schugart@wku.edu Department of Mathematics, Western Kentucky University
Schwemmer, Michael mschwemm@princeton.edu Program in Applied and Computational Mathematics, Princeton University
Shtylla, Blerta shtylla.1@mbi.osu.edu Mathematics and Statistics, Mount Holyoke College
Spardy, Lucy LES65@pitt.edu Mathematical Biosciences Institute, The Ohio State University
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematics, Cleveland State University
Srinivasan, Manoj srinivasan.88@osu.edu Mechanical and Aerospace Engineering , The Ohio State University
Stewart, Ian I.N.Stewart@warwick.ac.uk Dept. of Mathematics, University of Warwick
Stigler, Brandilyn bstigler@smu.edu Mathematics, Southern Methodist University
Tchepmo Djomegni, Patrick 211507806@stu.ukzn.ac.za Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal
Terman, David terman@math.ohio-state.edu Mathemathics Department, The Ohio State University
Thompson, Daniel thompson@math.osu.edu Mathematics, The Ohio State University
Tian, Jianjun Paul jtian@wm.edu Mathematics, College of William and Mary
Tien, Rebecca rtien@mbi.osu.edu Department of Evolution, Ecology, and Organismal Biology, The Ohio State University
Tien, Joe jtien@math.ohio-state.edu Department of Mathematics, The Ohio State University
Ullah, Ghanim ullah.10@osu.edu Theoretical Biology, Los Alamos National Laboratory
Vogt Geisse, Katia kvogtgei@math.purdue.edu Mathematics, Purdue University
Wang, Jin j3wang@odu.edu Mathematics, Old Dominion University
Wright, Geraldine jeri.wright@ncl.ac.uk School of Biology, Newcastle University
Xing, Jianhua jxing@vt.edu Biological Sciences, Virginia Bioinformatics Institute, Virginia Tech
Xue, Chuan cxue@math.osu.edu Department of Mathematics, The Ohio State University
Young, Todd youngt@ohio.edu Mathematics, Ohio University
Zhao, Kun kun-zhao@uiowa.edu Mathematics, Tulane University
Zhao, Di zhao.1029@osu.edu Psychology, The Ohio State University
Zhou, Ying yzhou@amath.washington.edu Department of Applied Mathematics, University of Washington
Zhu, Hong hzhu@cph.osu.edu Biostatistics, College of Public Health, The Ohio State University
The mathematics of biological regulatory networks
Interaction between gene products forms the basis of essential biological processes like signal transduction, cell metabolism or embryonic development. The variety of interactions between genes, proteins and molecules are well captured by network (graph) representations. Experimental advances in the last decade helped uncover the structure of many molecular-to-cellular level networks, such as protein interaction or metabolic networks. For other types of interaction and regulation inference methods based on indirect measurements have been used to considerable success. These advances mark the first steps toward a major goal of contemporary biology: to map out, understand and model in quantifiable terms the topological and dynamic properties of the various networks that control the behavior of the cell.

This talk will sample recent progress in two directions: intracellular network discovery and integration of different types of regulation (e.g. integration of metabolic and transcriptional networks), and connecting intra-cellular network structure, network dynamics and cellular behavior. A significant trust of the current research is to reveal or predict the topological or dynamic changes in the network responsible for abnormal behavior. This line of research will strenghten in time, and can be a fertile ground for mathematical biologists interested in adapting graph theory or nonlinear dynamical systems theory to biological systems.
Birds, brains, and B-cells: Statistical mechanics for real biological networks
Most of the phenomena of life that attract our attention result from interactions among many components in a network. Examples include the interactions among neurons in the brain, among birds in a flock or fish in a school, and even the interactions among amino acids in a single protein. In all these cases there are "emergent" or collective behaviors that are properties of the network but not the individual components. In the physics of systems at thermal equilibrium, we have many examples of such emergent phenomena (some mundane, like the rigidity of solids, others more spectacular, such as superconductivity), and we have a language for describing such phenomena, statistical mechanics. There is a long standing intuition that this same language should be useful in thinking about collective phenomena in biological systems, an idea which is best developed in the context of neural networks, but one has to admit that much of what is done theoretically is not terribly well connected to experiment. I will review the argument that the maximum entropy construction gives us a way of going directly from real data to the more abstract statistical mechanics models, emphasizing the opportunities created by new, larger scale experiments. I'll start with flocks of birds, where the simplest version of these ideas seems remarkably successful. I'll then say a few words about proteins, using recent data on complete antibody repertoires in zebrafish as motivation. Finally, I'll discuss neurons, focusing on the response of the vertebrate retina to natural movies. Along the way I hope to make clear the connections between things that seem natural and interesting in the statistical mechanics context and things that seem relevant for the organism. Most startlingly, in all of these systems we find that the particular models which describe the real systems sit close to critical surfaces in the space of all possible models. I'll explain several different ways of seeing that this is true, why it is surprising, and speculate on why it is important. It certainly suggests that there is something deeper going on here, which we don't yet understand.
The Mathematics of the Unconscious Brain Under General Anesthesia
General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest mysteries of modern medicine. We have been using three experimental paradigms to study general anesthesia-induced loss of consciousness in humans: combined fMRI/EEG recordings, high-density EEG recordings and intracranial recordings. By using a wide array of signal processing techniques, these studies are allowing us to establish precise neurophysiological, neuroanatomical and behavioral correlates of unconsciousness under general anesthesia. Combined with our mathematical modeling work on how anesthetics act on neural circuits to produce the state of general anesthesia we are able to offer specific hypotheses as to how changes in level of activity in specific circuits lead to the unconscious state. We will discuss the relation between our findings and two other important altered states of arousal: sleep and coma. Our findings suggest that the state of general anesthesia is not as mysterious as currently believed. Statistical and mathematical analyses have played a key role in deciphering this mystery.
Life Redesigned: The Emergence of Synthetic Biology
Synthetic biology is bringing together engineers, mathematicians and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, "green" means to fuel our car and clean our environment, and targeted therapies to attack "superbugs" and diseases such as cancer. In this talk, we highlight recent efforts to model and create synthetic gene networks and programmable cells, and discuss a variety of synthetic biology applications in biocomputing, biotechnology and biomedicine.
Dissimilarity distances between surfaces
We describe new distances between pairs of two-dimensional surfaces (embedded in three-dimensional space) that use both local structures and global information in the surfaces.

These are motivated by the need of biological morphologists to compare different phenotypical structures. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This necessity renders these studies inaccessible to nonmorphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns.

Unlike other algorithms presented for morphological correspondences, our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces.

We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.
The Missing Step: Statistical Inference from Big Data
The 20th century revolution in statistics focused on measurement, experimental design, modeling and computational issues in a world of "small" data where the number of observations and/or variables were typically limited and information available in single sources. Scientists face very different challenges in the current age where data is often streamed in real time, and the number of inputs, outputs or confounders are often massive. This presents challenges for reliable inference about "old" questions, while providing opportunities to investigate much more subtle issues about mechanisms of action, while reducing our reliance on unnecessary assumptions. We describe briefly some recent advances in data measurement, cleaning, and analysis that reflect these ideas, focusing finally on two applications (i) determining gene expression signatures of benzene exposure, and (ii) examining the influence of bisphenol A (BPA) in utero on patterns of weight gain in children.
Brain Rhythms in Health and Disease
The brain produces electrical activity whose spectral structure is highly correlated with cognitive state. Yet how rhythms participate in cognition, and how changes in rhythms in pathological states affect cognition, is just beginning to be explored. This talk will address several case studies comparing dynamics in normal and altered states, giving insight into the loss of consciousness, pathological rhythms in Parkinson's disease, and mechanisms for selective attention with implications for diseased states. It places these phenomena in the larger context of the multiple interactions of experimental neuroscience and mathematics, interactions that are certain to grow in the future.
Challenges In Mathematical Ecology: Scaling And Collective Phenomena
The subject of mathematical ecology is one of the oldest in mathematical biology, having its formal roots a century ago in the work of the great mathematician Vito Volterra, with links, some long before, to demography, epidemiology and genetics. Classical challenges remain in understanding the dynamics of populations and connections to the structure of ecological communities. However, the scales of integration and scope for interdisciplinary work have increased dramatically in recent years. Metagenomic studies have provided vast stores of information on the microscopic level, which cry out for methods to allow scaling to the macroscopic level of ecosystems, and for understanding biogeochemical cycles and broad ecosystem patterns as emergent phenomena; indeed, global change has pushed that mandate well beyond the ecosystem to the level of the biosphere. Secondly, the recognition of the importance of collective phenomena, from the formation of biofilms to the dynamics of vertebrate flocks and schools to collective decision-making in human populations poses important and exciting opportunities for mathematicians and physicists to shed light. Finally, from behavioral and evolutionary perspectives, these collectives display conflict of purpose or fitness across levels, leading to game-theoretic problems in understanding how cooperation emerges in Nature, and how it might be realized in dealing with problems of the Global Commons. This lecture will attempt to weave these topics together and both survey recent work, and offer challenges for how mathematics can contribute to open problems.
Modelling invasive processes in biology
The collective movement of cells in tissue is vital for normal development but also occurs in abnormal development, such as in cancer. We will review three different models: (i) A vertex-based model to describe cell motion in the early mouse embryo; (ii) A individual-based model for neural crest cell invasion; (iii) A model for acid-mediated tumour invasion.

In each case we shall use the model to answer important issues concerning biology. For example, in (i) we shall propose a role for rosette formation, in (ii) we propose that two cell types are necessary for successful invasion, and in (iii) we shall show how the model suggests possible therapeutic strategies for tumour control.
Evolution of eusociality
Eusociality is an advanced form of social organization, where some individuals reduce their reproductive potential to raise the offspring of others. Eusociality is rare but hugely successful: only about 2% of insects are eusocial but they represent 50% of the insect biomass. The biomass of ants alone exceeds that of all terrestrial non-human vertebrates combined. I will present a simple model for the origin of eusociality. In the solitary life style all offspring leave to reproduce. In the primitively eusocial life style some offspring stay and help raise further offspring. A standard natural selection equation determines which of those two reproductive strategies wins for a given ecology. The model makes simple and testable predictions without any need to evoke inclusive fitness theory. More generally, I will discuss the limitations of inclusive fitness theory. I will argue: once fitness is calculated in a standard model of natural selection every aspect of relatedness is included.

Further reading:

Nowak MA, CE Tarnita, EO Wilson (2010). The evolution of eusociality. Nature 466: 1057-1062. (see also: http://www.ped.fas.harvard.edu/IF_Statement.pdf)
Nowak MA, Highfield R (2011). SuperCooperators: Why We Need Each Other to Succeed. Free Press.
The human genome: 10 years later
The modern era of human genomics began ten years ago with the launch of the HapMap project following the publication of the first draft of the human genome. Although the sequencing of the genome was a major scientific achievement, it has become clear that naive analysis of sequence will not be sufficient to address the fundamental challenge in genomics: determination of the function of genes and the prediction of their regulatory dynamics.

We will discuss modern "Star-Seq" technologies that leverage cheap sequencing technology to enable high-throughput molecular biology and that are revealing, for the first time, the complexities of the genome and its dynamics at full resolution. The development, analysis and interpretation of the assays is based on a number of computational, statistical and mathematical primitives that we will survey.

The sequencing of the first vertebrate genomes coincided with the founding of the Mathematical Biosciences Institute, and we will highlight the huge impact that the marriage of mathematics and genomics has had on biology, with a view towards the exciting possibilities in the decade ahead.
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The Mathematics of the Unconscious Brain Under General Anesthesia
Emery Brown General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress

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Evolution of eusociality
Martin Nowak Eusociality is an advanced form of social organization, where some individuals reduce their reproductive potential to raise the offspring of others. Eusociality is rare but hugely successful: only about 2% of insects are eusocial but they represent 5

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Birds, brains, and B-cells: Statistical mechanics for real biological networks
William Bialek Most of the phenomena of life that attract our attention result from interactions among many components in a network. Examples include the interactions among neurons in the brain, among birds in a flock or fish in a school, and even the interactions

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Life Redesigned: The Emergence of Synthetic Biology
James Collins Synthetic biology is bringing together engineers, mathematicians and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-eng

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The human genome: 10 years later
Lior Pachter The modern era of human genomics began ten years ago with the launch of the HapMap project following the publication of the first draft of the human genome. Although the sequencing of the genome was a major scientific achievement, it has become clear

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Modelling invasive processes in biology
Philip Maini The collective movement of cells in tissue is vital for normal development but also occurs in abnormal development, such as in cancer. We will review three different models: (i) A vertex-based model to describe cell motion in the early mouse embryo;

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Challenges In Mathematical Ecology: Scaling And Collective Phenomena
Simon Levin The subject of mathematical ecology is one of the oldest in mathematical biology, having its formal roots a century ago in the work of the great mathematician Vito Volterra, with links, some long before, to demography, epidemiology and genetics. Clas

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The Missing Step: Statistical Inference from Big Data
Nicholas Jewell The 20th century revolution in statistics focused on measurement, experimental design, modeling and computational issues in a world of "small" data where the number of observations and/or variables were typically limited and information ava

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The mathematics of biological regulatory networks
Reka Albert Interaction between gene products forms the basis of essential biological processes like signal transduction, cell metabolism or embryonic development. The variety of interactions between genes, proteins and molecules are well captured by network (gr