ISBIq: A Framework for Simulation of Cell Cycle in...

ISBIq: A Framework for Simulation of Cell Cyclein Fluorecence Microscopy

Vladimır Ulman & David Svoboda

Centre for Biomedical Image Analysis, Masaryk UniversityBrno, Czech Republic

PV182 – CBIA seminar

March 14, 2013

Ulman & Svoboda (CBIA) ISBIq March 14, 2013 1 / 18

Motivation

Historically, gtgen and Static simulator were,quite independently, first published/born in 2007.

Recently, joint proper investigation of this field has begun:Generation of Synthetic Image Datasets for Time-Lapse Fluorescence

Microscopy. David Svoboda, and Vladimır Ulman. ICIAR 2, volume 7325 of

Lecture Notes in Computer Science, page 473-482. Springer (2012)

We faced several requests for time-lapse datasets during conferencemeetings and discussions when presenting CytoPacq (staticsimulator).

ISBI Cell Tracking Challenge 2013 ,


Task

The aim was to simulate how the cell looks during the cell cycle:

C H A P T E R 1 2 The Cell Cycle 231

� Figure 12.6 The cell cycle. In a dividing cell, the mitotic (M)phase alternates with interphase, a growth period. The first part ofinterphase (G1) is followed by the S phase, when the chromosomesduplicate; G2 is the last part of interphase. In the M phase, mitosisdistributes the daughter chromosomes to daughter nuclei, andcytokinesis divides the cytoplasm, producing two daughter cells. Therelative durations of G1, S, and G2 may vary.

Cytokin

esis

Mito

sis

G1

G2

S(DNA synthesis)

MITOTIC(M) PHASE

INTERPHASE

Phases of the Cell Cycle

Mitosis is just one part of the cell cycle (Figure 12.6). In fact,the mitotic (M) phase, which includes both mitosis and cy-tokinesis, is usually the shortest part of the cell cycle. Mitoticcell division alternates with a much longer stage calledinterphase, which often accounts for about 90% of the cycle.During interphase, a cell that is about to divide grows andcopies its chromosomes in preparation for cell division. Inter-phase can be divided into subphases: the G1 phase (“firstgap”), the S phase (“synthesis”), and the G2 phase (“secondgap”). During all three subphases, a cell that will eventually di-vide grows by producing proteins and cytoplasmic organellessuch as mitochondria and endoplasmic reticulum. However,chromosomes are duplicated only during the S phase. (We willdiscuss synthesis of DNA in Chapter 16.) Thus, a cell grows(G1), continues to grow as it copies its chromosomes (S), growsmore as it completes preparations for cell division (G2), and di-vides (M). The daughter cells may then repeat the cycle.

A particular human cell might undergo one division in24 hours. Of this time, the M phase would occupy less than1 hour, while the S phase might occupy about 10–12 hours,or about half the cycle. The rest of the time would be appor-tioned between the G1 and G2 phases. The G2 phase usuallytakes 4–6 hours; in our example, G1 would occupy about5–6 hours. G1 is the most variable in length in different typesof cells. Some cells in a multicellular organism divide very in-frequently or not at all. These cells spend their time in G1 (ora related phase called G0) doing their job in the organism—anerve cell carries impulses, for example.

Mitosis is conventionally broken down into five stages:prophase, prometaphase, metaphase, anaphase, and

telophase. Overlapping with the latter stages of mitosis, cy-tokinesis completes the mitotic phase. Figure 12.7, on thenext two pages, describes these stages in an animal cell. Studythis figure thoroughly before progressing to the next two sec-tions, which examine mitosis and cytokinesis more closely.

The Mitotic Spindle: A Closer LookMany of the events of mitosis depend on the mitoticspindle, which begins to form in the cytoplasm duringprophase. This structure consists of fibers made of micro-tubules and associated proteins. While the mitotic spindle as-sembles, the other microtubules of the cytoskeleton partiallydisassemble, providing the material used to construct the spin-dle. The spindle microtubules elongate (polymerize) by incor-porating more subunits of the protein tubulin (see Table 6.1)and shorten (depolymerize) by losing subunits.

In animal cells, the assembly of spindle microtubules startsat the centrosome, a subcellular region containing materialthat functions throughout the cell cycle to organize thecell’s microtubules. (It is also called the microtubule-organizingcenter.) A pair of centrioles is located at the center of the cen-trosome, but they are not essential for cell division: If thecentrioles are destroyed with a laser microbeam, a spindlenevertheless forms during mitosis. In fact, centrioles are noteven present in plant cells, which do form mitotic spindles.

During interphase in animal cells, the single centrosomeduplicates, forming two centrosomes, which remain togethernear the nucleus. The two centrosomes move apart duringprophase and prometaphase of mitosis as spindle micro-tubules grow out from them. By the end of prometaphase, thetwo centrosomes, one at each pole of the spindle, are at oppo-site ends of the cell. An aster, a radial array of short micro-tubules, extends from each centrosome. The spindle includesthe centrosomes, the spindle microtubules, and the asters.

Each of the two sister chromatids of a duplicated chromo-some has a kinetochore, a structure of proteins associatedwith specific sections of chromosomal DNA at each cen-tromere. The chromosome’s two kinetochores face in oppo-site directions. During prometaphase, some of the spindlemicrotubules attach to the kinetochores; these are calledkinetochore microtubules. (The number of microtubules at-tached to a kinetochore varies among species, from one mi-crotubule in yeast cells to 40 or so in some mammalian cells.)When one of a chromosome’s kinetochores is “captured” bymicrotubules, the chromosome begins to move toward thepole from which those microtubules extend. However, thismovement is checked as soon as microtubules from the op-posite pole attach to the other kinetochore. What happensnext is like a tug-of-war that ends in a draw. The chromo-some moves first in one direction, then the other, back andforth, finally settling midway between the two ends of thecell. At metaphase, the centromeres of all the duplicatedchromosomes are on a plane midway between the spindle’s


Problem Analysis

Cell cycle can be split into Interphase and Mitosis:

Interphase (95%) . . . simple ,G1 phase (50%)S phase (30%)G2 phase (15%)

Mitosis (5%) . . . tricky /ProphaseMetaphaseAnaphaseTelophaseCytokinesis

Note: 100% ≈ 24 hour cell cycle length


Problem AnalysisCell cycle phases step by step

G2 phase

Centrosomes(with centriole pairs)

Early mitoticspindle

Fragmentsof nuclear envelope

Centromere Nonkinetochoremicrotubules

Kinetochoremicrotubule

KinetochoreNucleolus Nuclearenvelope

Plasmamembrane

Chromosome, consistingof two sister chromatids

AsterChromosomes(duplicated,uncondensed)

� Figure 12.7

Exploring Mitosis in an Animal Cell

Prophase• The chromatin fibers become more

tightly coiled, condensing into discretechromosomes observable with a lightmicroscope.

• The nucleoli disappear.

• Each duplicated chromosome appears astwo identical sister chromatids joined attheir centromeres and, in some species,all along their arms by cohesins (sisterchromatid cohesion).

• The mitotic spindle (named for its shape)begins to form. It is composed of thecentrosomes and the microtubules thatextend from them. The radial arrays ofshorter microtubules that extend fromthe centrosomes are called asters(“stars”).

• The centrosomes move away from eachother, propelled partly by the lengthen-ing microtubules between them.

G2 of Interphase Prophase Prometaphase

Prometaphase• The nuclear envelope fragments.

• The microtubules extending fromeach centrosome can now invade thenuclear area.

• The chromosomes have become evenmore condensed.

• Each of the two chromatids of eachchromosome now has a kinetochore,a specialized protein structure at thecentromere.

• Some of the microtubules attach to thekinetochores, becoming “kinetochoremicrotubules,” which jerk the chromo-somes back and forth.

• Nonkinetochore microtubules interactwith those from the opposite pole ofthe spindle.

How many molecules of DNA are in theprometaphase drawing? How many mol-

ecules per chromosome? How many double he-lices are there per chromosome? Per chromatid?

?

G2 of Interphase• A nuclear envelope encloses the nucleus.

• The nucleus contains one or morenucleoli (singular, nucleolus).

• Two centrosomes have formed by dupli-cation of a single centrosome. Centro-somes are regions in animal cells thatorganize the microtubules of the spindle.Each centrosome contains two centrioles.

• Chromosomes, duplicated during Sphase, cannot be seen individuallybecause they have not yet condensed.

The light micrographs show dividing lungcells from a newt, which has 22 chromo-somes in its somatic cells. Chromosomesappear blue, microtubules green, and in-termediate filaments red. For simplicity, thedrawings show only 6 chromosomes.

232 U N I T T W O The Cell

cell gather nutrients/energy formitosis

nuclear envelope still enclosesnucleus

chromosomes have not yet beencondensed

creation of centrosomes

start of mitosis



Prophase







Plasmamembrane



� Figure 12.7

















?







nucleoli disappear

mitotic spindle begins to form(itself)

centrosomes move away toopposite poles of cell

chromatin condensates

each chromosome is composedof two sister chromatids



Metaphase







Plasmamembrane



� Figure 12.7

















?







nuclear envelope fragments

each chromatid is attached toone of two centrosomes

chromosomes become morecondensed



Metaphase

Daughterchromosomes

Metaphaseplate

Spindle

Nucleolusforming

Nuclearenvelopeforming

Cleavagefurrow

Centrosome at one spindle pole

10μm

Metaphase• The centrosomes are now at opposite

poles of the cell.

• The chromosomes convene at the meta-phase plate, a plane that is equidistantbetween the spindle’s two poles. Thechromosomes’ centromeres lie at themetaphase plate.

• For each chromosome, the kinetochoresof the sister chromatids are attached tokinetochore microtubules coming fromopposite poles.

Anaphase• Anaphase is the shortest stage of mitosis,

often lasting only a few minutes.

• Anaphase begins when the cohesinproteins are cleaved. This allows thetwo sister chromatids of each pair topart suddenly. Each chromatid thusbecomes a full-fledged chromosome.

• The two liberated daughter chromosomesbegin moving toward opposite ends ofthe cell as their kinetochore microtubulesshorten. Because these microtubules areattached at the centromere region, thechromosomes move centromere first (atabout 1 μm/min).

• The cell elongates as the nonkinetochoremicrotubules lengthen.

• By the end of anaphase, the two ends ofthe cell have equivalent—and complete—collections of chromosomes.

Telophase• Two daughter nuclei form in the cell.

Nuclear envelopes arise from thefragments of the parent cell’s nuclearenvelope and other portions of theendomembrane system.

• Nucleoli reappear.

• The chromosomes become less condensed.

• Any remaining spindle microtubules aredepolymerized.

• Mitosis, the division of one nucleus intotwo genetically identical nuclei, is nowcomplete.

Cytokinesis• The division of the cytoplasm is usually

well under way by late telophase, so thetwo daughter cells appear shortly afterthe end of mitosis.

• In animal cells, cytokinesis involves theformation of a cleavage furrow, whichpinches the cell in two.

Metaphase Anaphase Telophase and Cytokinesis

Visit the Study Areaat www.masteringbiology.comfor the BioFlix® 3-D Animation onMitosis.

ANIMATION


centrocomes are now atopposite poles of the cell

chromosomes converge tometaphase plate



Anaphase

Daughterchromosomes

Metaphaseplate

Spindle

Nucleolusforming


Cleavagefurrow


10μm


poles of the cell.




















ANIMATION


(the shortest stage in the cellcycle)

two liberated daughterchromosomes begin movingtoward opposite ends of cell

cell elongates

by the end of anaphase, the twoends of the cell have equivalentand complete collection ofchromosomes



Telophase and Cytokinesis

Daughterchromosomes

Metaphaseplate

Spindle

Nucleolusforming


Cleavagefurrow


10μm


poles of the cell.




















ANIMATION


two daughter nuclei form in thecell

nuclear envelopes arise

nucleoli reappear

chromosomes become lesscondensed

formation of a cleavage furrow,which pinches the cell in two



Telophase and Cytokinesis


� Figure 12.9 INQUIRYAt which end do kinetochore microtubulesshorten during anaphase?

EXPERIMENT Gary Borisy and colleagues at the University of Wisconsinwanted to determine whether kinetochore microtubules depolymerize atthe kinetochore end or the pole end as chromosomes move toward thepoles during mitosis. First they labeled the microtubules of a pig kidneycell in early anaphase with a yellow fluorescent dye.

Kinetochore

Spindlepole

Mark

Chromosomemovement

Kinetochore

Tubulinsubunits

Chromosome

MotorproteinMicrotubule

(a) Cleavage of an animal cell (SEM)

(b) Cell plate formation in a plant cell (TEM)

Daughter cells

Cleavage furrow

Contractile ring ofmicrofilaments

Daughter cells

Cell plate

Wall ofparent cell

Vesiclesformingcell plate New cell wall

100 μm

1 μm

� Figure 12.10 Cytokinesis in animal and plant cells.

Then they marked a region of the kinetochore microtubules betweenone spindle pole and the chromosomes by using a laser to eliminate thefluorescence from that region, while leaving the microtubules intact(see below). As anaphase proceeded, they monitored the changes inmicrotubule length on either side of the mark.

RESULTS As the chromosomes moved poleward, the microtubule seg-ments on the kinetochore side of the mark shortened, while those onthe spindle pole side stayed the same length.

CONCLUSION During anaphase in this cell type, chromosome move-ment is correlated with kinetochore microtubules shortening at theirkinetochore ends and not at their spindle pole ends. This experimentsupports the hypothesis that during anaphase, a chromosome is walkedalong a microtubule as the microtubule depolymerizes at its kineto-chore end, releasing tubulin subunits.

SOURCE G. J. Gorbsky, P. J. Sammak, and G. G. Borisy, Chromosomesmove poleward in anaphase along stationary microtubules that coordi-nately disassemble from their kinetochore ends, Journal of Cell Biology104:9–18 (1987).

If this experiment had been done on a cell type in which“reeling in” at the poles was the main cause of chromosome move-ment, how would the mark have moved relative to the poles? Howwould the microtubule lengths have changed?

WHAT IF?

two daughter nuclei form in thecell

nuclear envelopes arise

nucleoli reappear

chromosomes become lesscondensed

formation of a cleavage furrow,which pinches the cell in two



G1 phase

cell grows to the regular size ofcell slowly

nucleus still contains only half ofall chromosomes

chromatin soon decondensates

cell gather nutrients/energy forthe next (S) phase

this is the longest stage in thecell cycle



G1 phase

cell grows to the regular size ofcell slowly

nucleus still contains only half ofall chromosomes

chromatin soon decondensates

cell gather nutrients/energy forthe next (S) phase

this is the longest stage in thecell cycle



S phase

DNA replicates

cell keeps to its volume

this is the second longest stagein the cell cycle


Design of the new simulatorModel of cell

The following data structures were used to model the cell phantom

cell . . . binary mask

nucleus . . . binary mask

nucleoli . . . binary mask

chromosomes . . . sets of dots (molecules of fluorescent dye)

Note: Aside to binary masks, lists of boundary points were used as well.

The following (basic) conditions are valid

number of chromosomes . . . 23 (46)

during interphase, the chromosomes are located inside nucleus

during mitosis, the nucleus disappears and chromosomes are spreadover the whole cell


Design of the new simulatorSingle cell simulation

The Cell::DoNextPhase() template

Simulates particular cell cycle phase completely and atomically.

It manages visual appearance and motion of a cell together.

It is controlled only by time-sampling parameter.

It is split into

“internally-induced stuff” aka local interior affairs,“externally-induced stuff” aka global cell movement.



Local interior affairs

This stage supervises any changes that are

relevant to the specific cell cycle phase,subject to cell current needs.

Examples: re-organization of chromatin, drifts (if desired) or othervisually apparent changes of cell nucleus or nucleoli, changes in cellshape, etc.



Global cell movement

This stage supervises any changes that are

(usually) commonly happening during every cell cycle phase,(usually) influenced by cell environment.

Examples: movement and shape changes of cell within itsenvironment.


Design of the new simulatorCell population simulation

The Scheduler::Run()

Single cell life by means of iteratively executingspecializations of the cycle phases template function.

The Scheduler governs execution of these.

Rule: The youngest cell is the first to be processed.


Techniques we used . . .Phases step by step

G2-Phase

Finish of cell growth, creation ofcentrosomes

Brownian motion of dots

Detection of major and minor axisinside cell shape using PCA

Location of centrosomes driven bydistance transform

Universal motion of cell



Prophase

Chromatin condensates and nucleolidisappear

Dots belonging to one chromosometend to aggregate (move to meanposition) and form highlycondensed clusters

Nucleoli masks are removed formthe phantom




Prophase

Chromatin condensates and nucleolidisappear

Dots belonging to one chromosometend to aggregate (move to meanposition) and form highlycondensed clusters

Nucleoli masks are removed formthe phantom




Metaphase

Move of chromosomes to metaphaseplate position

1 Nucleus membrane disappears

2 New positions for 23 chromosomesin metaphase plate are randomlygenerated

3 Old positions of 23 chromosomes,spread over the cell, are assigned tothe new ones (min cost assignmentproblem – Kuhn-Munkresalgorithm)

4 The movement of chromosomesfrom old positions to the new onesis generated



Metaphase








Metaphase








Metaphase








Anaphase

Chromosomes are split and drawn toopposite poles

Simple model of forces in whicheach chromosome is pulled to onecentrosomes while the individualchromosomes push away each other

In parallel the cell mask if slightlyexpanded along major axis usingfast level set methods

Universal motion of cell withoutadditional deformations



Anaphase







Anaphase







Telophase

Creation of nucleus membrane, nucleoli;The chromatin is uncoiled

Masks of two new daughter nucleicreated

Masks of new nucleoli in eachnucleus created

The chromatin is uncoiled viaBrownian motion




Telophase








Telophase








Telophase








Cytokinesis

Cell is pinched and new independentdaughter cells are created

PCA is used for detection foroptimal cut (minor eigenvectorsdefine cutting plane)

Not yet completely implemented asthis step is usually not noticeable(too short)




G1-Phase

Growth of “new born daughter” cell tofull size

An expanding flow field stretchesall masks and moves dot positions





G1-Phase







G1-Phase







S-Phase

Replication of DNA, i.e. growth ofnucleus


Dots are duplicated per partes untilall dots are duplicated



Techniques we used . . .. . . commonly


It consists of

rigid: translation and rotationnon-rigid: decent local deformations of cell shape

translation is preferred towards widest escape-tunnel

in unconstrained environment: it simulates Brownian motion

rotation is Gaussian with mean 0deg and sigma 13deg

(+-15deg angles are with probability half of the probability for 0deg)

inflating-deflating flow field that preserves volume

in any case: coherency of motion is preserved


Techniques we used . . .. . . commonly

Rendering of final images

It consists of

PSF simulation (simulates optics)“Poissoned” gained signal (uncertainty in the number of incomingphotons)added “little” Poisson (dark current, params from docs)added Gaussian (read-out noise, params from docs)

two sets of params: low (cca 0.5dB) and high (cca 0.8dB) SNR


Results

demonstration of high and low SNR frames

demonstration of phanthom video

demonstration of final images video


References

Simmons M. J., Snustad D. P. Genetika, Masarykova Univerzita, 2009

Reece J. B., Urry L. A., Cain M. L., Wasserman S. A., Minorsky P. V.,Jackson R. B. Campbell Biology, 9th ed., Pearson Education, 2011

Krontorad-Koutna I., slides for course PV185 Biology Panorama I(autumn 2012)

Liu L., Shell D. Assessing Optimal Assignment under Uncertainty: AnInterval-based Algorithm. International Journal of Robotics Research(IJRR). vol. 30, no. 7, pp 936-953. Jun 2011


Any questions?


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