T-cell commitment inheritance—an agent-based multi-scale model

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https://doi.org/10.1038/s41540-024-00368-y

T-cell commitment inheritance

—

agent-based multi-scale model

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Emil Andersson

, Ellen V. Rothenberg

, Carsten Peterson

& Victor Olariu

T-cell development provides an excellent model system for studying lineage commitment from a

multipotent progenitor. The intrathymic development process has been thoroughly studied. The

molecular circuitry controlling it has been dissected and the necessary steps like programmed shut off

of progenitor genes and T-cell genes upregulation have been revealed. However, the exact timing

between decision-making and commitment stage remains unexplored. To this end, we implemented

an agent-based multi-scale model to investigate inheritance in early T-cell development. Treating

each cell as an agent provides a powerful tool as it tracks each individual cell of a simulated T-cell

colony, enabling the construction of lineage trees. Based on the lineage trees, we introduce the

concept of the last common ancestors (LCA) of committed cells and analyse their relations, both at

single-celllevelandpopulationlevel.Inadditiontosimulatingwild-typedevelopment,wealsoconduct

knockdown analysis. Our simulations predicted that the commitment is a three-step process that

occurs on average over several cell generations once a cell is

fi

rst prepared by a transcriptional switch.

This is followed by the loss of the Bcl11b-opposing function approximately two to three generations

later. This is when our LCA analysis indicates that the decision to commit is taken even though in

general another one to two generations elapse before the cell actually becomes committed by

transitioning to the DN2b state. Our results showed that there is decision inheritance in the

commitment mechanism.

Commitment of T-cell progenitors o

ffers an opportunity to dissect the

molecular circuitry establishing cell

identity in response to environmental

signals. This intrathymic developme

nt process encompasses programmed

shutoff of progenitor genes

, upregulation of T-cell speci

fi

cation genes,

proliferation, and ultimately commitment

. The core gene regulatory net-

work controlling this process was identi

fi

ed from results from perturbation

studies

. It was also shown that Bcl11b expression correlates with the

functional committed state cell

sandcanthusserveasaproxyfor

commitment

The stages of early T-cell development are well known experimentally.

The T-cell progenitor cells are CD4

and CD8 double negative (DN) and do

not express T-cell receptors. The Kit

high

early thymic progenitors (ETPs or

DN1s) transition to the DN2a state which is marked by CD25 surface

expression

. The DN2a cells upregulate the

expression of Bcl11b, which

correlates with the commitment to the

T-cell lineage fate, as they transition

to the DN2b state

–

. The cells continue through the DN3 and DN4 stages

and progress with the late T-cell development, however, these stages of

development are not within the scope of this work. The cells proliferate

during the DN1 stage with an increas

ing proliferation rate as the cells

progress to DN2. The steps of the early

T-cell development are summarised

in Fig.

a and we refer to references

for detailed reviews.

We have earlier developed and independently veri

fi

ed a a model of the

core gene regulatory network (GRN) go

verning the early stages of T-cell

progenitor commitment

.ThisGRNisbuiltonexperimentallyshown

interactions between T-cell speci

fi

cation genes Tcf7 (TCF1)

,Gata3

and

Runx1

,andtheopposingSpi1(PU.1)gene

. The dynamics governed by

this network are in

fl

uenced by an extrinsic T-cell positive input from Notch

signalling present due to the thymic microenvironment. It has been shown

that Runx1 levels control the timing of T-cell development

andthatTcf7is

needed in order for Bcl11b to turn on

. Connecting Bcl11b directly to the

core GRN would predict an upregulat

ion of Bcl11b synchronised with the

expression of the T-cell-speci

fi

c factors. However, it has been experimentally

shown that Bcl11b is turned on a few cell cycles after CD25 expression and

T-cell-speci

fi

c factors upregulation

. The expression of Bcl11b is con-

trolled by a regulatory region consistin

g of many regulatory sites which each

can be open, closed or in an intermediate state

.Ifenoughsitesbecome

Computational Science for Health and Environment, Centre for Environmental and Climate Science, Lund University, Lund, Sweden.

Division of Biology and

Biological Engineering, 156-29, California Institute of Technology, Pasadena, CA 91125, USA.

e-mail:

victor.olariu@cec.lu.se

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| (2024) 10:40

1234567890():,;

open, the whole region is considere

d to be open and Bcl11b is expressed.

Furthermore, the ultimate activation of Bcl11b has been found to depend on

a slow cis-acting epigenetic mechanis

m, because direct observation of live

cells showed that the two equivalent al

leles within a single cell can be acti-

vated days apart

, and activation timing is stro

ngly modulated by repressive

histone marks across the regulatory region

. Therefore, we proposed a

model for a transcription level of regu

lation which propagates into an epi-

genetic level of Bcl11b regulation

. This single-cell model was trained with

data from RNA

fl

uorescence in situ hybridisation (FISH). Moreover, this

two-level regulation model was aug

mented with a proliferation level,

resulting in a multi-scale model which allowed us to investigate the T-cell

commitment mechanism at bulk level

.Thepredictionsfromthismodel

were validatedwith clonal kinetic data. Our multi-scale modelpredicted that

DN1 population developmental heterogeneity can arise solely from GRN

noise. It also showed that the obser

ved heterogeneous delay in lineage

commitment marked by Bcl11b arises both from GRN and epigenetic

stochasticity. Furthermore, we observed that the delay between the loss of

the Bcl11b opposing function X and expression of Bcl11b was similar to the

delay between the CD25 surface expression and the expression of Bcl11b.

However, we could not specify the exa

ct timing of the decision to commit

with respect to the observed Bcl11b upregulation or whether there is an

inheritance of progression towards the T-cell fate.

To this end, we have further developed our model by putting the full

multi-scale model into an agent-based setting. By this augmentation, we

unlock the ability to study in silico single-cell properties of T-cell develop-

ment. With this framework, we can investigate if inheritance of decisions

plays a role in the T-cell commitm

ent mechanism. We do so by studying

lineage trees of simulated T-cell colonies and introducing the concept of last

Fig. 1 | Agent-based multi-scale model for early

T-cell development commitment. a

Schematics

over the in vivo early T-cell development. Early

thymic progenitors (ETPs or DN1) transition to the

DN2a state which is marked by CD25 surface

expression. Commitment to the T-cell fate is

observed by Bcl11b upregulation as the cells pro-

gress to the DN2b state. The T-cell lineage devel-

opment continues through DN3 and DN4 stages

and eventually becomes mature T-cells. The early

T-cell development takes place under the in

fl

uence

of Notch signalling inside the thymus.

Depiction of

the multi-scale agent-based model for the T-cell

development stages from DN1/ETP to DN2b. As

CD25 is a surface marker it is not included in the

model. The magenta-coloured box illustrates level 1

and contains the GRN topology. The black arrows

and thick red blunted arrows represent positive and

negative direct regulation respectively. The thin red

blunted arrows represent inhibition of regulation.

The blue and grey arrows represent that Runx1 and

Notch promote the opening of Bcl11b regulatory

sites, while the green arrow shows that X keeps the

sites closed. The orange box illustrates the epigenetic

mechanism of level 2. The regulatory sites can

change between three different states (closed,

intermediate and open) and are affected by input

signals from level 1. Each cell of level 3 (green circles)

contains a copy of levels 1 and 2. The agent-based

model implementation tracks the relation between

the proliferating cells in lineage trees.

DN1/

ETP

DN3/4

αβT-cells

DN2a

uncommitted

DN2b

committed

Notch signaling

CD25

Bcl11b

Agents

Notch +

Runx1

Notch +

Runx1

Level 2

Notch

Runx1

Tc f 7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Runx1

Notch

Runx1

Level 1

Notch +

Runx1

Notch +

Runx1

Level 2

Notch

Runx1

Tc f 7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Notch

Runx1

Level 1

Notch +

Runx1

Notch +

Runx1

Level 2

Notch

Runx1

Tcf7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Notch

Runx1

Level 1

CIO

Notch +

Runx1

Level 2

Notch

Runx1

Tcf7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Notch

Runx1

Notch

Runx1

Level 1

CIO

Notch +

Runx1

Level 2

Notch

Runx1

Tcf7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Runx1

Notch

Level 1

Notch +

Runx1

Notch +

Runx1

Notch +

Runx1

Level 2

Notch

Runx1

Tc f 7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Notch

Runx1

Level 1

Level 3

Notch +

Runx1

Notch +

Runx1

Level 2

Notch

Runx1

Tcf7

Gata3

PU.1

P(Bcl11b

CLOSED)

P(Bcl11b

OPEN)

Notch

Runx1

Notch

Runx1

Level 1

Notch +

Runx1

Notch +

Runx1

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Article

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common ancestors (LCAs) of Bcl11b-positive cells. With inheritance of

decision we mean that a cell is in

fl

uenced by events that occurred in its

ancestors, e.g. event

could only occur if event

already happened in an

ancestor cell. If decisions are not inherited, then events may occur in any

order without affecting cells downstream, i.e. pure stochastic decisions. We

fi

nd that inheritance of decisions doe

s indeed play an important role and

that the commitment mechanism takes place over several cell generations.

Importantly, we

fi

nd that a cell

’

s decision to commit can actually be made

one to two generations before Bcl11b is upregulated.

Results

The model

We investigate decision inheritance in T-cell commitment by performing in

silico experiments. We propose an agent-based model with a core consisting

of our previously publishedstochastic multi-scale model

.Bytreatingsingle

cells as separate agents, we can constru

ct lineage trees corresponding to an

entire cell colony, enabling us to access d

etails like inheritance and relations

between cells which was previously not r

eadily available. The model consists

of three levels: level 1 is a transcriptional level inside a cell, containing a GRN

governing the core differentiation process; level 2 is an epigenetic level, also

inside a cell, where the Bcl11b regula

tory region is treated by opening and

closing of regulatory sites depending on signals from the transcriptional

level; and

fi

nally, level 3, a proliferation level, where the cells as separate

agents divide and pass down properties to their descendants (see Fig.

b).

The mathematical details of all three levels in the agent-based model are

described in Methods. Differentia

tion is simulated starting from the

equivalent of the ETP stage. Note that

althoughBcl11bcanbeturnedonin

many DN2a precursors without cell division

, ETPs normally undergo

several cell cycles before turning Bcl11b on

. Hence, our model encom-

passes multiple cycles of cell division.

Level 1: transcriptional level

. The gene regulatory network in the

transcriptional level consists of 6 interacting genes: Runx1, Gata3, PU.1

(Spi1), Tcf7 (TCF1), Notch signalling, and a Bcl11b inhibitory function X

(see Fig.

b). X includes a slow initial chromatin opening mechanism and

other possible Bcl11b-antagonists, inhibiting the opening of the Bcl11b

regulatory sites. Runx1 and Notch act positively for opening the Bcl11b

regulatory sites and Notch is promoting Runx1, Tcf7 and Gata3. Both

Tcf7 and Gata3 operate towards opening the Bcl11b regulatory sites by

inhibiting X and PU.1. In turn, PU.1 inhibits Tcf7 and Gata3 as well as

their Notch activation. Experimental data supporting these linkages were

from refs.

–

; these were largely con

fi

rmed in a compre-

hensive update using recent genome-wide perturbation analysis data

Experimentally, CD25 marks the transition from ETP to DN2a, but since

CD25 is just a surface marker, we have not included this gene in the

model. Intrinsic transcriptional noise is present in experimental data

thus we simulate the GRN stochastically with the Gillespie algorithm

(see Methods). Bcl11b is not treated directly as a node in the GRN, but is

instead regulated in level 2. The communications between the tran-

scriptional level and epigenetic level are conducted through the signals

from X, Runx1 and Notch.

Level2:epigeneticlevel

. In vivo and in vitro, Bcl11b becomes expressed

in the transition from the T-cell development stage DN2a to DN2b. In

our in silico model, Bcl11b is regulated by an epigenetic mechanism

consisting of the opening and closing of regulatory sites instead of

treating the gene expression directly. The 500 Bcl11b regulatory sites can

either be closed (C), intermediate (I) or open (O). Cells at generation 0

have the Bcl11b regulating region completely closed. Cells with more

than 75 % of the regulatory sites open are considered to have an open

Bcl11b regulatory region, corresponding to Bcl11b being expressed.

When the Bcl11b regulatory region has opened up, the cell is considered

to have committed to the T-cell lineage fate

. The epigenetic level is

regulated by the transcriptional level. Runx1 and Notch increase the

probability of opening regulatory sites while X increases the probability of

closing them. More details about the stochastic implementation can be

found in Methods.

Level 3: proliferation level

. The proliferation level of the model simu-

lates an entire cell population. The simulations always start with one

individual cell at generation 0. The dynamics of the multi-scale model

containing the transcriptional and epigenetic levels inside the cell are

simulated over time. Cell division is also implemented with the daughter

cells containing the same multi-scale model as the mother, continuing the

transcriptional and epigenetic simulations. The colony evolves through

multiple divisions and its simulation corresponds to 120 h in experi-

mental time. We sample the division times from

fi

tted distributions that

vary with cell generations, to account for cell cycle length variability

experimentally observed

. This creates heterogeneity of the age of cells

from different generations, i.e. one simulated colony may undergo 6 cell

cycles while another may undergo 11.

During cell division, all the gene expression levels are copied to the

daughter cells, keeping them at the same levels as inside the mother cell.

However, the divisions follow a set of conditional rules imposed on the

regulatory sites

. If X is expressed, the regulatory sites are copied from the

mother cell, while the complete loss of X promotes the opening of the

regulatory sites (see Methods). Thus, a strong driving force to opening up

the Bcl11b regulatory region is the repression of X.

Agent-based model

. Our agent-based implementation enables us to

record the relations between the cells within a lineage tree. This way, we

can investigate the existence of inheritance in T-cell commitment. This

type of modelling makes it possible to know the transcription levels,

epigenetic status and age of each cell at any simulation time point. Having

access to this type of cell information is very informative for future

experimental efforts.

Investigating commitment inheritance

As illustrated in Fig.

a, surface expression of CD25 marks the transition

from ETP to DN2a and Bcl11b expression marks the advent of T-cell

commitment in experiments

. Bcl11b heterogeneity was shown in colonies

of differentiating T-cell progenitors bo

th in vitro and in silico in Olariu et al.

(2021)

. Furthermore, the model predicted a delay between when the

colonies reached 50 % of the cells with loss of X activity and when 50 % of

cells in these colonies became Bcl11b positive. Similarly, for in vitro

experiments, a large heterogeneity was observed for the number of cell

divisions and the time when the colonies reached 50 % CD25 positive cells

and 50 % Bcl11b positive cells.

These

fi

ndings raise a few questions which we attempt to answer using

our new agent-based implementation of the multi-scale model:

•

What are the mechanisms leading to the observed heterogeneity within

a single colony?

•

When is the decision taken to open or keep closed a cell

’

s Bcl11b

regulatory region?

•

How are system perturbations affecting the decision to commit?

Lineage trees

. To answer the questions above, we use a tool that

represents the simulated colonies as phylogenetic trees

or lineage tree

diagrams. Figure

a illustrates a simple version of a lineage tree, with key

features highlighted. The initial cell at generation 0 is the root of the tree

and every cell division leads to two new branches. Each cell is a node in

the tree and the radial length of a connection in the tree is proportional to

the cell

’

s lifetime, i.e. the time-axis points radially outwards. The colour of

the node represents the status of the cell where black depicts a cell with the

Bcl11b regulatory region closed and X expression greater than 0, a red

node represents a cell where the Bcl11b is closed but X is not expressed,

and white represents a cell where the Bcl11b region is open. With this

colouring scheme, one can observe heterogeneity of open Bcll1b within a

colony along with the variable delay between the loss of X and the

opening of Bcl11b.

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Last Common Ancestors

. Since the delay between CD25 activation and

Bcl11b opening varies between cells in experiments, both in time and

number of divisions, we have to track time relative to interesting events

rather than experimental time or generation counting when analysing

our model simulation outcomes. The cells

’

main characteristic con-

sidered here is whether the Bcl11b regulatory region is open or closed.

This is due to the fact that a cell with Bcl11b open has normally com-

mitted to the T-cell fate and has become DN2b. Therefore, we introduce a

system of categorising the in silico cells uniquely according to their

relations with cells with open Bcl11b within a simulated lineage tree (see

Fig.

b and c).

We de

fi

ne the

fi

rst category

‘

open

’

which includes all cells with open

Bcl11b regions. Two arbitrarily chosen cells from the

‘

open

’

-category which

have mother cells with Bcl11b closed

have a last common ancestor (LCA)

which is the last Bcl11b-closed cell they both originate from. Therefore, we

fi

ne any Bcl11b-closed cell that has at least one

‘

open

’

descendant in each

of its two daughter branches as an

‘

LCA

’

-cell. The

‘

LCA

’

-cells are further

classi

fi

ed depending on how many generations down the lineage the closest

‘

open

’

cell is located. For instance, if a closed cell has both of its daughter cells

‘

open

’

, it is of order 1, i.e. categorised as

‘

LCA 1

’

. If a closed cell instead has an

‘

open

’

cell

fi

ve generations downstream in one branch, but six generations

downstream in the other branch, it is of order 5, i.e.

‘

LCA 5

’

Bcl11b-closed cells upstream from the earliest LCA in a lineage are

fi

ned as

‘

closed pre-LCA

’

. The so-far unclassi

fi

ed cells are Bcl11b-closed

but located downstream from LCAs. These are de

fi

ned as

‘

closed post-LCA

’

These cells are also given an order d

epending on how many generations

downstream from the latest LCA the cell is. The de

fi

nitions of the four

categories are summarised in Fig.

bandc.

All the cells in the example tree in Fig.

a have been categorised

according to this system. From this tree, it is clear that a colony can be

heterogeneous in Bcl11b. The root cell, cell 0, is

‘

Closed pre-LCA

’

since every

cell in its lower branch, rooted in cell 1, is closed. The top half of the tree,

rooted in cell 2, has both open and closed sub-branches. Cell number 2 is an

LCA 3

’

cell since both its daughters have descendants which are

‘

open

’

where the closest is three generations a

way. Cell 2 together with cell 5 (which

is a

‘

closed post-LCA 1

’

-cell) are interesting cells since their branches have

different fates; some sub-branches open up while others stay closed.

Branching points like these are key points to investigate in order to elucidate

the inheritance mechanism in T-cell commitment.

By de

fi

ning these categories, we can examine the internal relations

between the cells in a tree in a generation-number-independent way. This is

important since the cells in some colonies in our model may only go through

5 divisions while the cells in other colonies could go through 10 divisions

over the time span of the simulation, c

onsistent with the wide variation in

cell cycle numbers between entry into DN2a and the onset of Bcl11b

expression that our experimen

tal results showed previously

.TheLCA-

category system is a tool to dissect wh

en the decision to undergo commit-

ment happen, as distinct from the ex

ecution of commitment itself. Pre-

sumably, no decision should have b

een made before an LCA-cell, thus, all

‘

closed pre-LCA

’

-cells should have similar gene expressions. By indexing the

LCA-cells, it is possible to track how many generations before the observed

cell state transition the actual decisio

n was taken and then relate this decision

to the most reproducible features o

f gene expression at this point. One

example when the decision to commit

wouldhavetobetakenverycloseto

the actual cell state transition is if al

lLCAsoforder2orhigheraresimilarto

‘

closed pre-LCA

’

in their gene expression states. Another very different

example would be if LCA-cells of order 6 express similar gene network

activity traits as open cells, then the decision to commit is taken long before

the observed transition. The

‘

closed post-LCA

’

-cells represent those cells

that fell short of obtaining complete

ly open Bcl11b regulatory region and

does also include cells that exited the T-cell lineage fate.

In silico simulations of lineage trees

We simulated 300 wild-type (WT) T-cel

l committing colonies, all identi-

cally initialised in the ETP cell state,

and produced corresponding lineage

trees for each colony. Figure

a shows an example lineage tree and in

Supplementary Figs. 5 to 10 a larger subset is presented. The lineage tree in

(Fig.

a) branched seven times, corresponding to seven divisions, yielding

128

fi

nal cells. Out of these, 22 are open, all located at the lower half of the

tree. Every cell in the branch rooted at cell 10 is open, and the remaining

open cells are all located in the branch rooted at cell 8 (from here, a branch

rooted at cell

is shorted to branch

). The cells in branch 6 show no sign of

Fig. 2| Small lineage tree and last common ancestor (LCA) de

fi

nitions. a

A lineage

tree example. Every node is a cell which is uniquely identi

fi

able by an index. Each cell

branches into two daughter cells. The radial connecting lines are proportional to a

cell

’

s lifetime. The colour of the node indicates the status of the cell

’

s Bcl11b reg-

ulatory region and X expression, as described by the legend. Each cell is labelled with

its LCA label.

fi

nitions of the LCA categories.

The graphical de

fi

nition of each

LCA category for the cells encircled with cyan. Note the subtle difference between

‘

closed post-LCA

’

and

‘

closed pre-LCA

’

, i.e. the only difference is whether they

have an LCA-ancestor or not.

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being about to open up, while a few ce

lls in branch 5 have lost X expression

but are still closed.

This tree shows clear heterogeneit

y in the different branches which

makes it a prime candidate to investigate what happens during development

at different important branching poi

nts. The simulated gene expression

levels are shown for three chosen cell lineages in Fig.

b, where each panel

shows the evolution of one lineage. The three lineages are 187 (blue path in

Fig.

a which is an open cell in branch 10; 205 (orange path) which is a closed

cell in branch 5, but with X depleted; and 241 (green path) which is a closed

cell in branch 6. The vertical lines in Fig.

b indicate cell divisions and are

labelled with the cells

’

LCA labels. Figure

c shows the computed expression

of Tcf7, PU.1, X and the fraction of open Bcl11b regulatory sites in one panel

Fig. 3 | Stochastic simulations of cell lineages.

Lineage tree for a simulated colony. Three different

lineages with different fates are marked with blue,

orange, and green lineage paths respectively. Black

nodes depict cells with the Bcl11b regulatory region

closed and X expression greater than 0, red nodes

represent cells where the Bcl11b is closed and X is

depleted, and white nodes represent cells where the

Bcl11b region is open.

Each panel shows the gene

expression dynamics for each of the three marked

lineages respectively. The vertical lines represent cell

divisions and are labelled with the cells' corre-

sponding last common ancestor (LCA) categories.

Each panel show the expression for Tcf7, PU.1, X

and the fraction of open Bcl11b regulatory sites

respectively for the three marked cell lineages. The

coloured dots indicate cell divisions.

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each to more conveniently compare how the activity of these genes are

calculated to differ in the three lineages. Here, the coloured dots indicate cell

divisions.

The three lineages only have the

fi

rst cell in common. It is clear that

already during the second generation of cells, the blue path starts to become

different from the green and orange paths. PU.1 decreases at the same time

as Tcf7 starts to increase. These two components are tightly connected in the

GRN (Fig.

b). PU.1 represses Tcf7 both directly and through repression of

the Tcf7-activating Notch signal, whil

e Tcf7 jointly represses PU.1 together

with Runx1 and Gata3. Runx1 is stable o

ver time and Gata3 follows Tcf7 but

is expressed at a much lower level. T

herefore, it is probably a small

fl

uc-

tuation of either decreasing PU.1 or increasing Tcf7 which throws the

preparatory switch towards the T-cell fate to start producing an excess of

Tcf7. Once there is an abundant amount of Tcf7, PU.1 is

fi

rmly repressed

while Tcf7 is kept at a high level by both its direct self-activation and its

indirect activation through Gata3. The orange lineage also goes through this

switch, but at a later time point on day 3, while the green lineage does not go

through this switch at all. Once Tcf7 (and Gata3) is highly expressed, X is

repressed. For the blue lineage, X is depleted before day 3 while, for the

orange lineage, this happens at day 4. On the other hand, X stays highly

expressed in the green lineage where PU.1 is also high and Tcf7 is low. For

the blue and orange lineages, when Tcf7 has gone through the switch and X

starts to decrease, the fraction of open Bcl11b regulatory sites slowly starts to

increase. However, when X is completely depleted, the epigenetic remo-

dellingrulespromotingtheopeningoftheBcl11bregulatorysitesbeginto

operate, resulting in Bcl11b

’

s accessibility making great increasing leaps at

every cell division. The blue lineage

opens up Bcl11b two generations after X

is depleted, exhibiting a delay between the loss of X and the opening of

Bcl11b. Presumably, in the orange lineage, Bcl11b would also open up after

the next division, if the simulation would have been longer; the orange

lineage exhibits similar traits as the blue one but roughly two days delayed.

The green lineage is similar to the early behaviour of the blue and orange

lineages and would probably also be able to throw the preparatory T-cell fate

switch if the simulation was run much longer, this way giving the system a

chance to achieve high expression of

Tcf7 and low PU.1. Two additional

lineages are shown in Supplementary Fig. 1 in purple and red. The purple

lineage represents a cell lineage which progress from

‘

LCA

’

‘

closed post-

LCA

’

back to

‘

LCA

’

again. The red cell lineage goes from

‘

LCA

’

‘

closed

post-LCA

’

, but does not return to

‘

LCA

’

.Boththelineagesundergothe

transcriptional switch when they are

‘

LCA

’

. The difference between

the lineagesis that the red lineage has X

expression for a longer time, with the

result that the Bcl11b regulatory sites only open up as governed by Eq. (

Thus, the red lineage does not open up as many sites at once step-wise as the

purple lineage does once X has becomes depleted.

Statistics of multiple simulated cell colonies

. In the previous section,

we dissected the gene expression dynamics for three speci

fi

c cell lineages

in the lineage tree shown in Fig.

. In this section, we use the LCA labels

(Fig.

b, c) to gauge the commitment dynamics at the population level

over all 300 colonies.

The number of divisions in the 300 simulated colonies spanned

between

fi

ve and twelve, with eight to ten divisions being the most common

(see Fig.

a). The colonies vary in sizes since the cell cycle lengths are

randomly sampled from the distributions speci

fi

ed in Table

,whichwere

fi

tted with experimental data in Olariu et al. (2021)

.Figure

bshowsthat

the model generated a variation in the fraction of Bcl11b-open cells per

colony. The colonies that divided 7, 8 or 9 times had similar median frac-

tions of open cells, while colonies th

at divided 10 or 11 times had a slightly

higher fraction of open cells. The reas

onforthisisthatthelargercolonies

had the possibility to divide more time

s after cells started to become Bcl11b-

open compared to the smaller colonies

. There were too few colonies with 5, 6

and 12 divisions to make any remark about their distributions. We also

observe that the absolute cell generation number does not seem to be of

particular importance for the commitment process. Thus, in order to

meaningfully compare the commitmen

t mechanisms between colonies, we

need a reference point to count cell divisions from. This is provided by the

LCA classi

fi

cation.

The colonies were classi

fi

ed according to their LCA properties as

described in Sections Last Common Ancestors and Methods and Fig.

The mean expression for each gene was calculated for each LCA cate-

gory, using the cells

’

fi

nal gene expression values before division. The

mean expression levels for Tcf7, PU.1 and X and the fraction of open

Bcl11b regulatory sites for the

‘

closed pre-LCA

’

‘

open

’

and

‘

LCA

’

categories are shown in Fig.

c. The categories are sorted in an

approximate developmental order. The grey numbers in each bar

indicate the number of cells belonging to each LCA category. The mean

Fig. 4 | Last common ancestor (LCA) statistics. a

The number of colonies reaching

each colony size.

Boxplot over the distribution of the fraction of open cells per

colony for different-sized colonies. Each dot represents a colony. The centre line of a

box is the median, the bounds of the box represent the

fi

rst and third quartile, and

the whiskers extend to 1.5 times the interquartile range. Points falling outside of this

range are shown as outliers.

Mean expression level for Tcf7, PU.1, X, and the

fraction of open Bcl11b regulatory sites for cells belonging to the different LCA

categories. The categories are ordered in an approximate developmental order. The

grey numbers indicate the number of cells belonging to each category. The red

arrows point out the preparatory switch towards the T-cell fate. The pink arrow

indicates the most common LCA stage where X function is lost. The blue arrow

shows that the opening of the Bcl11b regulatory region is delayed with two gen-

erations. The error bars represent standard deviations.

https://doi.org/10.1038/s41540-024-00368-y

Article

npj Systems Biology and Applications

| (2024) 10:40