Resources

We are committed to open sharing of our data and methodologies. Here, we provide software codes, application notes, and datasets including atomic structures. In some cases as noted, this includes materials that are of high quality, but were ultimately extraneous and irrelevant to our papers and thus remain unpublished. Contact us for requests for physical materials…DNA constructs, cells, Drosophila strains, and other reagents.

Quantitative Biology: From Complexity to Simplicity

The term “complexity” is routinely used to characterize biological systems. But what does it mean, precisely? We have designed a course that comprises lectures that introduces the basic process of data analysis, modeling, and formulation of theory, and includes a number of case studies in which understanding of biological systems has emerged through the application of this approach. An overall theme is to think deeply about a rigorous definition of system complexity and to learn about strategies to rationally address such systems. As a counterpoint, we begin with the study of linear systems and the rich mathematical foundations for understanding and predicting their behaviors. We then move to non-linear systems; what makes them complex and difficult, and why is the mathematical treatment of these systems so much harder? We will explore several biological examples of non-linearity in fields ranging from structural biology to evolution, ending ultimately with a proposed general definition of complexity in biology and an operational strategy for studying such systems.

Part 1: Introduction

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(1) What is complexity? A classification of problems and current status. An introduction to the principles, process, and goals of modeling with examples from simple kinetic systems.

A classification of problems and current status. The principles, process, and goals of modeling with examples from simple kinetic systems. [PDF]

Part 2: Linear Systems

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(2) Linear systems, part 1. A microscopic and macroscopic treatment. General principles of linearity, graphical approaches to “seeing” system behavior, and the concept of transforms. The fundamental decomposability of linear systems.

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(3) Linear systems, part 2. Theory of linear systems and solutions to first, second order, and higher-order systems. The space of possible solutions for 2D ODE systems. The designability of linear systems.

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(4) Stochastic models. Models at the limit of small numbers of interacting components. The importance of fluctuations, and examples.

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(5) Diffusion and driving forces. The phenomenology of diffusion, microscopic and macroscopic descriptions. Solutions to the diffusion equation. The underlying thermodynamic potentials, and reaction diffusion equations.

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(6) The theory of diffraction. The theory of light scattering, and the spatial Fourier transform. Again the power of linearity even in face of large numbers of variables..

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(7) Patterns in large data. Linear decomposition, and its applications and interpretations. The concepts of dimension reduction and effective variables.

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Part 3: Non-Linear Systems

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(8) Introduction to non-linear systems…what is non-linearity? The complexity possible from even simple non-linear systems. Various manifestations in biology.

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(9) A detailed example, part 1…the van der Pol non-linear oscillator: theory, simulation, and analysis. Building a physical implementation.

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(10) A detailed example, part 2…construction and experimental analysis of a van der Pol oscillator at the linear and non-linear limit.

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(11) Simple non-linear systems…the MAP kinase switch. The basic origins of bistability and irreversibility. Again, “seeing” system behavior graphically..

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(12) Mesoscale non-linear systems…the visual system in invertebrates. The stochastic relaxation oscillator, its analysis and characteristics. Relationship to other systems.

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(13) Large non-linear systems…the problem of protein structure and function. Introduction to statistical approaches to decompose and build intuition in large non-linear problems.

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(14) Epistasis. The principles of genetic epistasis and its role in shaping both function and evolution. Turned around, also the physical and evolutionary constraints on epistasis. More transforms.

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(15) Information Theory. Coupled actions, quantitative descriptions of “information”, and the notion of mutual information. What is a good information theory for biology?

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Part 4: Conclusion and next steps

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(16) So, what is complexity? A proposal for a general strategy for studying “complex” biological systems.

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Center for Physics of Evolution

Biochemistry & Molecular Biology The Institute for Molecular Engineering The University of Chicago 929 E. 57th Street Chicago, IL 60637