Lecture 10: Quantitative Analysis of Visual Data November 24, 2014
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1 ICQB Introduction to Computational & Quantitative Biology (G4120) Fall 2014 (Jim) Erdinc Atilgan, Ph.D. Columbia University Department of Microbiology & Immunology Lecture 10: Quantitative Analysis of Visual Data November 24, 2014
2 Quantitative Analysis of Visual Data by (Jim) Erdinc Atilgan Chang Lab 1
3 Dynamics of thin membrane protrusions driven by ratcheting mechanism of polymerizing parallel actin bundle. Lamellipodium morphology, organization of actin network and their implications for the geometrical properties of branching hot zones and branching complex orientation. Nucleation and dynamics of initial focal adhesions. Filopodia Lamellipodia Liposomes Focal Adhesions Cell division Cell morphogenesis Fusion and fission of liposomes by energetically favorable curvature match mechanism. Computational and experimental methods to explain cytokinesis though a model depends on walk and diffuse motion of signal particles. Physical properties of fission yeast cell wall and morphogenesis upon cell division. 2
4 Course Plan: A short intro for some of the tools and methods useful for quantitative biology/image analysis Practice ImageJ : gel image Intro to fission yeast cell wall biophysical properties Practice ImageJ : Images: Live cells Images: Ghosts 3
5 Step1: model, concept Lots of simplifications and assumptions Step2: math, ODE Step 3: Analytic or numeric solutions + Eliminate subjectivity + Large population - Bio complex Fourier transformation Radon transformation o Useful for lines / linear objects Canny algorithm o useful for edge detection o and to clean data 4
6 5
7 6
8 Results from Vcell: Experimental Image (data) Vcell output & comparison 7
9 Simulations Realistic approach 1) Math + physics = calculations & checks and balances, etc. 2) Representation = graphs & plots, etc 8
10 Matlab: + codify + figures easy + lots of packages - not free ($$$) - a lil slow Alternative: Python + free - depends on packs (?) speed 9
11 spore CRIB-GFP 10
12 Automated Analysis of Visual Data 11
13 12
14 ImageJ : 1. Open the file 2. Select the first (use rectangle box tool) 3. Analyze > Gels > Ctrl+1 4. Select by using the same box 5. Analyze > Gels > Ctrl+2 6. Go to step 2 till finished lanes. Notice that it automatically numbers the boxes! 7. When done, Analyze > Gels > Ctrl+3 will see the plots. 8. Use line tool cut the noise level on each plot 9. Use wand (tracing) tool to integrate on each plot. 10. Copy and paste your results onto an Excel sheet and plot the result 13
15 Biophysical Properties of Fission Yeast Cell Wall 14
16 Motivation Mechanical properties of cell wall is related to Control of cell size Morphogenesis Development and growth Life style of fungal, bacterial, plant cells. Two major physical players are Stiffness (Young s Modulus [Y] and Poisson s ratio [ν]) of the wall Osmotic pressure inside the cell body Eventual aim is to understand cell morphogenesis in biophysical and molecular level.
17 INTRODUCTORY INFO on FISSION YEAST CELL WALL and CELL SHAPE EM images BF image 1. Rod shape (capsule shape) with a thick cell wall, t=200nm. 2. Grow only at tips to a length L=14um and divide at middle by a putting a septum wall by the guide of actin ring. 3. Septum consists of 3 layers. In the middle there is primary septum which is flanked by two layers called secondary septum. h=<100nm. 4. Initially all septum discs are planar. After division primary septum dissolves and secondary septum rounds and becomes the new end of daughter cells. 5. Width of the cell is about 3.9+/-0.2um but birth marks exhibit scars. 6. There exist a pressure inside the cell and it is osmotic-ally regulated by glycerol concentration.
18 EM images SIDE CELL WALL vs SEPTUM WALL There are some differences between side wall and septum wall, chemically and physically. New fresh wall is seen as dark rings close to birth marks in calcofluor images, or spherical caps before the growth. Primary septum 1,3-β-glucan Calcofluor staining Secondary septum 1,3-α-glucan 1,6-β-glucan α-galactomannan AFM image, Woods Hole 2012 Asylum Research Inc. Side wall 9 14% α-galactomannan, 18 28% 1,3-α-glucan, 42% 1,3-β-glucan 2% 1,6-β-glucan reference: (Manners and Meyer, 1977; Kopecka et al., 1995).
19 PROPERTIES OF OUR MODEL RELAXED STATE NATURAL STATE internal osmotic factors water External osmotic factors 1. Capsule shape at both natural and relaxed state : cylindrical shell body closed by two hemispherical shells. Two parameters are enough to define this geometry: L, R 2. We assume a strong connection between the wall and membrane. 3. Natural State: P>0. 4. Relaxed State: P=0. 5. We assume a uniform and isotropic cell wall material and wall thickness. 6. Poisson ratio is assumed to be zero. 7. Longitudinal and circumferential directions considered only: thin shell model and radial direction is infinitely stiff and decoupled from the system. 8. P = m RT, i.e. osmotic pressure is linearly proportional to molality of dominant osmotic agents (or cytoplasm in general). 9. Only currency in shape shifts is assumed to be water.
20 Analytic estimates for the expansion rates of thin walled capsule inflated with a constant pressure inside. For a cylindrical thin shell: Relaxed state Natural state Formulae come from simple force balance equations. r l 1 0 l 1 r 0 Rate of change in length Rate of change in radius %R Pr 1 Y r t %l = l 1 l 0 l 0 = Pr 1 2Y l t %r = r 1 r 0 = Pr 1 r 0 Y r t %L 1 2 Pr 1 Y l t For a spherical thin shell: Relaxed state %r = r 1 r 0 r 0 = Pr 1 2Y r t Natural state r 0 r 1 r 0 : relaxed radius l 0 : relaxed length l 1 : length in natural state r 1 : radius in natural state t : thickness of the wall P: pressure difference Y: Young modulus If the cell wall is uniform, i.e. Y = Y l = Y r then (%R) (%L) = 2. 19
21 Let s find the stiffness of the wall & the pressure of the fission yeast cells from cell images! 1. wall120207* 1 st frame live cells (natural state). Scale=1.12e ghosts* ghosts. Scale =7.5e-4 3. Find (%R) from live cell images and ghosts images 4. Find Y/P ratio. 5. From live cells sorbitol shift experiment images find (%R) and (%L). 6. What is the value of (%R)/(%L)=? 7. Can you find the Y and P? 20
22 Next class will be on Statistics Thx all 21
23 Formula and work out sheet %L = L 1 L 0 = PR 1 L 0 2Yt R 0 : relaxed radius L 0 : relaxed length L 1 : length in natural state R 1 : radius in natural state t : thickness of the wall =0.2µm P: pressure difference Y: Young modulus P = c RT c 0 = 1.25 M RT = 2.24 Pa/M %R = R 1 R 0 = PR 1 R 0 Yt 1. Find R 1 in live cells 2. Find R 0 from ghosts 3. Find (%R) 4. Find Y/P=? 5. Find (%R) and (%L) from live cell images (1.25 M shift) 6. Compare it previous (%R). 7. Can u find P and Y now? 1. Estimate the volume change 2. Find molarity of cytoplasm in natural state 3. Find pressure 4. Find stiffness 22
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