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.
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 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.
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.
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.
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.
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.
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.
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.
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.