> ` $bjbj .(
\ , t (
$BhCE
C
@$
p0H}HHt
CC
dd Dd 46"XProtocol S5
In all our computer simulations, we estimated the ppERK response of individual T cells to a given number of ligands. To compare our simulation outputs with the experimental results, one must take into account the noise in the level of presentation of ligands by antigen presenting cells. Indeed, for a given concentration of pulsing peptide, the distribution of ligands being presented by the antigen presenting cell (APC) follows a log-normal distribution with a coefficient of variation of 55% (see Supplementary material S2). Hence, we had to convolve this noise in presentation with the results from our computer simulations to estimate the characteristic time of ERK response of T cells to a typical level of presentation of ligand, as measured experimentally.
We used the following five-term polynomial fit for the computer-simulated dependence of the cells response time (T) as a function of the number of presented ligands (x):
T(x)= 318.49-212.13*log(x)+65.166*[log(x)]2-9.4663*[log(x)]3+0.60105*[log(x)]4.
At a given time t, a T cell will respond with ERK phosphorylation if the number x of ligands presented by the antigen presenting cell in contact is such that:
x0 (t)< x < x1(t),
where x0 (t) and x1 (t) are such that T (x0 (t))= T (x1 (t))=t.
For a typical presentation of Y ligands per APC, the distribution of ligand presentation follows a log-normal distribution. Thus, we can estimate the probability of a T cell to be activated (noted q(t,Y)), by computing the number of APC presenting x ligands between x0(t) and x1(t):
EMBED Equation.DSMT4
where s is the standard deviation of the distribution of ligand presentation.
For a typical presentation of Y ligands per APC, the characteristic time t(Y) of the ppERK response of T cells is then estimated with:
EMBED Equation.DSMT4
We use a small computer routine to derive this characteristic time t(Y) of ppERK response of T cells for different levels Y of presentation on APC.
Through this computation taking into account the noise in the level of presentation of the agonist ligands, we explain how the divergence of the response time obtained in our computer simulation (at low ligand number and high ligand number) is abrogated at low levels of presentation and matches well with our experimental results.
Figure: definition of x0 (t) and x1 (t). For a given time t, only cells that are in contact with APC presenting x ligands, such as x0 (t)؛@E_7( CD19sIz3%~w};7p6;"Kj5U:L:'5\ t~ g8Q[@fR`Q{[O(.D{/B%.mt8
iՅm&yhK@tMOC dƯ[w,ySNm]7b3b4tŮEU/QQ:D?3_*ߍwk+2y#[CC6|znIQ{v>M$ԦឩAW'\Ld}'2%'
Wj?K4azVFMRدa:c<_1d_W{u!
,о$h`Xvk^
PmI"vp*EoJi>f#u&(cD{|SlxǝbfQ%[rGnG=ee;o䑴 ߊcvGV/ qf+>4PBۆm/#ƑnGiheLXlR~ޒ4ſ?{K7e.Ձ]TpV<vL.Ux42Ǎ9L?wbWPS\\&
v17^ Pw;ŧie`,N8<HL|N%Tj2M'",xfl/+MeVx|&Vrq_G-bH@8RCyHys2=AG%u~T}`y}.4sA0),vEB iXHsB
`1ȩy)^fY&@h3y݁]mD|(D~Sv܃A=6Xk "%ALpCk)6*&Itn59xeׯr3h)DADx5;xwF~16}OyT+W!.l>K,FpÆ
mu=cEDd
lb
c$A??3"`?2M#mR)j_Ytc5B)"`!!#mR)j_Ytc5BjxڵTKSQ?mmSzoBt-D$P$'_Z/}ͥ{Y!APW
A?dXǚ`utH.{vϹ.`а䌙JE쨩k]3
bJ]ڠB0j
(¹$`cHϩ\lZVcڜ^pOeDd-#P(In_FJeK&%Efcf!itnz;t$
}#hrRqi G\W 5{}'P%{̽$@D'KmeLkwTBvZazZWo|ܵ^h
r]'αlFS0.~x">{BOM]Dd.(j
C8A Plot NoiseIssue"`2*Y6 `!*Y6XEt8cxmlSUnM`DCaEg сL2p@MGU%,F`I 3&:p̈IiXufQ|/ɼ=24>w_soS%"Lk%ʵ+,MĪRQf5SGR:eˎƼB{=BL&˯V8)ɱ+T:Vf"uf"PDnk*Ri3zPi3ڠj3ڨVh3zX5j3Qj-E[@=Dn^f"uzWh_YKU5?eF+Œb,)b{:ζl7
*Gg+JK^mvPG)ƺlRƪSA̯RX`Q,mǶc;Xօvc=Xv;
`XK`g36%$6
cJSi!VcX VaeXV0VUbX-[ ւ`XیE(։ubq,ÎaX/ևaX?v;%v;=7ljFܿ
Rų$.z4 fzs0"XbQl;ہ.l7zqlX;!,%al3o(+Ċb+ʰ2|*Z[ƂXkZیmƢX:8ǎaǰ^~;X;]Nj.$ۘi2[AOԺ߬otk)'TMvpUrvI{x~idKr-ۣѺͻqL;nMvZ.ʗ2'Ӯ۽RoOQG]|ۯ͜WvNmo/Uc~Bq͜dtv,zz8}Vo~6Hv4/
c¬=gĥ-[r
JfǦ_,
rKZپJ2i_zޙ!V?*FN榀ghm5"`Ōs7&,m橗g2䵌_Zt'yZmP[m+5V[?k,}d@'(
{CՑ<9?_s}<_jb-Xb1!,
bIl3uaX V*jb-Xb1!,k>%-hu/{[5bcV)l;aX V*jb-Xb1!o~Ź먱mh"Tdqj)W^N^E,r
gWm/-Rcs9܋&lroxo|'NؾL}2)n*|WO]wSQÛpS>Lg}im'p{xbzϓ2oc
45y:!N56KlImwJf6pHTt.γ&.۟/97JeXFG]ND?Dd.(h
C6APlot w"o noise"`2PKʳ&0`!PKʳ&0`XEt8c|xoH]ew?s&.8fI`E$E]Vw^צkb^E-fEṈ5amP0A/Be["vν{t~9ss9LD>'(6r5)_Hv\d0۔-X$ܴGr(5PD~VNPu*餋4~zmMR.i2i2R;i2i2Gi2r?Ȼ5Mzgk5MF"|Ś&#{5MF^lZj ںuЇ4> :iMtƚ&#=5MF5MFFgk\߬i2rnXd>[#MFk<˛i2Ki2[d_H_;u8uZɚ&#kYqql{
۞BgYBOj2Xl4zaaXص_Ǘ#:>Z+V&iR°kۀMFaEVjF l`&ώ>ɳNX'Kl6
F`# l
65|X>V+U*a*X,aհX
VkaXu`},`cq8l6 fay<_\
tFIoaA /D):>:aX,K`!l6&`)l6!B
,+
a0*`JX%
VBjX5V`mvX;uaݰ>X,Ka1l6Mf`3Y,l6!\Öka|7f~d[f/o=.dʶ·;av^qulCW%Љ3zo*s;ʝn+'Q]3m^~ڡ^{a*]fY\o38˜k%kqcZ\۽|-uDOs
ܩO٭Ռu;uϻiXx.*