Variance analysis (python program)

8/12/2019 Variance analysis (python program)

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A Quantitative Method to Track Protein Translocation Between Intracellular

Compartments in Real-Time in Live Cells Usin !eihted Local "ariance

Imae Anal#sis

Abstract

The enetic e$pression o% cloned %luorescent proteins coupled to time-lapse %luorescence

microscop# has opened the door to the direct visuali&ation o% a wide rane o% molecular

interactions in livin cells' In particular( the d#namic translocation o% proteins can now )e

e$plored in real time at the sinle-cell level' *ere we propose a relia)le( eas#-to-

implement( +uantitative imae processin method to assess protein translocation in livin

cells )ased on the computation o% spatial variance maps o% time-lapse imaes' The

method is %irst illustrated and validated on simulated imaes o% a %luorescentl#-la)eled

protein translocatin %rom mitochondria to c#toplasm( and then applied to e$perimental

data o)tained with %luorescentl#-la)eled he$okinase , in di%%erent cell t#pes imaed )#

reular or con%ocal microscop#' The method was %ound to )e ro)ust with respect to cell

morpholo# chanes and mitochondrial d#namics %usion( %ission( movement. durin the

time-lapse imain' Its ease o% implementation should %acilitate its application to a )road

spectrum o% time-lapse imain studies'


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Introduction

Proteins are o%ten motile( shuttlin )etween di%%erent su)cellular destinations to

per%orm various %unctions' "isuali&ation and +uanti%ication o% a protein/s su)cellular

location and movement over time is there%ore important %or understandin how proteins

%unction inside cells' Traditional approaches %or monitorin protein translocation have

relied on )iochemical methods to measure protein levels in various cellular compartments

over time e'' western )lottin su)cellular %ractions at se+uential time points.' !hile

these approaches have produced seminal advances in elucidatin molecular mechanisms

o% protein %unction( the# also have limitations' 0or e$ample( the# are not suita)le %or

trackin protein translocation in sinle cells( limitin kinetic anal#sis to populations o%

cells' The# also have limited time resolution due to tissue destruction re+uired %or

)iochemical assa#s at each time point' In addition( protein locali&ation ma# )e sensitive

to the concentration o% c#tosolic ions and meta)olites that are likel# to )e lost durin the

%ractionation procedure '

The development o% techni+ues to la)el proteins with eneticall#-encoded

%luorescent tas( com)ined with advances in live cell %luorescent microscop#( has

circumvented man# o% these limitations' In particular( these new techni+ues permit direct

visuali&ation o% )iochemical processes in livin cells in real1time' A current challene is

to couple imae processin techni+ues with statistical and computational tools to

interpret and e$tract +uantitative in%ormation %rom the vast amounts o% unstructured

imae data enerated )# time-lapse imain e$periments'

*ere we demonstrate a relia)le and eas#-to-implement +uantitative imae


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processin method to assess protein translocation )etween su)cellular compartments in

livin cells( )ased on the computation o% the spatial variance o% time-lapse microscope

imaes( which minimi&es user-introduced )iases' To demonstrate the use%ulness and

advantaes( we %irst validated the method usin simulated imaes and then applied the

techni+ue to anal#&e the translocation o% %luorescentl#-la)eled he$okinase *2.( a ke#

l#col#tic enme which shuttles )etween the c#toplasm and mitochondria' Currentl#(

translocation o% %luorescentl#-la)eled proteins )etween intracellular compartments is

most commonl# +uanti%ied as ratio o% %luorescence intensit# )etween two user-de%ined

intracellular reions o% interest R3I. in microscop# imaes' In the case o% *2( an R3I

with a hih concentration o% mitochondria is compared to an ad4acent R3I with %ew

mitochondria ' !hile this method o% measurement is enerall# use%ul( it su%%ers %rom

three ma4or draw)acks5 i. The choice o% the R3I is ar)itrar# and su)4ect to investiator

)ias ii. Appropriate R3I can onl# )e de%ined i% the discrete oranellar compartments are

easil# identi%ia)le and separa)le in the imaes( as( %or e$ample( in Chinese *amster

3var# C*3. cells or neonatal cardiac m#oc#tes in which mitochondria are concentrated

in the perinuclear &one and sparse elsewhere' *owever( the method is pro)lematic %or

cell t#pes with a uni%orml# distri)uted oranellar network( such as the mitochondrial

network in adult cardiac m#oc#tes' iii. The R3I is also sensitive to chanes in cell shape

and miration o% oranelles throuhout the cell durin the time course o% the e$periment(

makin read4ustment o% the R3I necessar# to avoid error' The spatial variance method

descri)ed herein minimi&es all o% these shortcomins'

Methods


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Ethics statement.This stud# was approved )# the UCLA Chancellor6s Animal Research

Committee ARC ,778-798-,8B. and per%ormed in accordance with the :uide %or the

Care and Use o% La)orator# Animals pu)lished )# the United ;tates mm lass )ottom culture

dishes' Adult rat ventricular m#oc#tes AR"M. were enmaticall# isolated %rom the

hearts o% 8-to F-month old male 0isher rats as descri)ed previousl# ' Brie%l#( %ollowin

anesthesia( hearts were removed and per%used retroradel# at 8G HC in Lanendor%%

%ashion with nominall# Ca,-%ree T#rode6s )u%%er containin ?', mml collaenase t#pe

II catalo num)er F?G9D !orthinton. and 7'?, mml protease t#pe JI" catalo

num)er P>?FGD ;ima. %or ,>1,= min' A%ter washin out the enme solution( hearts

were su)se+uentl# removed %rom the per%usion apparatus and entl# aitated to

dissociate the m#oc#tes' The Ca,concentration was raduall# increased to ?'= mmolL


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over 87 min' This procedure t#picall# #ielded F7197 o% rod-shaped( Ca,-tolerant

m#oc#tes that were then plated on 8> mm lass )ottom culture dishes' mM. lucose medium supplemented with 9

vv. %etal )ovine serum 0B;.( penicillin ?77 unitsml.( streptom#cin ?77 unitsml. and

,mM lutamine.

Gene expression. Rat *2I and *2II were enerousl# provided )# r' E' !ilson' 0usion

o% rat *2s to 0P was accomplished )# insertin a Bam *? site at the last amino acid o%

the codin se+uence and su)clonin into a modi%ied pK0P


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Pascal > imae so%tware Carl eiss( Inc'( Thornwood( oC.'

Numeric treatment and algorithm generation. Imae anal#sis( alorithm eneration(

statistical anal#sis and simulations were implemented in the P#thon prorammin

lanuae ( usin the CI as well as


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e$aminin the sini%icant di%%erence )etween roups e%%ect si&e statistics. ' All anal#ses

were per%ormed )# su)routines %or )ootstrappin developed in the P#thon prorammin

lanuae( usin the


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in the dilution o% the mitochondrial %luorescence and makin the interior o% the cell more

homoeneousl# %luorescent in the imaes' There%ore( in addition to the commonl# used

ratio-)ased measurement trackin the %luorescence intensit# chanes over time )etween

an R3I containin a hih concentration o% mitochondria( and an R3I representin the

ad4acent c#tosolic area with spare mitochondria ( assessment o% %luorescent protein

translocation can )e also handled as a %eatures detection pro)lem( i'e' assessin the

disappearance o% the mitochondrial o)4ects'

Imae derivative )ased approaches such as the ;o)el and Cann# operators are

amon the most popular imae processin alorithms usin ede detection %or o)4ect

detection ' *owever( spatial variance mappin-)ased approaches have )een shown to )e

superior %or o)4ect detection under conditions o% )lurred or low contrast imaes ' B#

comparin the variation in pi$el intensit# %rom reion to reion throuhout the entire cell(

spatial variance also provides a +uantitative measure o% the overall spatial comple$it#

inside a cell' ;ince mitochondria are discrete oranelles( the spatial variance o% re# scale

values in a iven window is lare when %luorescence %rom a protein arises predominantl#

%rom mitochondria( and decreases as it is released and di%%uses evenl# throuhout the

c#toplasm'

In the spatial variance alorithm( the variance operator is a local neih)orhood

operation that calculates the sum o% s+uares o% the )rihtness di%%erences %rom the mean

%or the neih)orhood surroundin each pi$el in the oriinal imae ' The variance value is

small in reions o% the imae with uni%orm )rihtness and )ecomes lare whenever sharp

dark-)riht transitions occur( which allow eas# detection o% oranelles such as

mitochondria %iure ?B and C.' In our alorithm( %or each pi$el P$(#in the input imae


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%iure ?A.( the variance was calculated %or a iven window si&e usin the %ormula )elow

which allows local computations to )e per%ormed simultaneousl# and e%%icientl# within

windows o% man# si&es 5

window

2=

i=1

n xi2

n

( i=1n xi )

2

n2

where $ and n are the intensit# o% each pi$el and the num)er o% pi$els within the window(

respectivel#'

In practice( most windows are s+uared( providin uni%orm weiht to all points

within the window area( and &ero weiht to points outside this area' Computations

per%ormed within a s+uared window( however( ma# )e overl# sensitive to imae points

near the ede o% the window( so that estimates o% imae properties chane a)ruptl# as the

window is moved across pi$els that represent imae noise' This e%%ect ma# )e avoided )#

measurin properties within :aussian-like windows in which the reatest weiht is iven

to the pi$els near the sample position and proressivel# less weiht is iven to more

distant pi$els ' The :aussian outputs a weihted averae6 o% each pi$el6s neih)orhood(

with the averae weihted more towards the value o% the central pi$els' This is in contrast

to the mean %ilter6s uni%orml# weihted averae' Because o% this( a :aussian %ilter

provides entler smoothin and preserves edes )etter than a similarl# si&ed mean %ilter

this is illustrated in the supplemental %iure ;?.'

There%ore( in our alorithm( the :aussian-weihted variance O,. o% all the pi$els in a

chosen window is computed( and the value is attri)uted to the central pi$el P $(#. o% this

window %iure ?A.' The window is then moved )# one pi$el( and the operation is

repeated( and so %orth %or all the pi$els in the input imae to o)tain the variance map o%

the oriinal imae %iure ?B.'


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Results

Method validation

Simulated images of protein translocation. To test our method( we %irst enerated

arti%icial imaes simulatin translocation o% a protein %rom mitochondria to c#toplasm

over time %iure ,.' Mitochondrial protein-)ound areas were modeled as isotropic or

anisotropic , :aussians with added random noise( and translocation was simulated

throuh redistri)ution o% the volume under the :aussians over the ad4acent area in the

imae decrease in amplitude and increase in width( so that the volume is kept constant.

%iure ,.' In our e$perimental imaes( the mitochondria are appro$imatel# > pi$els wideD

there%ore( in our computational imaes 87$87 pi$els.( we modeled mitochondria with 8

to G pi$el-wide , :aussians %iure ,.'

Computation o% the spatial variance %or the se+uence o% imaes in %iure ,C

simulatin protein dissociation %rom mitochondria is presented in %iure 8A' In our

alorithm( the variance map command computes a map o% the input imae( where the

intensit# o% a pi$el in the output map represents the variance within the pi$els window

centered at the correspondin pi$el o% the input imae' This operation is applied to all the

pi$els o% the oriinal imae throuh a local neih)orhood operation' ;ince mitochondria

are discrete oranelles( the spatial variance is lare when %luorescence arises

predominantl# %rom mitochondria %iure 8A( %irst imae.' As the protein is released and

di%%uses evenl# throuh the c#toplasm( intensit# o% the variance imae decreases and

o)4ects )ecome less and less detecta)le in the imaes %iure 8A( su)se+uent imaes.'

Calculation o% the mean o% the variance values %or each imae allows to +uanti%# the


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:aussians has )een randoml# assined( without simulatin protein translocation si&e and

width o% the , :aussians unchaned over time.' An e$ample o% se+uence o% imaes

recapitulatin the movement o% mitochondria over time that could )e o)served in

e$perimental imaes is presented in %iure FA' Unlike the ratiometric method( which

per%orms poorl# when the o)4ects in the imaes are motile see supplemental %iure ;8C.(

our alorithm is insensitive to mitochondrial movement and a similar variance is

calculated over time %or this se+uence o% imaes %iure FB.' 0iure FC( in which the

similar anal#sis has )een e$tended to ?777 simulations with di%%erent derees o%

mitochondrial motilit#( shows that our method is ro)ust toward mitochondrial motilit# as

similar spatial variance is o)served %or all the imaes'

To compare a :aussian kernel over a unit# kernel to compute the variance in our

method( we did a statistical pair-wise comparison usin the Bland-Altman %ramework o%

the results o)tained with the two kernels %or di%%erent se+uences o% imaes simulatin

protein dissociation %rom mitochondria( without or with mitochondrial motilit#' As seen

in the supplemental %iure ;FA( when the data o)tained %rom the anal#sis o% ?777

se+uences o% imaes simulatin protein dissociation %rom nonmotile mitochondria usin

the :aussian kernel are plotted aainst the data o)tained with a unit# kernel( all the points

lie on the e+ualit# line' Moreover( the raphical depiction o% di%%erences )etween paired

o)servations %rom the two methods versus their averae supplemental %iure ;FB. shows

that( even i% the unit# kernel tends to ive slihtl# hiher values( the calculated mean

di%%erence )etween measurements orane s+uare in the %iure. is not sini%icantl#

di%%erent %rom &ero( and the slope o% the linear %it o% the di%%erences is hori&ontal' These

results suest that there is a ver# hih deree o% areement )etween the two methods


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variance anal#sis alorithm to the imaes %iure >B. allowed us to +uanti%# *2,

dissociation %iure >C. and re-association %iure >. with mitochondria durin the

ano$iareo$#enation episode( data %rom which use%ul in%ormation can )e o)tained( such

as the hal%-time constant o% dissociationre-association'

;imilar %indins were o)tained in


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known to remain )ound to mitochondria durin meta)olic stresses and does not

translocate to the c#toplasm upon ano$iareo$#enation' !hen *2?-0P was

overe$pressed in A"RM and ano$iareo$#enation was applied 0i' GA( upper series o%

imaes.( the spatial variance measurement did not chane 0i' GB and GC.'

0inall#( we also demonstrate that the spatial variance method works e+uall# well

%or %luorescent pro)es which are loaded into mitochondria )# other means than enetic

encodin' 0i' = shows an e$ample o% an AR"M in which mitochondria were selectivel#

loaded with the %luorescent d#es TMRM 87nM. and calcein-AM' !hen e$posed to

Phen#larsine 3$ide PA3. to induce the mitochondria permea)ilit# transition MTP.(

mitochondria depolari&e causin loss o% TMRM %luorescence %rom the mitochondrial

matri$( with little chane in c#toplasmic %luorescence 0i' =A( lower panel. ue to its

neative chare( TRMR is concentrated more than a thousand-%old in the matri$ o%

polari&ed mitochondria( )ut when released is rapidl# diluted.' !hen calcein leaves the

matri$( however( c#toplasmic %luorescence increases as mitochondrial %luorescence

decreases 0i' =A( upper panel.' espite these di%%erences in the pattern o% %luorescence

chanes( )oth spatial variance measurements #ielded compara)le hal%-times o%

dissociation >'G9min vs >'=8min %or the variance calculated %rom the calcein and TMRM

data respectivel#.( indicatin the ro)ustness o% the techni+ue 0i' =B.'

Discussion

3)tainin accurate +uantitative data %rom live cell imaes is ke# %or testin


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mechanistic h#potheses a)out molecular and cellular processes' 0or e$ample( cell)ased

protein translocation assa#s can )e used to pro)e cellular sinalin pathwa#s that are

otherwise di%%icult to stud# usin traditional )iochemical assa#s' !hen taed with

%luorescent molecules( translocation o% proteins o% interest can )e appreciated )# visual

inspection o% imaes %rom %luorescence microscop#' *owever( these su)4ective

impressions can )e challenin to +uanti%#' *ere we developed a relia)le and eas#-to-

implement imae processin method to assess protein translocation )etween oranelles

and c#toplasm in livin cells( usin mitochondria as a test oranellar s#stem( )ased on the

computation o% the spatial variance o% time-lapse imaes' !e have demonstrated that the

method is ro)ust with respect to mitochondrial d#namics %usion( %ission( movement. and

chanes in cell morpholo# durin the time-lapse imain' !e validated the method )#

+uanti%#in *2, dissociation and re-association %rom mitochondria durin

ano$iareo$#enation as well as mitochondria transition pore openin in livin cells(

demonstratin its use%ulness %or )oth eneticall#-encoded and standard %luorescent

pro)es'

The spatial variance method has the %ollowin advantaes' i. The method

minimi&es user )ias )# eliminatin the need to choose and ad4ust R3I inside the cells as

re+uired )# the ratiometric method' Indeed( spatial variance provides a lo)al measure o%

spatial %luorescence heteroeneit# which is relativel# insensitive to chanes in oranellar

and cellular morpholo#' ii. The method can )e applied to individual sinle cells' ;inle

cell imain techni+ues overcome the averain e%%ects inherent in ensem)le

measurements and ena)le characteri&ation o% the )ioloical varia)ilit# )etween individual

cells' iii. The method is capa)le o% ivin hih detection responses in the settin o% low


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contrast edes( as illustrated in detectin the mitochondrial network in low contrast

reions o% imaes' This is )ecause ede detection is implemented on the )asis o% local

variances rather than on the local radients' As a result( ramp edes with low variation

can )e detected e%%icientl#D iv The method is readil# applied to the whole cell( providin

a lo)al measure o% shi%ts in %luorescence compared to the R3I method or calculation o%

the variance alon a sinle line drawn throuh the cell see %i > o% .'

In their recent report( "ena)le and al' ,7?8. showed the pit%alls o% usin spatial

averaed mean %luorescence imain %or detectin su)cellular )ehavior o% %luorescent

pro)es( in particular )ecause averaed spatial %luorescence cannot readil# assess the

deree o% d#e redistri)ution i% the imaes are not resolved enouh to detail all the

compartments ' !hile our method is also )ased on the measure o% a chane in an averae(

usin the variance instead o% the raw %luorescence still permits detection o% a chane in

compartment even i% the total amount o% %luorophored#e remains unchaned 0iure ,B.(

as the variance imaes hihliht the chanes in distri)ution o% the content in %luorescence

)etween di%%erent compartments' In addition( the advantae o% usin the variance is that it

can detect either a redistri)ution o% the %luorophore %rom one compartment to another( or

a loss o% the %luorophore' This is demonstrated in the 0iure =( where the variance

method per%orms e+uall# well %or )oth scenarios simultaneousl#( detectin the

redistri)ution o% Calcein and the loss o% TMRM durin the induction o% PTP openin in

adult cardiac m#oc#tes'

In summar#( the ease o% implementation o% this method should ena)le its

application to a )road spectrum o% time-lapse imain studies' Althouh to date we have

onl# validated the method %or the mitochondrial network( we e$pect that it will prove


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valua)le %or measurin translocation )etween other oranellar compartments as well'

Acknowledgements

!e thank Bernard Ri)alet and ;cott Eohn %or their help%ul discussion'


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References


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Figures

Fig 1::aussian weihted local variance computation process' A. urin the process( the

source pi$el is replaced with a :aussian weihted variance o% all the pi$els inside the

chosen window si&e' Kach pi$el inteer value in the source imae is multiplied )# the

correspondin value in the overl#in :aussian kernel( and the variance o% all the resultin

products is computed' The ra# value o% the source pi$el P$(#. is then replaced )# this

:aussian weihted local variance' This operation is repeated %or each pi$el in the oriinal

imae' B. ;ource imae and C. correspondin output imae a%ter application o% the

alorithm'

Fig :;imulation o% he$okinase *2. translocation %rom mitochondria to c#toplasm' A.

Area o% hih %luorescence arisin %rom mitochondrial *2-)ound was simulated )# a

series o% , :aussians( whose redistri)ution o% the %luorescence simulates the

translocation %rom mitochondria to c#toplasm' B. urin this process( the heiht and the

width o% each , :aussian are chaned so the volume under the , :aussian is kept

constant( to simulate a redistri)ution o% the %luorescence over the entire cell' C. Top view

o% the simulation o% the translocation o% *2 %rom mitochondria to c#toplasm' A uni%orm

random noise is added to enerate the %inal simulation imaes'

Fig !: The local variance alorithm e%%icientl# detects redistri)ution )etween

compartments' A. Application o% the weihted variance map alorithm to the model


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illustrated in %iure ,' As seen in the imaes( the spatial local variance is hih in the

reions o% hih %luorescence and decreases over time as the %luorescence is redistri)uted

over the whole imae' B. 0rom the time course o% the chane in variance( the time

constant o% dissociation can )e measured'


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Correspondin spatial variance imaes' C $ D. Plot o% the averae spatial variance at the

various time points( showin the time course o% the dissociation C. and re-association

. o% *2, with mitochondria durin the ano$iareo$#enation episode'


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measurement time points on di%%erents cells varied( e$plainin the di%%erent num)er o%

measurements %or each time point'

Fig (:Calcein-)ased assessment o% the mitochondrial permea)ilit# transition MPT. in

live adult cardiac m#oc#tes' A. The mitochondrial network in A"RM was pre-loaded

with Calcein-AM and then super%used with TMRM to record mitochondrial mem)rane

potential' Upon e$posure to 7'?mM Phen#larsine 3$ide PA3. to induce MTP( calcein

%luorescence redistri)utes within ?7 min to the c#toplasm indicatin MPT upper series o%

imaes.( and TMRM %luorescence concomitantl# decreases dramaticall# indicatin

mitochondrial depolari&ation' Under each imae( the correspondin spatial variance

imae is reported' B'' espite the di%%erences in total %luorescence %or the calcein and

TMRM imaes( the correspondin spatial variance imaes predict similar times course o%

redistri)ution'

Fig )1:Implementation o% a :aussian window weihted kernel. preserves edes )etter

compared to a uni%orml# weihted windows unit# kernel.( especiall# %or lare window

si&es' !indow si&es %rom 8$8 pi$els. to ,@$,@ pi$els. were tested'

Fig ):0luorescence )leachin correction' A. Linear )leachin over time was simulated

on our model )# dividin the re%erence imae with increasin %actors # V 7',>$ ?.' B*

D. !ithout normali&in to the total %luorescence o% the imae( the intensit# o% the

variance map imaes decreases over time B.( with the values reported in ' C* +.


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variance map imaes C.( as seen in the values K.'

Fig )!:Comparison spatial variance and ratiometric R3I methods' A. R3I chosen %or

the c#toplasmic ?. and mitochondrial ,. area' B. etection o% he$okinase *2.

dissociation with the variance )lack. and ratiometric R3I )lue. imae processin

methods' C. The spatial variance method is insensitive to mitochondrial movement

whereas the ratiometric R3I method is stronl# distorted )# mitochondrial movement'

Fig )":Pair-wise comparison o% the variance mean computed with a :aussian-weithed

:. and a unit# U. kernel %rom imaes simulatin translocation o% a protein %rom %i$ed

mitochondria to the c#tosol' A. The dashed red line is the line o% e+ualit# on which all

points would lie i% the two kernels ave e$actl# the same variance mean %or each imae'

As shown )# data( the unit# and :aussian kernel ive similar results in this scenario

where the mitochondria are %i$ed' B. :raphical depiction o% di%%erences )etween paired

o)servations %rom the two methods versus their averae le%t. and historam o% those

di%%erences riht.' The mean o% the di%%erences orane s+uare and orane dashed line. is

not statisticall# di%%erent %rom &ero red dashed line.( revealin that there is no constant

)ias when usin the unit# kernel to calculate the variance compared to the :aussian

kernel' The slope o% the reression o% di%%erences on means ra# line. is also non

di%%erent %rom &ero( indicatin an a)sence o% proportional )iais' These results suest that

there is a ver# hih deree o% areement )etween the unit# and the :aussian kernel

variance computation when measurin the translocation o% %luorophored#es %rom non

motile compartments'


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Fig )#:Pair-wise comparison o% the variance mean computed with a :aussian-weithed

:. and a unit# U. kernel %rom imaes simulatin translocation o% a protein %rom motile

mitochondria to the c#tosol' A. The dashed red line is the line o% e+ualit# on which all

points would lie i% the two kernels ave e$actl# the same variance mean %or each imae'

As shown )# data( the unit# kernel tends to overestimate the variance compared to the

:aussian kernel especiall# %or hih values o% variance' B. :raphical depiction o%

di%%erences )etween paired o)servations %rom the two methods versus their averae le%t.

and historam o% those di%%erences riht.' As shown )# the slope o% the reression line

ra#. that di%%ers sini%icantl# %rom &ero pN7'7>.( usin a unit# kernel instead o% a

aussian-weihted kernel ives a proportional )ias on the measure o% the variance when

compartments are motiles' In addition( the mean value %or the di%%erences orane s+uare

and dashed line. also di%%ers sini%icantl# %rom 7 pN7'7>.( revealin a %i$ed or

Wrelative/. )ias' Those )iases miht )e the conse+uence o% the e$cessive sensitivit# o% the

unit# kernel to imae points near the ede o% the unit# window ivin ver# hih values

when the simulated movin mitochondria suddenl# enter the window'

Variance analysis (python program)

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