Mechanical stimulation of primary cilia Mechanical stimulation of primary cilia Andrew Resnick 1 , Ulrich Hopfer 2 1 Department of Physiology and Biophysics, Case Western Reserve School of Medicine, 10900 Euclid Avenue, Cleveland OH 44106, 2 Department of Physiology and Biophysics, Case Western Reserve School of Medicine, 10900 Euclid Avenue, Cleveland OH 44106 TABLE OF CONTENTS 1. Abstract 2. Introduction 3. Flow through ducts 3.1. Coordinate system 3.2. Poiseuille flow 3.3. Limitations of model 3.4. Effect of projections 3.5. Evaluation of ‘k’ 3.6. Further developments 4. In vitro approximation for U(r) 4.1. Flow chamber 4.2. Body forces 4.3. Optical tweezer 4.3.1. Principles of operation 4.3.2. Biological considerations 4.3.3. Trap strength measurement 4.4. Summary 5. Bending of a cilium 6. Perspective 7. Biological effects 7.1. Cellular level 7.2. Organ level 7.3. Organism level 8. Defining experiments 9. Conclusion 10. Acknowledgement 11. References 1. ABSTRACT The ciliary/flagellar system is perhaps unique in biology in that not only are biochemical manipulations used to elucidate the function, but physical manipulations as well. Thus, there is a considerable need to have an integrated physical-biochemical model of a cilium and its function. The emphasis of this paper will be to firstly, provide a mechanistic picture of the cilium and its environment because the biological community is perhaps less aware of this type of model development, and second, to point the way towards future experiments that will elucidate the role of the cilium in organ and organism level signaling and regulation. 2. INTRODUCTION Just as there are ‘mouse models’ for disease and in vitro models for biochemical processes, and in as much as cell cultures are model systems to study physiological processes, mathematical models of real objects simplify and omit extraneous details. What is important when selecting a particular model is to retain some essential component of the problem of interest. In this spirit, the bulk of this paper will cover ductal flow over primary (nonmotile) cilia as this represents from a physical point of view the most simple relevant system while still retaining the essential ingredients. We will indicate along the way how this simple model can be extended to other systems,