Papers by Simon F Nørrelykke
Review of Scientific Instruments, 2010
Optical tweezers and AFM cantilevers are often calibrated by fitting their experimental powerspec... more Optical tweezers and AFM cantilevers are often calibrated by fitting their experimental powerspectra of Brownian motion. We demonstrate here that if this is done with typical weighted leastsquares methods the result is a bias of relative size between −2/n and +1/n on the value of the fitted diffusion coefficient. Here n is the number of power-spectra averaged over, so typical calibrations contain 10-20% bias. Both the sign and the size of the bias depends on the weighting scheme applied. Hence, so do length-scale calibrations based on the diffusion coefficient. The fitted value for the characteristic frequency is not affected by this bias. For the AFM then, force measurements are not affected provided an independent length-scale calibration is available. For optical-tweezers there is no such luck, since the spring constant is found as the ratio of the characteristic frequency and the diffusion coefficient. We give analytical results for the weight-dependent bias for the wide class of systems whose dynamics is described by a linear (integro-)differential equation with additive noise, white or colored. Examples are optical tweezers with hydrodynamic self-interaction and aliasing, calibration of Ornstein-Uhlenbeck models in finance, models for cell-migration in biology, etc. Because the bias takes the form of a simple multiplicative factor on the fitted amplitude (e.g. the diffusion coefficient) it is straightforward to remove, and the user will need minimal modifications to his or her favorite least-square fitting programs. Results are demonstrated and illustrated using synthetic data, so we can compare fits with known true values. We also fit some commonly occurring power spectra once-and-for-all in the sense that we give their parameter values and associated error-bars as explicit functions of experimental power-spectral values.
Review of Scientific Instruments, 2006
We explain and demonstrate a new method of force-and position-calibration for optical tweezers wi... more We explain and demonstrate a new method of force-and position-calibration for optical tweezers with back-focal-plane photo detection. The method combines power spectral measurements of thermal motion and the response to a sinusoidal motion of a translation stage. It consequently does not use the drag coefficient of the trapped object as an input. Thus, neither the viscosity, nor the size of the trapped object, nor its distance to nearby surfaces need to be known. The method requires only a low level of instrumentation and can be applied in situ in all spatial dimensions. It is both accurate and precise: true values are returned, with small error-bars. We tested this experimentally, near and far from surfaces. Both position-and force-calibration were accurate to within 3%. To calibrate, we moved the sample with a piezo-electric translation stage, but the laser beam could be moved instead, e.g. by acousto-optic deflectors. Near surfaces, this precision requires an improved formula for the hydrodynamical interaction between an infinite plane and a micro-sphere in non-constant motion parallel to it. We give such a formula.
Langmuir, 2007
Optical tweezers are widely used to measure molecular forces in biology. Such measurements are of... more Optical tweezers are widely used to measure molecular forces in biology. Such measurements are often influenced by a nearby surface that can perturb both the calibration of the tweezers as well as the hydrodynamic forces acting on microspheres to which the biomolecules are attached. In this study, we have used a very stable optical tweezers setup employing a recently developed calibration method (
Physical Review E, 2011
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an alg... more The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) Effects of finite sampling-rate and-time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile microorganisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensionalization.
Biophysical Journal, 2006
The TATA-box Binding Protein (TBP) is required by all three eukaryotic RNA polymerases for the in... more The TATA-box Binding Protein (TBP) is required by all three eukaryotic RNA polymerases for the initiation of transcription from most promoters. TBP recognizes, binds to, and bends promoter sequences called "TATA-boxes" in the DNA. We present results from the study of individual Saccharomyces cerevisiae TBPs interacting with single DNA molecules containing a TATA-box. Using video microscopy, we observed the Brownian motion of beads tethered by short surface-bound DNA. When TBP binds to and bends the DNA, the conformation of the DNA changes and the amplitude of Brownian motion of the tethered bead is reduced compared to that of unbent DNA. We detected individual binding and dissociation events and derived kinetic parameters for the process. Dissociation was induced by increasing the salt concentration or by directly pulling on the tethered bead using optical tweezers. In addition to the well-defined free and bound classes of Brownian motion, we observed another two classes of motion. These extra classes were identified with intermediate states on a three-step, linear binding pathway. Biological implications of the intermediate states are discussed.
Bioimage Data Analysis Workflows
What You Learn from This Chapter You will be introduced to some of the powerful and flexible imag... more What You Learn from This Chapter You will be introduced to some of the powerful and flexible image-analysis methods native to MATLAB. You will also learn to use MATLAB to simulate a time-series of Brownian motion (diffusion), to analyse time-series data, and to plot and export the results as pretty figures ready for publication. If this is the first time you code, except from writing Macros in ImageJ, then this will also serve as a crash course in programming for you. 5.1 Tools We shall be using the commercial software package MATLAB as well as some of its problem specific toolboxes, of which there are currently more than 30. 5.1.1 MATLAB Don't panic! MATLAB is easy to learn and easy to use. But you do still have to learn it. MATLAB is short for matrix laboratory, hinting at why MATLAB is so popular in the imaging community-remember that an image is just a matrix of numbers. MATLAB is commercial software for numerical, as opposed to symbolic, computing. This material was developed and tested using versions R2015b, R2016a, R2017a, and R2018a of MATLAB. 5.1.2 Image Processing Toolbox Absolutely required if you want to use MATLAB for image analysis. 5.1.3 Statistics and Machine Learning Toolbox, Curve Fitting Toolbox Somewhat necessary for data-analysis, though we can get quite far with the core functionalities alone. 5.2 Getting Started with MATLAB That is what we are doing here! However, if you have to leave now and still want an interactive first experience: Head over here, sign up, and take a free, two hour, interactive tutorial that runs in your web-browser and does not require a MATLAB license (they also have paid in-depth courses). 5.2.1 Baby Steps Start MATLAB and lets get going! When first starting, you should see something similar to. Fig. 5.1 17 12 Tool-strip Script-editor Command-line Variables Directory. Fig. 5.1 The full MATLAB window with default layout of the windows. Some preset layouts are accessible in the tool-strip, under the HOME tab, in the Layout pull-down menu. Double-click on the top-bar of any sub-window to maximize it, double-click again to revert S. F. Nørrelykke. Fig. 5.2 The command window in MATLAB after entering 5+7 and hitting the return key. The result, 12, is displayed and stored in the variable ans
The historical co-evolution of biological motility models with models of Brownian motion is outli... more The historical co-evolution of biological motility models with models of Brownian motion is outlined. Recent results for how to derive cell-type-specific motility models from experimental cell trajectories are reviewed. Experimental work in progress, which tests the generality of this phenomenological model building is reported. So is theoretical work in progress, which explains the characteristic time scales and correlations of phenomenological models in terms of the dynamics of cytoskeleton, lamellipodia, and pseudopodia. 1 The co-evolution of theories for Brownian and biological random Motion Robert Brown did not discover Brownian motion. Brown, a botanist, got his name associated with this physical phenomenon because in 1827 he carefully demonstrated what it is not, a manifestation of life. The puzzle of its true origin he left for others to solve. It being a property of inert matter, those others were the physicists. They ignored the problem for decades, then slowly began to sh...
F1000Research
We introduce the NEUBIAS Gateway, a new platform for publishing materials related to bioimage ana... more We introduce the NEUBIAS Gateway, a new platform for publishing materials related to bioimage analysis, an interdisciplinary field bridging computer science and life sciences. This emerging field has been lacking a central place to share the efforts of the growing group of scientists addressing biological questions using image data. The Gateway welcomes a wide range of publication formats including articles, reviews, reports and training materials. We hope the Gateway further supports this important field to grow and helps more biologists and computational scientists learn about and contribute to these efforts.
Angiogenesis
Due to their involvement in many physiologic and pathologic processes, there is a great interest ... more Due to their involvement in many physiologic and pathologic processes, there is a great interest in identifying new molecular pathways that mediate the formation and function of blood and lymphatic vessels. Vascular research increasingly involves the image-based analysis and quantification of vessel networks in tissue whole-mounts or of tube-like structures formed by cultured endothelial cells in vitro. While both types of experiments deliver important mechanistic insights into (lymph) angiogenic processes, the manual analysis and quantification of such experiments are typically labour-intensive and affected by inter-experimenter variability. To bypass these problems, we developed AutoTube, a new software that quantifies parameters like the area covered by vessels, vessel width, skeleton length and branching or crossing points of vascular networks in tissues and in in vitro assays. AutoTube is freely downloadable, comprises an intuitive graphical user interface and helps to perform otherwise highly time-consuming image analyses in a rapid, automated and reproducible manner. By analysing lymphatic and blood vascular networks in whole-mounts prepared from different tissues or from gene-targeted mice with known vascular abnormalities, we demonstrate the ability of AutoTube to determine vascular parameters in close agreement to the manual analyses and to identify statistically significant differences in vascular morphology in tissues and in vascular networks formed in in vitro assays.
Nature communications, Jun 28, 2018
Sinusoidal endothelial cells and mesenchymal CXCL12-abundant reticular cells are principal bone m... more Sinusoidal endothelial cells and mesenchymal CXCL12-abundant reticular cells are principal bone marrow stromal components, which critically modulate haematopoiesis at various levels, including haematopoietic stem cell maintenance. These stromal subsets are thought to be scarce and function via highly specific interactions in anatomically confined niches. Yet, knowledge on their abundance, global distribution and spatial associations remains limited. Using three-dimensional quantitative microscopy we show that sinusoidal endothelial and mesenchymal reticular subsets are remarkably more abundant than estimated by conventional flow cytometry. Moreover, both cell types assemble in topologically complex networks, associate to extracellular matrix and pervade marrow tissues. Through spatial statistical methods we challenge previous models and demonstrate that even in the absence of major specific interaction forces, virtually all tissue-resident cells are invariably in physical contact wi...
Papers, Nov 6, 1998
We present a dynamical many-body theory of money in which the value of money is a time dependent ... more We present a dynamical many-body theory of money in which the value of money is a time dependent ``strategic variable'' that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus represents a continuous symmetry. The dynamics breaks this continuous symmetry by fixating the value of money at a level which depends on initial conditions. The fluctuations around the equilibrium, for instance in the presence of noise, are governed by the ``Goldstone modes'' associated with the broken symmetry. The idea is illustrated by a simple network model of monopolistic vendors and buyers.
Aps Meeting Abstracts, Mar 1, 2008
We study the stochastic properties of trajectories of individual keratocytes that move on a solid... more We study the stochastic properties of trajectories of individual keratocytes that move on a solid substrate. The distribution of observed velocities exhibits a characteristic maximum at finite speed and a local minimum at zero velocity. This velocity distribution depends on the averaging ...
Details left out in the model described in (9.1-9.4) will be found missing, of course, if one loo... more Details left out in the model described in (9.1-9.4) will be found missing, of course, if one looks in the right places. For example, the length of the trajectory x(t) is infinite for any finite time interval considered 2. Ornstein and 1 Just how much he knew seems an open question that may never be answered [2]. 2 Consider an interval of duration t. Split it into N intervals of duration ∆t = t/N. In each of these, the mean squared displacement of the Brownian particle is 2D∆t. So on the average, the distance travelled in a time interval of duration
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Papers by Simon F Nørrelykke