Noise and Sensitivity in Cell Signalling
Total Page:16
File Type:pdf, Size:1020Kb
Noise and sensitivity in cell signalling Brendan A. Bicknell BSc (Hons) A thesis submitted to the University of Queensland for the degree of Doctor of Philosophy Queensland Brain Institute & School of Mathematics and Physics 2017 ii Abstract The ability of cells to receive and process chemical information is fundamental to the function of biological systems. Cell responses to salient chemical cues are characteristically reliable and precise, a striking example being the guidance of axons to their targets during brain develop- ment. However, chemical signalling pathways are subject to multiple sources of unavoidable noise, due to the random nature of molecular motion and interactions. This suggests that cellular systems may be optimised for transduction of noisy signals, which provides a guiding principle for understanding cell function at a biophysical level. In pursuit of this idea, we study three model problems, motivated by sensing and signalling in axon guidance. Our approach is to construct mathematical models, and through analysis and simulation, extract general prin- ciples and hypotheses about the quantitative nature of biological noise and mechanisms for sensitive chemosensation. First, we quantify the physical limits of chemosensation imposed by the random thermal motion of the molecules that need to be counted. In particular, we show how this depends on the dimension and spatial extent of the domain of diffusion. Although recurrent diffusion in 1d and 2d is detrimental to measurement precision, we find these effects are suppressed when sensing is performed within a confined space. Second, we study the stochastic behaviour of the inositol 1,4,5-trisphosphate receptor ion channel, which couples receptor activity at the membrane to the downstream calcium response that regulates axon growth and turning. By modelling the basic biophysical events that control ion channel opening, we introduce a new principle for understanding the origin of the multiple gating modes observed in single channel recordings. Third, we examine the finely-tuned response of dorsal root ganglia neurons to very shallow neurotrophin gradients. We show how paracrine signalling within the ganglion could explain this extreme sensitivity, as well as the currently unexplained biphasic dose response of many axon growth and guidance cues. Overall, this thesis gives new quantitative insights into chemical signalling in biological systems, across multiple stages of processing and spatial scales. Our models make testable predictions to motivate new experiments, and provide a strong foundation for further theoretical and computational study in both axon guidance and broader domains of biophysics. iii Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, financial support and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my higher degree by research candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis and have sought permission from co-authors for any jointly authored works included in the thesis. iv Publications during candidature Bicknell, B.A. & Goodhill, G.J., (2016), Emergence of ion channel modal gating from inde- pendent subunit kinetics. Proc Natl Acad Sci USA, 113(36), E5288-E5297. Bicknell, B.A. , Dayan, P. & Goodhill, G.J., (2015), The limits of chemosensation vary across dimensions. Nat Comms, 6, 7468. Goodhill, G.J., Faville, R.A., Sutherland, D.J., Bicknell, B.A. Thompson, A.W., Pujic, Z., Sun, B., Kita, E.M. & Scott, E.K. (2015). The dynamics of growth cone morphology. BMC Biology, 13, 10. Publications included in this thesis Bicknell, B.A. & Goodhill, G.J., (2016), Emergence of ion channel modal gating from inde- pendent subunit kinetics. Proc Natl Acad Sci USA, 113(36), E5288-E5297. Incorporated as Chapter 3. B.A.B G.J.G. designed research 80 % 20 % performed research 100 % 0 % wrote manuscript 80 % 20 % Bicknell, B.A. , Dayan, P. & Goodhill, G.J., (2015), The limits of chemosensation vary across dimensions. Nat Comms, 6, 7468. Incorporated as Chapter 2. B.A.B P.D. G.J.G. designed research 70 % 10% 20% performed research 100 % 0 % 0 % wrote manuscript 80 % 10 % 10 % v Contributions by others to the thesis Contributions by others to chapters 2 and 3 are as listed in Publications included in this thesis. Zac Pujic performed the experiments reported in chapter 4, as described in Methods: Neurite growth assay, and advised on the associated immunostaining and microscopy. Geoff Goodhill and Peter Dayan contributed to the design and writing of the research presented in chapter 4. Statement of parts of the thesis submitted to qualify for the award of another degree None. Research involving human or animal subjects Experiments involving animals were conducted in accordance with the Animal Care and Pro- tection Act Qld (2002), and the Australian Code of Practice for the Care and Use of Animals for Scientific Purposes, 8th edition (2013). Ethics approval was obtained from the University of Queensland Ethics Committee, Approval Number QBI/548/16. The approval certificate is included as appendix A. vi Acknowledgements I am very grateful to Geoff Goodhill, whose guidance throughout every stage of this process has been a wonderful privilege. My time in the lab has been formative, and I go forward with broadened horizons and heightened zeal for brain research. I very much appreciate all of the encouragement and opportunities, and for the timely reminders of the forest while wandering amongst the trees. And to Peter Dayan, whose incisive comments and questions were invalu- able, and whose generosity is an inspiration. Thank you Zac Pujic, for introducing me to the combination of technique, time and superstition required for successful experimental work, and other Goodhill lab members, for their feedback and entertaining discussions throughout. Outside the lab, there are many people I would like to thank. A non-exhaustive selection: Isobel, for the selfless support and patience for which I will be forever grateful. There is a long list of adventures postponed by this endeavour, which I now look forward to working through with you. My family, for their unwavering support and encouragement, and for their essential and expert counsel on matters mathematical, musical, whimsical and bicycle. Finally, James, Kim and Tristan for the welcome extracurricular noise. vii Financial support This research was supported by an Australian Postgraduate Award. Keywords cell signalling, chemosensation, diffusion, ion channel, inositol 1,4,5-trisphosphate receptor, axon guidance, nerve growth factor Australian and New Zealand Standard Research Classifi- cations (ANZSRC) ANZSRC code: 010202, Biological Mathematics (40 %) ANZSRC code: 029901, Biological Physics (40 %) ANZSRC code: 110905, Peripheral Nervous System (20 %) Fields of Research (FoR) Classification FoR code: 0102, Applied Mathematics (40 %) FoR code: 0299, Other Physical Sciences (40 %) FoR code: 1109, Neurosciences (20 %) viii Contents List of Figures xiii List of Tables xv 1 Introduction 1 1.1 Thesis outline . .4 2 The limits of chemosensation vary across dimensions 7 2.1 Introduction . .8 2.2 Results . 10 2.2.1 Derivation of theoretical results . 10 2.2.2 Simulations . 14 2.2.3 Biological implications . 17 2.3 Discussion . 20 2.4 Methods . 21 2.4.1 Simulations . 21 2.5 Supplementary Information . 22 2.5.1 Evaluation of sums . 22 2.5.2 Derivation without spatial averaging . 28 2.5.3 Ring of receptors in 2D . 29 2.5.4 Supplementary figures . 31 3 Emergence of ion channel modal gating from independent subunit kinetics 35 3.1 Introduction . 36 3.2 Results . 37 3.2.1 Bursting motif . 38 3.2.2 Timescale separation . 40 3.2.3 Modal gating motif . 41 3.2.4 Simulations . 43 ix x Contents 3.2.5 Full model . 45 3.2.6 Model fitting . 47 3.2.7 Modal gating analysis . 48 3.3 Discussion . 52 3.3.1 Model assumptions . 53 3.3.2 Role of IP3R modal gating in Alzheimer's disease . 55 3.3.3 Application to other ion channels . 56 3.4 Methods . 57 3.5 Supplementary Information . 57 3.5.1 Conditional mean open time . 57 3.5.2 Supplementary figures . 59 3.5.3 Supplementary tables . 64 4 Control of neurite growth and guidance by an inhibitory cell-body signal 65 4.1 Introduction . 66 4.2 Results . 67 4.2.1 Growth inhibition at high concentration is neither single-cell intrinsic, nor due to fasciculation . 67 4.2.2 Biased outgrowth in shallow gradients implies remarkable sensitivity . 71 4.2.3 A mathematical model of inhibitory growth control . 71 4.2.4 Coupled growth and gradient detection . 77 4.2.5 Model predictions .