Tracking the Motion of the Outer Ends of Microtubules

Stathis Hadjidemetriou, Derek Toomre, James S. Duncan

Yale University, School of Medicine,New Haven, CT 06520

Microtubule (MT) Assembly

•Self-assembling biopolymers of cytoplasm,width≈25 nm

MTs

Fluorescence labeling in confocal microscopy, ≈200 nm/pixel

•Provide structure and support to the cell

Why are Microtubule Dynamics Interesting?

MT: tracks for granules (dark dots) in fish cell

•Dynamic ‘highways’ for trafficking of vesicles

MT: spindle in yeast cell

•Regulate cell migration and cell division

Importance in Cell Pathology

• Anticancer drugs (e.g. Taxol®, Taxotere®) inhibit

polymerization of MTs to retard:

– Cancer growth through cell division

– Cancer spread through cell migration

• Deficient neurotransmitter transport implicated in

neurodegenerative diseases, e.g. Alzheimer’s

Objective

Fibroblast & epithelial cells

•Segment of MTs [Hadjidemetriou et al, 05]

•Tracking of MTs motion [Hadjidemetriou et al, 04]

Previous Work in Segmentation of Biomedical Curvilinear Structures

•Microscopy: –Actin, chromosomes [Noordmans et al, 98]

•Organ imaging:–Colon [Cohen et al, 01]

–Vasculature [Chung et al, 01] , bronchial tree [Fridman et al, 03]

–White matter tractography [Parker et al, 02][Jackowski et al, 04]

Previous Work in Motion Tracking of Biomedical Structures

• Microscopy:

– Manual: Annotation of video [Waterman et al, 00]

– Automated: Single molecules, cytoplasmic particles [Cheezum et al 01]

• Organ imaging:

– Lungs, heart [Papademetris et al, 02]

– Cineangiography of coronary arteries [Shechter et al, 03]

• Registration of longitudinal data [Weiner et al, 2004]

Confocal Microscopy• Pinhole microscopy, 2D or 3D• Resolution:

x-y≈200 nm/pixel, z≈500 nm/pixel, weff≈2-3 pixels• Laser causes photobleaching

I:D→[0, Imax], fluorescence

Preprocessing• Filtering: Largest eigenvalue of matrix of 2nd

derivatives

MT Segmentation in Initial Frame

• Segment MTs starting from the ends

• Get pinner

Microtubule end

Microtubule

pinner

1. Start from pinner to compute cost map Uo:

•P1 : Isotropic, favors MT fluorescence:

Cumulative Cost Over Valid Neighborhood

intensity maximum

1)(

max

max1

I

I

IxP x

21 PPUo

P1(x)

Ix

1

Imax

.

.

•P2 : Anisotropic, favors MT centerline:

2. Solve with one pass algorithm

Centerline Component

x

x rxe

xr

xeU

xr

xeUUxP

ii

at sderivative

2nd ofmatrix ofPCA )(),(

)(

)(.

)(

)(.),(

1

20

2

1002

11, re

22 , re

x.

Extraction of Curve Segment

3. Curve segment is streamline of U0

• Backtrack along Uo from starting point:

startpM

sM

Us

M

)0(

)(

,0

segmentMT

Extraction of First MT Segment

Null region of UloValid region for Ul

o,

r=5weff

MicrotubuleMicrotubule end

Valid region for Ulo,

r=5weff

Extraction of Subsequent MT Segments

2weff

Null region of Ulo

Microtubule

Most recently segmented point, pstart

MT tangent

Evaluation of Curve Segment

Contrast measure across its axis:

segment eMicrotubul

1I

I

outer

innercontrast

Inner zone

Outer zone

Outer zone

Microtubule segment

weff weff weff

Microtubule 2D Segmentation

Compute Ulo in segment

neighborhood

Backtrack along Ulo

to get segmentYes

Evaluate curve

Backtrack along Ulo

to get segment

Compute Ulo in segment

neighborhood

Examples of Segmentations of 2D MT

MT Extrapolation in Average Frame• Compute average image over time:

MT Extrapolation in Average Frame

• Extrapolate MTs starting from the outer ends

• Get pouter

Thresholding of Data•Estimate mean and st.dev. of intensities on MT centerlines

Threshold=mean-st.dev.

Streamline Passing from Microtubule

For all t=tstart+1→tend:

•Compute local U0t starting from

pinner

•Extract streamline Lt between pinner

and pouter

•Lt includes microtubule

pinner

MT

.

.pouter

Lt

Examples of Streamlines Through Microtubules

Compute MT End Feature

0UR u

For all t=tstart+1→tend:

• Compute end feature , R along streamline Lt,

R=directional derivative of Uo along tangent u of Lt:

pinner

pouter

u

. .Lt

.

MT End Point Trajectory

tstart

Lt-1

Lt

tend

t

.

.

.

.etstart

.etend

..et-1

.et

•Condition 1: Limit motion shift:

|et-et-1| < shift

et -MT end at time t

•Condition 2: Point of maximum R along Lt:

tLt Re maxarg

L1

Outline of Motion Tracking Algorithm

MT end

Microtubule

tstart

Segment microtubules to get pinner

Extrapolate microtubules to get pouter

For all t: Extract streamline, Lt

btw pinner and pouter

For all t: Compute MT end feature, R

Form MT end point trajectory

t

tend pouter

.

pinner

. .

Preprocessing

Next subsequence

•Implementation in C++•Enhancement for visualization

Phantom Sequence for Noise

Size=150x150x100, Time=2 min 45 sec

•Green: Ground truth•Red: Algorithm

Phantom Sequence for Proximity

•Size=150x150x100, •Time=2 min 38 sec

•Green: Ground truth•Red: Algorithm

Examples 1 of Real Sequence

Example 1: Ground Truth

•Size=635x471x100, •Time=30 min 6 sec• Error=3.3 pixels

•Green: Ground truth•Red: Algorithm

Example 2 of Real Sequence

Example 2: Ground Truth

•Green: Ground truth•Red: Algorithm

•Error in MTs tracked=17/19•Error in tracking=2.6 pixels

Example 3 of Real Sequence

•Size=136x112x100, •Time=5 min 7 sec

Example 4 of Real Sequence

•Size=350x262x36, •Time=3 min 25 sec,•Error in MTs tracked=17/19•Error in tracking=2.6 pixels

•Green: Ground truth•Red: Algorithm

Summary

•Preprocessing

•MT segmentation and extrapolation:

–First and average image

–Consecutive MT segments

•MT end feature ≡ derivative of Uo along streamline

•Form MT end trajectory

Discussion

•Evaluate:Phantom, real

•Robust:

–Noise,

–Deformation,

–Proximity

–MT end polymerization

•Sensitive:

–Intersections,

–Lateral motion

End

Example 4 of Real Sequence

Light source

Beam splitter

CCD

Specimen

Objective lens

Beam splitter

CCD

Specimen

Laser illumination

Objective lensWide field of view

Narrow field of view

Confocal vs Conventional Microscopy

Widefield Microscopy Confocal Microscopy

ApertureNo aperture

Quantification of Microtubule Motion

•Specification of tips at first frame

•Motion tracking of ends•Measure average (de)-polymerization:

–Duration,–Rates

C

C

Quantification of Microtubule End Motion

•Microtubule states: –Polymerization, –Depolymerization, –Quiescent

P D

Q

•Statistics:–States:(de)polymerization rates, avg time duration–State transitions: Rescue, catastrophe

RR

Examples of Motion Statistics

Example 2: Statistics

•Size=636x472x100, •Time= min sec