Model Development and Assumptions

Figure S1: Model development cycle. An initial model of T follicular helper and regulatory cell differentiation was created from known factors. The network was assigned equations, calibrated and analyzed. With the increased understanding of system behaviors, the model was used for in silico experimentation for novel predictions. Within the experimentation stage, new interactions and factors were evaluated and implemented into the model network.

The small model (described by the network in Figure 1 of the main article body) was developed through a literature search on the most important factors contributing to the differentiation of T follicular helper and T follicular regulatory cells. Reactions within the model may indicate the differentiation into a cell phenotype, the activation of a protein, or the expression of a protein. These reactions may be activated or inhibited by other species present within the model in a concentration-dependent manner. The model assumes that interactions between the cell types are conveyed through effects on the activation of Bcl-6 and Blimp1 rather than direct effects between cell types. Therefore, the only inhibition occurring within the network is between the proteins. These inhibitions are assumed to limit the ability of a reaction to progress rather than function in a subtractive manner. Consequently, inhibition interactions are implemented through the use of denominator terms, described by the sum of a parameter and the model concentration of the inhibitor. In the larger model, when multiple inhibitions to a single reaction are present, the effects, and therefore the inhibition terms, are assumed multiplied. Bcl-6 is assumed to be the critical determinant for the differentiation of the T follicular cell subsets. In both the small and expanded models, many of the effects on the cell types are mediated through an effect on the status of Bcl-6. All death and degradation rates are assumed to be mass-action, dependent only on a single parameter and the respective species.

Calibration Process

Figure S2: Model calibration workflow. Data for the fitting process was compiled into two datasets. A standard parameter estimate was used for initialization purposes along with a range of values to define the search space. The information was input into COPASI, where an optimization algorithm was used to search the parameter space for the optimal parameter set. The parameter sets were tested for measures of fit and ability to capture the behavior of the system.

The unknown parameters within the computational model derived from the network topology were fit using the parameter estimation feature of COPASI [1], which is able to fit the SBML compliant model to multiple experiments simultaneously. We used two global optimization algorithms: Particle Swarm[2] and Genetic algorithms [3] provided within COPASI . The search algorithms attempt to minimize the sums of squares of the variation between the provided experimental data, termed the calibration dataset, and the simulated dynamics. The Particle Swarm method functions through creating a number of parameter sets within the allowable range. Each of these sets is given a position and velocity. During each iteration of the method, the sets generate a new velocity based on the comparative fit of itself to its neighboring sets. The best optimization of the sum of squares is kept in memory. The Genetic algorithm

creates a population of parameter sets. These parameter sets reproduce by combining traits with another set to create a hybrid set along with random mutations. During each round of the algorithm, the sets compete and the highest performing sets survive the reduction to the original number of sets. For both algorithms, the process is repeated until the fit to the calibration dataset is optimized or the maximum number of iterations (2000 iterations) is reached. In both cases, a second dataset, termed the validation dataset, is used during the parameter fitting process. The sum of squares for the validation dataset is monitored but not minimized. Rather an increase in the sum of squares for the validation dataset is used as a stop criterion for the search algorithm which serves as a preventative measure against over-fitting. Parameters values are available in supplemental information section Parameter Values.

In general, initial estimate for each varied parameter were obtained using simulations to observe dynamics at multiple parameter values. After an initial estimate was obtained, each parameter was allowed to vary within a 10-fold range above or below the initial value, according to upper and lower bounds set during the search process. Each search algorithm was run a minimum of five times. The final parameter set was chosen by comparison of objective values, root mean squares, and standard deviations generated in different runs of the calibration. In all stages of the calibration process, the cell death and degradation parameters for each species were fixed at 0.03 and 0.1, respectively, unless a proper fit with these parameters fixed was not found.

The parameter fitting for the small model (defined by the network in Figure 1 of the main article body) was carried out in a two-step process. First, the production of molecules from stable populations of Tfh and Tfr cells was calibrated using in vitro results sourced from previously published studies on the production of CXCR5, Bcl-6 and Blimp-1 specific to these cell types. This initial fitting was conducted using reported averages as the calibration dataset. Additionally, a constraint was used that the fit needed to fall within the reported standard deviation or standard error. Using the parameters from this first step, the populations of Tfh and Tfr cells was calibrated to time-course data generated from a mouse model of H. pylori infection. In this step, the model was fit to data from four time points, with each time point containing 8 replicates. Within each 8-replicate set, three values were randomly assigned to the validation dataset and 5 values to the calibration dataset. The remaining parameters were allowed to vary in order to fit the data. Average values for every data point used within the parameter fitting process are included with supplemental information (S3 File).

The parameter fitting for the larger model (defined by the network in Figure 5 of the main article body) was carried out in an iterative process. Parameter values undisturbed in their function with an equation during the expansion process were retained in the transition. The network was then expanded one new loop or pathway at a time from the existing smaller model. For example, starting with the core of the model in place, the pathway from Tfh to IL-21 to STAT3 to Bcl-6 would be added in one step. The corresponding in vitro production for these proteins would then be used as the calibration dataset, in a similar process described in the previous paragraph. In order to retain the core behavior, the time-course data for the Tfh and Tfr population was used as part of the validation dataset within each iteration of the expansion.

Model Equations

The model described by the network in Figure 1 is defined by the following differential equations.

Table S1. Small model variables.Variable Model quantityN Naïve CD4+ T cellsFh T follicular helper cellsR T regulatory cellsFr T follicular regulatory cells

B6 Bcl-6

B1 Blimp-1C CXCR5

dNdt

=sN−γ1 B6 N−dN N

d Fh

dt=γ 1 B6 N−dFh

Fh

dRdt

=sR−γ2 B6 R−γ 3CR−dR R

d F r

dt=γ2 B6 R+γ3 CR−d Fr

F r

d B6

dt=

σ1 Fh

α 1+B1−d B6

B6

d B1

dt=

σ2 F r

α2+B6−d B1

B1

dCdt

=σ 3 F r+σ 4 Fh

α3+B1−dC C

The model described by the network in Figure 5 is defined by the following differential equations.

Table S2. Expanded model variables.Variable Model quantityN Naïve CD4+ T cellsFh T follicular helper cellsR T regulatory cellsFr T follicular regulatory cells

B6 Bcl-6

B1 Blimp-1C CXCR5F3 FoxP3

S3 STAT3

S5 STAT5

I2 IL-2

I4 IL-4

I6 IL-6

I10 IL-10

I21 IL-21

Ic ICOS

Tb TGFb

T1 Tgif1

Rx Retinoid X receptor

dNdt

=sN−γ 1 B6 N−d N N

d Fh

dt=

γ 1 B6 Na1(α 0+ I10)

−d FhFh

dRdt

=sR−γ2 B6 R−γ 3CR−dR R

d F r

dt=γ2 B6 R+γ3 CR−d Fr

F r

d B6

dt=

σ1 i I c+σ1s S3

(α1+B1)(α1 s+S5)(α 1 r+Rx )−dB6

B6

d B1

dt=

σ2 F r

α2+B6−d B1

B1

dCdt

=σ 3 F r+σ 4 Fh

α3+B1−dC C

d F3

dt=σ5 R−dF3

F3

d S3

dt=σ6 I 6+σ 7 I 21−dS 3

S3

d S5

dt=σ16 I 2−d S5

S5

d I 2

dt=σ17 N−d I2

I 2

d I 4

dt=σ8 Fh−dI4

I 4

d I 6

dt=

σ 9

α 4+ I 4−d I 6

I 6

d I 10

dt=σ10 F r−d I10

I10

d I 21

dt=σ11 Fh−d I 21

I 21

d I c

dt=σ12 Fh−d I c

I c

d T b

dt=σ 13 I 10−dTb

T b

d T 1

dt=σ14 Fh−dT1

T1

d Rx

dt=

σ15T b

α5+T 1−dR x

R x

Parameter Values

In general, parameters are as follows: s denotes a source constant, γ denotes a differentiation activator, d denotes death or degradation, σ denotes protein activation, α denotes inhibition.

Table S3. Parameter values within the model presented by the network of Figure 1.

Parameter Value Description Dimensions Species Objective Value Species RMS100 source constant of naïve T cells [c]/[t] 0.000347 0.00114

0.0010 activation of Tfh differentiation by Bcl6 1/([c]*[t]) 0.00143 0.02650.030 death of naïve T cells 1/[t] 0.000347 0.001140.030 death of Tfh cells 1/[t] 0.00143 0.0265

50 source constant of regulatory T cells [c]/[t] 0.563 0.9740.056 activation of Tfr differentiation by Bcl6 1/([c]*[t]) 3.17E-06 0.0003860.11 activation of Tfr differentiation by CXCR5 1/([c]*[t]) 3.17E-06 0.0003860.030 death of regulatory T cells 1/[t] 0.563 0.9740.030 death of Tfr cells 1/[t] 3.17E-06 0.0003864.70 activation of Bcl6 by Tfh cells [c]/[t] 1.18E-08 0.0001720.20 inhibition of Bcl6 by Blimp1 [c] 1.18E-08 0.0001720.10 degradation of Bcl6 1/[t] 1.18E-08 0.0001725.11 activation of Blimp1 by Tfr cells [c]/[t] 8.39E-04 0.02052.39 inhibition of Blimp1 by Bcl6 [c] 8.39E-04 0.02050.10 degradation of Blimp1 1/[t] 8.39E-04 0.02053.04 activation of CXCR5 by Tfr cells [c]/[t] 1.66E-07 0.0009122.92 activation of CXCR5 by Tfh cells [c]/[t] 1.66E-07 0.0009120.054 inhibition of CXCR5 by Blimp1 [c] 1.66E-07 0.0009120.10 degradation of CXCR5 1/[t] 1.66E-07 0.000912

Table S4. Parameters according to the number assigned on the heatmap presented in Figure 4.

Parameter Value Description Parameter Number0.10 degradation of Bcl6 15.11 activation of Blimp1 by Tfr cells 250 source constant of regulatory T cells 3

0.030 death of Tfh cells 40.030 death of naïve T cells 50.20 inhibition of Bcl6 by Blimp1 60.030 death of regulatory T cells 70.10 degradation of CXCR5 80.054 inhibition of CXCR5 by Blimp1 90.030 death of Tfr cells 102.92 activation of CXCR5 by Tfh cells 110.11 activation of Tfr differentiation by CXCR5 122.39 inhibition of Blimp1 by Bcl6 133.04 activation of CXCR5 by Tfr cells 144.70 activation of Bcl6 by Tfh cells 150.056 activation of Tfr differentiation by Bcl6 160.10 degradation of Blimp1 17100 source constant of naïve T cells 18

0.0010 activation of Tfh differentiation by Bcl6 19

Table S5. Parameter values within the model presented by the network of Figure 5.

Parameter Value Description Dimensions Species Objective Value Species RMS100 source constant of naïve T cells [c]/[t] 0.000445 0.0211

0.0010 activation of Tfh differentiation by Bcl6 1/([c]*[t]) 0.00352 0.05930.0997 inhibition of Tfh differentiation by IL10 [c] 0.00352 0.05931.0000 modifier of Tfh inhibition 1/[c] 0.00352 0.05930.030 death of naïve T cells 1/[t] 0.000445 0.02110.030 death of Tfh cells 1/[t] 0.00352 0.0593

50 source constant of regulatory T cells [c]/[t] 1.45E-05 0.00380.056 activation of Tfr differentiation by Bcl6 1/([c]*[t]) 2.69E-06 0.001640.11 activation of Tfr differentiation by CXCR5 1/([c]*[t]) 2.69E-06 0.001640.030 death of regulatory T cells 1/[t] 1.45E-05 0.00380.030 death of Tfr cells 1/[t] 2.69E-06 0.001640.10 degradation of Bcl6 1/[t] 1.39E-07 0.0003735.11 activation of Blimp1 by Tfr cells [c]/[t] 0.00106 0.1032.39 inhibition of Blimp1 by Bcl6 [c] 0.00106 0.1030.10 degradation of Blimp1 1/[t] 0.00106 0.1033.04 activation of CXCR5 by Tfr cells [c]/[t] 1.67E-06 0.001292.92 activation of CXCR5 by Tfh cells [c]/[t] 1.67E-06 0.001290.054 inhibition of CXCR5 by Blimp1 [c] 1.67E-06 0.001290.10 degradation of CXCR5 1/[t] 1.67E-06 0.00129

3.244175 activation of Bcl6 by ICOS [c]3/[t] 1.39E-07 0.0003733.2195 activation of Bcl6 by STAT3 [c]3/[t] 1.39E-07 0.000373

0.2000098 inhibition of Bcl6 by Blimp1 [c] 1.39E-07 0.0003731.367523273 inhibition of Bcl6 by STAT5 [c] 1.39E-07 0.000373

0.1253 inhibition of Bcl6 by RXR [c] 1.39E-07 0.0003730.104 activation of FoxP3 by regulatory cells 1/[t] 4.69E-06 0.002170.10 degradation of FoxP3 1/[t] 4.69E-06 0.00217

0.1253 activation of STAT3 by IL6 1/[t] 0.000183 0.01350.10 activation of STAT3 by IL21 1/[t] 0.000183 0.01350.10 degradation of STAT3 1/[t] 0.000183 0.0135

0.014555 activation of IL4 by Tfh cells 1/[t] 1.44E-05 0.003790.10 degradation of IL4 1/[t] 1.44E-05 0.00379

0.9901 activation of IL6 [c]2/[t] 1.81E-09 4.26E-050.43475 inhibition of IL6 by IL4 [c] 1.81E-09 4.26E-050.69675 degradation of IL6 1/[t] 1.81E-09 4.26E-050.0677 activation of IL10 by Tfr cells 1/[t] 0.000489 0.0221

0.10 degradation of IL10 1/[t] 0.000489 0.02210.06005 activation of IL21 by Tfh cells 1/[t] 4.12E-14 2.03E-07

0.10 degradation of IL21 1/[t] 4.12E-14 2.03E-070.01787 activation of ICOS by Tfh cells 1/[t] 2.04E-06 0.00143

0.10 degradation of ICOS 1/[t] 2.04E-06 0.00143

α0

a1

Table S6. Parameters according to the number assigned on the heatmap presented in Figure 6. Note that parameters associated with precursor cells (sN, sR, dN, dR) and death of Tfh and Tfr (dFh and dFr) were excluded from the heatmap due to large differences between these parameters and the remaining set.

Parameter Value Description Parameter Number0.10 degradation of STAT3 10.10 degradation of Bcl6 210.00 activation of STAT5 by IL-2 35.11 activation of Blimp1 by Tfr cells 40.10 activation of IL2 by precursor cells 50.015 activation of IL4 by Tfh cells 60.10 degradation of IL21 70.70 degradation of IL6 80.10 degradation of CXCR5 90.10 degradation of ICOS 100.068 activation of IL10 by Tfr cells 110.20 inhibition of Bcl6 by Blimp1 120.054 inhibition of CXCR5 by Blimp1 130.43 inhibition of IL6 by IL4 141.37 inhibition of Bcl6 by STAT5 150.10 degradation of FoxP3 160.10 activation of FoxP3 by regulatory cells 170.10 inhibition of Tfh differentiation by IL10 182.39 inhibition of Blimp1 by Bcl6 19

0.0010 activation of Tfh differentiation by Bcl6 200.056 activation of Tfr differentiation by Bcl6 212.92 activation of CXCR5 by Tfh cells 223.24 activation of Bcl6 by ICOS 230.018 activation of ICOS by Tfh cells 240.10 degradation of IL10 250.10 degradation of IL4 263.04 activation of CXCR5 by Tfr cells 270.11 activation of Tfr differentiation by CXCR5 280.99 activation of IL6 290.13 activation of STAT3 by IL6 300.10 degradation of STAT5 310.10 degradation of IL2 320.060 activation of IL21 by Tfh cells 330.10 activation of STAT3 by IL21 343.22 activation of Bcl6 by STAT3 350.10 degradation of Blimp1 36

Table S7. Parameter values associated with the expansion to include Tgif1 within the network.

Parameter Value Description Dimensions Species Objective Value Species RMS0.10 activation of TGFb by IL10 1/[t] 0.0169 0.130.10 degradation of TGFb 1/[t] 0.0169 0.130.097 activation of Tgif1 by Tfh cells 1/[t] 0.512 0.07160.10 degradation of Tgif1 1/[t] 0.512 0.07160.05 activation of RXR by TGFb [c]/[t] 5.57E-13 7.47E-07

3.04985 inhibition of RXR by Tgif1 [c] 5.57E-13 7.47E-070.08465 degradation of RXR 1/[t] 5.57E-13 7.47E-07

(eq. 1)

(eq. 2)

Numerical Analysis

To analyze the stability of the steady states of the system, the differential equations for the molecular components were assumed to be at a quasi-steady state. The corresponding differential equations were set to zero and solved for each of species. The system was then reduced through substitutions into two differential equations: one equation describing the Tfh population (eq. 1) and one equation describing the Tfr population (eq. 2). The following system was then used in the evaluation of stability and generation of the phase plane in Figure 3 (main article body).

d Fh

dt=

γ1 sN (x)γ1(x )+dN

−dF hFh

d F r

dt=

γ 2 sR ( x )+γ3 sR ( y )γ 2(x)+γ3( y )+dR

−dF rFr ,

in which x=σ1 Fh

dB6(α1+z ), y=

σ 3 F r+σ 4 Fh

dc (α 3+z) and

z=dB6

σ 2 F r−dB6dB1

α1 α 2−dB 1σ 1 Fh+√(dB6

dB1α 1α 2+dB1

σ1 Fh−dB6σ 2 F r )2+4 dB6

2 dB1α 1α 2 σ2 F r

2d B6dB1

α1 α 2.

The Jacobian matrix was assembled and calibrated parameter values from Table 3 were substituted into the partial differentials. A characteristic equation was obtained for each of the non-negative steady states. Routh-Hurwitz conditions for stability were used to assess the stability at each steady state. As the number of equations in this simplification is two, the conditions are that the trace of the Jacobian is negative and the determinant is positive. The Jacobian and characteristic equations are presented in the format:

J=[ ∂ Fh'

∂ Fh

∂ Fh'

∂ F r

∂ F r'

∂ Fh

∂ F r'

∂ F r]

λ2−( traceJ ) λ+detJ=0

The following Jacobian and characteristic equation is for the steady state Tfh~Tfr defined by S1 = (Tfh = 1672 and Tfr =1658).

J (S 1)=[0.1742 −0.20590.0020 −0.0320]

λ2−0.1422 λ−0.0052=0

traceJ=0.1422>0 , detJ=−0.0052<0

The following Jacobian and characteristic equation is for the steady state Tfh < Tfr defined by S2 = (Tfh=1 and Tfr =1392).

J (S2)=[−0.0247 00.0137 −0.0300 ]

λ2+0.0547 λ+0.0007=0

traceJ=−0.0547<0 ,detJ =0.0007>0

The following Jacobian and characteristic equation is for the steady state Tfh > Tfr defined by S3 = (Tfh=3333 and Tfr = 1667).

J (S3)=[−0.0300 00 −0.0300 ]

λ2+0.0600 λ+0.0009=0

traceJ=−0.0600<0 , detJ =0.0009>0

The analysis concluded that the Tfh < Tfr and Tfh > Tfr steady states were both stable while the zero steady state and the Tfh ≈ Tfr were both unstable. The presence of an unstable node between two stable nodes indicates the existence of a bi-stable region within the system.

Furthermore, the entire system given by the seven equations listed below Table 1 was numerically analyzed using a Routh array on the eigenvalues of the system. The first two rows of the array are constructed according the characteristic equation in the format:

a7 λ7+a6 λ6+a5 λ5+a4 λ4+a3 λ3+a2 λ2+a1 λ+a0=0

Remaining coefficients were calculated in accordance with:

b i=a6∗an−2 i−a7∗an−2i−1

a6, c i=

b1∗an−2 i−1−a6∗b i+1

b1. ..

The resultant array displayed a single sign change within the first coefficients, confirming the existence of a single unstable node with the calibrated parameter set.

a7 a5 a3 a1a6 a4 a2 a0b1 b2 b3c1 c2d1 d2e1f1

-1 -2.5634 -0.01913 5.16607E-06-6.38447 -0.35089 -0.0003 1.35743E-07-2.50844 -0.01909 5.14E-06-0.30232 -0.00031 1.36E-07-0.01648 4.02E-06-0.00039 1.36E-07-1.8E-061.36E-07

Calibration Data

Table S8: Calibration data of simplified model. Data compiled from in-house experiments of H. pylori challenged mice (time course Tfh/Tfr data) and previously published experiments from literature (molecular data) [4-6].

Bcl-6 Blimp-1 CXCR5 Bcl-6 Blimp-1 Tfh TfhTfh CXCR5 - Blimp1 - Bcl6 -

Average 13.5 0.5 2.5 Average 1 0.8 Average 1 Average 1StDev 2 0.1 0.4 StDev 0.1 0.1 StDev 0.1 StDev 0.1

Tfr CXCR5 + Blimp1 + Bcl6 +Average 8 20 2.6 Average 7 7.9 Average 1.92 Average 2.16StDev 1 2.5 0.4 StDev 2 1.2 StDev 0.15 StDev 0.15

Week post-infection Tfh Tfr10 1260 150517 1380 129222 900 175025 60 1540

Week post-infection Tfh Tfr10 1340 171517 1510 123022 720 183025 170 1420

Calibration

Validation

Table S9: Calibration data of expanded model. Data was compiled from a microarray dataset of sorted T cell phenotypes and adjusted to fold change relative to naïve CD4+ T cells [7]. Data was combined with that of Table 8 for the calibration of the expanded model.

Protein IL-21 IL-6 STAT3 ICOS IL2 STAT5 FoxP3 TGFb IL10 IL4 RXR Tgif1Tfh

Average 4.69 1.12 1.96 2.29 2.51 1 1 1 1.01 4.72 1.02 1.94StDev 0.3 0.1 0.05 0.45 0.15 0.22 0.36 0.11 0.17

TfrAverage 1 1 1.72 3.13 1.35 1.17 2.62 1.33 1.64 1 1.28 1.03

StDev 0.21 0.67 0.38 0.42 0.13 0.16 0.14 0.2 0.12

Week post-infection Tfh Tfr10 1290 158417 1429 126922 832 178025 101 1495

Validation

Calibration

Quality Control Simulations

The effect of knockouts of IL-6 and IL-21, independently and combined, on T follicular helper (Tfh) cellular differentiation in vivo has previously been reported. The independent knockout of IL-6 creates a slight reduction of Tfh differentiation to about 85% of levels observed in the wild type. Meanwhile, independent knockout of IL-21 displays no significant changes. However, in a dual knockout system of IL-21 and IL-6, Tfh differentiation is reduced to approximately 55% of the wild-type [8]. In simulations with the expanded model a similar pattern emerged. The simulated knockouts were created by setting the initial concentration and the σ production parameter to zero for the respective species. The IL-21 simulated knockout displayed 93% Tfh differentiation. The IL-6 simulated knockout displayed 79% and the dual knockout displayed 60% Tfh differentiation. Results are displayed in Figure 1 below.

Figure S3. Simulated knockouts of IL6 and IL21.

The constitutive expression of Prdm1, the gene encoding for Blimp1, through retrovirus has been shown to decrease Tfh differentiation by about 80% [9]. In silico, the simulated retroviral expression was created by fixing the Blimp1 at a constant level slightly above the peak observed expression level in a standard calibrated time course. This altered simulated expression allowed a Tfh differentiation of 23% of the wild type levels at the standard, unaltered peak of the response. Inversely, a simulated knockout of Blimp1 forces the Tfh population to its high steady state, representative of Tfh cell numbers present in an inflammatory state. Results are displayed in Figure 2 below.

Figure S4. Simulated knockout and constitutive expression of Blimp1.

ICOS is a costimulatory molecule that promotes Tfh differentiation. Upon knockout of ICOS, Tfh differentiation is reduced to 28% in vivo [10]. With an in silico knockout, the model predicts a 20% Tfh

differentiation with respect to calibrated parameters. Results are displayed in Figure 3 below.

Figure S5. Simulated knockout of ICOS.

Modeling Extensions

Cytokine concentrations were compiled from the expanded Tfh cell differentiation model from behaviors associated with both the high and low steady states. In total, five sets were produced: the initiation of the high steady state, the stabilized high steady state, the peak of the calibrated time course and the resolution of the calibrated time course and the stabilized low steady state. These cytokine sets were then used as input for the extracellular cytokine pools in a previously described model of CD4+ T cell differentiation [11]. From this model, the relative amounts of Th1, Th17 and iTreg resulting from the Tfh model cytokine input were estimated based on the activation of transcription factors. The results were normalized to the output from the CD4+ T cell differentiation model without any input from the T follicular helper cell differentiation model. The CD4+ T cell differentiation model predicts that the largest increases in Th1 and Th17 are expected as a result of the stabilized high steady state. However, the Th1 response is greatly elevated in the peak of the calibrated time course as well. Notably, the results associated with the initiation of the high steady state do not greatly differ from either set related to the calibrated time course, suggesting that differences in downstream effects may not be noticeable until the Tfh population is reaches a stabilized elevation. Additionally, the stabilized low steady state exhibited the greatest relative increase in the iTreg subset. Results are displayed below in Figure 4.

Figure S6. Predictive modeling of downstream effects of Tfh and Tfr cytokine production.

Flow Cytometry Gating Strategy

Figure S7. Gating of T follicular helper (Tfh) and regulatory (Tfr) cells. Cells were gated to first eliminate non-viable cells and doublets in the first three plots. CD45+ cells were then gated as a dependent of the first three plots. From the CD45+ population, a CD4+ population was obtained by plotting CD4 versus CD3. This population was then gated for CXCR5 and BCL6, two factors present in both cell types. The Tfr population was taken to be the FOXP3+ proportion of this CXCR5+BCL6+ population and the Tfh population was taken to be the FOXP3- proportion.

RT-PCR primer sequences

SequenceBeta-actinForward 5' - CCG AGG CAT TGC TGA CAG G - 3'Reverse 5' - TGG AAG GTC GAC AGT GAG GC - 3'

Rps18Forward 5' - GGAGAACTCACGGAGGATGAG - 3'Reverse 5' - CGCAGCTTGTTGTCTAGACCG - 3'

Bcl-6Forward 5' - CCAACCTGAAGACCCACACTC - 3'Reverse 5' - GCGCAGATGGCTCTTCAGAGTC - 3'

Cxcr5Forward 5' - GTACCTAGCCATCGTCCATGC - 3'Reverse 5' - GTGCACTGTGGTAAGGAGTCG - 3'

Tgif1

Forward5' - AAGAGAAGGAGGAGAGGCAATCT - 3'

Reverse 5' - CTCTGAGGGATAGGCGTTGTATCT - 3'

RxraForward 5' - TCGAGCCCAAGACTGAGACATAC - 3'Reverse 5' - GCTTGTCTGCTGCTTGACAGAT - 3'

Table S10: Primer sequences. Sequences used for RT-PCR analysis of gene expression.

References1. Hoops, S., et al., COPASI--a COmplex PAthway SImulator. Bioinformatics, 2006. 22(24): p. 3067-

74.2. Kennedy, J. and R. Eberhart. Particle swarm optimization. in Neural Networks, 1995.

Proceedings., IEEE International Conference on. 1995: IEEE.3. Michalewicz, Z., Genetic algorithms, numerical optimization and constraints. International

Conference on Genetic algorithms, 1995.4. Nurieva, R.I., et al., Bcl6 mediates the development of T follicular helper cells. Science, 2009.

325(5943): p. 1001-5.5. Vaeth, M., et al., Follicular regulatory T cells control humoral autoimmunity via NFAT2-regulated

CXCR5 expression. J Exp Med, 2014. 211(3): p. 545-61.6. Yu, D., et al., The transcriptional repressor Bcl-6 directs T follicular helper cell lineage

commitment. Immunity, 2009. 31(3): p. 457-68.7. Linterman, M.A., et al., Foxp3+ follicular regulatory T cells control the germinal center response.

Nat Med, 2011. 17(8): p. 975-82.8. Karnowski, A., et al., B and T cells collaborate in antiviral responses via IL-6, IL-21, and

transcriptional activator and coactivator, Oct2 and OBF-1. J Exp Med, 2012. 209(11): p. 2049-64.9. Johnston, R.J., et al., Bcl6 and Blimp-1 are reciprocal and antagonistic regulators of T follicular

helper cell differentiation. Science, 2009. 325(5943): p. 1006-10.10. Choi, Youn S., et al., ICOS Receptor Instructs T Follicular Helper Cell versus Effector Cell

Differentiation via Induction of the Transcriptional Repressor Bcl6. Immunity, 2011. 34(6): p. 932-946.

11. Carbo, A., et al., Systems Modeling of Molecular Mechanisms Controlling Cytokine-driven CD4+ T Cell Differentiation and Phenotype Plasticity. PLoS Computational Biology, 2013. 9(4): p. e1003027.