Cells and Materials: At the Interface between Mathematics, Biology and Engineering
March 13 - June 16, 2006
Background and Motivation
"The most exciting science in the 21st century is likely to evolve among, not within, traditional disciplines" (Sung et al. 2003, Science 301:1485). Bioengineering programs have transformed from training of engineers to work in hospitals in the 60's and 70's, to training of principal investigators about scientific problems in medicine and biology. This transition has paralleled unprecedented advances in the medical sciences, basic sciences, and engineering, and created unique educational and research opportunities. Driven initially by intellectual pursuit of solutions to medical problems, the field of bioengineering has emerged internationally as an established discipline which integrates engineering and analytical tools with principles in the medical and life sciences.
The long-term program involves a community of researchers as core participants who will spend the March 13 - June 16 period in residence at IPAM. The intent is for the core participants to have an opportunity to learn about cells and materials from the perspectives of many different fields - mathematics, statistics, biology, engineering and medicine--and to meet a diverse group of people and have an opportunity to form new collaborations. There will be an active program of research activities, seminars and workshops throughout the March 13 - June 16 period.
Objectives of the Long Program
This program is aimed at providing an environment for researchers to explore new applications of mathematics in a variety of the bioengineering fields. Our hope is that modern mathematical techniques and ideas can be brought to bear on fundamental problems in bioengineering and biomaterials research, much as they have impacted materials science and engineering. Specifically, the Long Program will offer an opportunity for participants to: learn about various sub-disciplines of bioengineering; gain perspective by engaging in extended discussions with mathematicians, physical scientists, physicians, life scientists, and engineers; and develop new collaborations. To achieve these objectives, the Bioengineering Long Program will feature tutorials, workshops, social activities, and a culminating workshop at Lake Arrowhead.
Bioengineering Overview Morphogenesis; Cell adhesion, cellular motility, cell migration; cell signaling; cell cycle; receptor-ligand interactions; apoptosis; protein interactions near biological surfaces; stem cells.
Computational Methods Overview Applications of Inverse problems; level set method; multiscale methods; moving boundary problems; adaptive mesh techniques; Stefan problems.
Membrane proteins are a huge and widely diverse family: with functions including valves, pumps, sorters, sensors, energy transducers, and more, it is not surprising that a large fraction of the human genome has been found to comprise membrane proteins. However, due to the difficulty in crystallizing these proteins, structures are only known for a fraction of them. This is the current rate-limiting step in the overall understanding of this protein family, since the structure/function relationship is responsible for the unique performance of each protein. Far from being a purely biological problem, there is a growing realization within the community that the transport properties of some proteins can be described from a device perspective, using mean field theories, the development of which may allow the determination of the positions of specific key atoms and charges through an inverse problem formalism by measurement of "device" transport characteristics of these proteins. Aside from structural determination, further work concerns the behavior of a subset of membrane proteins whose structures and transport properties can change with electrostatic potential. These so-called "voltage gated" proteins function through an as yet unknown mechanism, although they are fundamental to the function of the heart and brain. Due to the importance, ubiquity, and functions of membrane proteins, they are targets of high pharmaceutical interest, and their ability to govern transmembrane transport addressable electrically opens new engineering vistas as well. In this program, we will bring together experimental and theoretical experts in membrane protein structure and function highlighting the state-of-the-art in the science and integrate these perspectives with those of applied science and future applications.
Mathematical approaches: Stochastic processes, Monte-Carlo and Molecular Dynamics simulations, membrane elasticity theory, Inverse problems
Convective fluid transport is critical for most physiological processes. At the microscopic level it ranges from flow around a swimming Spirillum bacterium to active transport of molecules across membranes by pumps. Many life threatening diseases progress due to reduction in microfluidic flows. Diabetes affects transmural exchange in kidney nephrons and capillaries. Stroke and reperfusion injury interrupt capillary bloodflow. Edema results when fluid cannot escape a tissue, as occurs in compartment syndromes. In bone microfluidic transport—bone interstitial fluid flow (BIFF)—has been identified as the stimulus that is detected by osteocyte and osteoblast mechano-receptors and modulates their physiology. There is evidence that BIFF is generated by poroelastic deformation of the bone matrix and may be influenced by bone capillary blood pressure. Since the mechanical impulse modulating endothelial cells is fluid shear stress it is reasonable to propose that the same mechanism operates in bone cells. An alternative—possibly collateral--mechanism may be streaming potentials. Enhancement of BIFF may be the key to improving fracture healing and preventing osteoporosis. Appropriate BIFF assist devices may, accordingly, be worn during healing, prolonged periods of disuse (bed rest) and microgravity exposure. Microfluidic flows are also critical for maintenance of tissue engineered scaffolds. If the implant is erodible, convection will hasten decomposition. If it carries cytokines/growth factors convection will hasten their dissemination. If it is a bioreactor, i.e. carries functioning cells, convection will supply the nutrients to keep its seeded cells alive until host vasculature can penetrate the scaffold. Mathematical modeling of such flows in and around individual cells is relatively straightforward. Observations generating data which can be used to determine model coefficients are plentiful. In the intact organism, these data are less available. Accurate measurements from within the intact organ usually involve probes which disturb the flow being measured. Mathematical modeling extrapolated from data from less invasive approaches can help decide which measures are "real" and which "artifacts".
Mathematical approaches: microfluidics, flow through random media, finite elements, homogenization
The development and life-cycles of all living beings are characterized by striking changes in morphology ranging from cell-differentiation to organ development. Morphogenesis occurs in response to gradients of morphogens whose concentrations determine the pathway cells will take during development. Angiogenesis and neovascularization are a specific example of morphogenesis and describe the recruitment and proliferation of vascular endothelial cells from the existing vascular system in order to develop a new vascular network that provides blood and nutrients to specific tissues. Angiogenesis occurs during the natural course of wound healing and tissue regeneration as well as in fetal development. A pathological form of angiogenesis occurs during tumor growth and the resulting neovasculature is much more leaky than is normally the case. Thus, during tissue regeneration it is desirable to promote angiogenesis while during tumor growth angiogenesis should be suppressed. Angiogenesis involves through a number of biochemical and biophysical pathways that have been extensively studied experimentally although there is still much more work to be done. Mathematical modeling, analysis and numerical simulations of angiogenesis are the subject of current research efforts. In this program, we will bring together experts to discuss the state-of-the-art of this field.
Mathematical approaches: Equations of reaction-diffusion-chemotaxis, stochastic processes, percolation, numerical simulations
Systems biology involves the quantitative and simultaneous integration of different and multiple biological components and their relationships with one another. For example, the components may be proteins, while their relationships may be described by signal transduction pathways. Unlike systems biology, molecular modeling focuses on a single complex between biomolecules and computes the interactions that exist in the complex. Although the two fields appear dissimilar, they are both quantitative in nature and involve many components and relationships. In the case of molecular modeling, the components are the atoms and their partial charges, and their relationships are the different interactions between them. Therefore, it’s no surprise that some molecular modeling methods are now being applied to systems biology. Moreover, there has been recent success in combining these two fields to rationally design effective therapeutics. In this program, we will bring together experts in these two fields of computational biology to discuss their frontier research.
Mathematical approaches: Differential equations, finite difference methods, Bayesian approaches, molecular dynamics, stochastic systems, clustering, nonlinear dynamics, Monte Carlo simulations, simulated annealing
Institute for Pure and Applied Mathematics (IPAM)