# Geometry-sensitive protrusion growth directs confined cell migration

Johannes Flommersfeld  Department of Physics and Astronomy, Vrije Universiteit
Amsterdam, 1081HV Amsterdam, Netherlands  Arnold Sommerfeld Center for
Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-
Maximilian-University Munich, Theresienstraße 37, D-80333 Munich, Germany
Stefan Stöberl  Faculty of Physics and Center for NanoScience, Ludwig-
Maximilian-University, Geschwister-Scholl-Platz 1, D-80539 Munich, Germany
Omar Shah  Department of Physics and Astronomy, Vrije Universiteit Amsterdam,
1081HV Amsterdam, Netherlands  Joachim O. Rädler  Faculty of Physics and
Center for NanoScience, Ludwig-Maximilian-University, Geschwister-Scholl-Platz
1, D-80539 Munich, Germany  Chase P. Broedersz<EMAIL_ADDRESS>Department
of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081HV Amsterdam,
Netherlands  Arnold Sommerfeld Center for Theoretical Physics and Center for
NanoScience, Department of Physics, Ludwig-Maximilian-University Munich,
Theresienstraße 37, D-80333 Munich, Germany

(August 28, 2024)

###### Abstract

The migratory dynamics of cells can be influenced by the complex micro-
environment through which they move. It remains unclear how the motility
machinery of confined cells responds and adapts to their micro-environment.
Here, we propose a biophysical mechanism for a geometry-dependent coupling
between the front of the cell and the nucleus that leads to directed
migration. We apply our model to geometry-guided cell migration to obtain
insights into the origin of directed migration on asymmetric adhesive micro-
patterns and the polarization enhancement of cells observed under strong
confinement. Remarkably, for cells that can choose between channels of
different size, our model predicts an intricate dependence for cellular
decision making as a function of the two channel widths, which we confirm
experimentally.

Cell migration underlies several major physiological processes, such as tissue
development [1, 2], cancer metastasis [3], and wound healing [4]. During
mesenchymal migration, cells rely on the expansion and contraction of
protrusions to explore the micro-environment through which they migrate [5,
6]. The expansion of protrusions in the cell membrane is driven by the
polymerization of actin, while contraction forces are generated by the
interaction between the motor protein myosin II and actin filaments. This
protrusion-driven process is used, for example, by invading cancer cells to
squeeze through tight pores in the extracellular matrix [5] or to guide the
growth of neurons [7] and new blood vessels [8] inside structured tissue.
However, biophyiscally it is still unclear how protrusion-based exploration is
influenced by physical cues, such as the geometry or the adhesive properties
of the local micro-environment, posing a challenge to understand confined cell
migration.

To reduce complexity, several experimental assays were established that focus
on specific aspects of physically guided cell migration. These include micro-
patterning techniques [9, 10] such as homogeneously coated narrow lanes [11,
12], as well as unisotropic substrates where migration is guided by physical
cues such as surface topography [13, 14, 15], confinement [16, 17, 18], and
directed surface patterning [19, 20, 21, 22]. While the migration behavior
observed on isotropic surfaces can be understood in terms of detailed
microscopic models that account for underlying molecular processes [23, 24,
25, 26, 27], the migration on unisotropic and confining environments has
mostly been studied using phenomenological and data-driven models that are
largely agnostic to the underlying molecular and biophysical processes [18,
19, 20]. To understand confined cell migration from basic biophysical
principles, a mechanistic model is needed that describes the effects of
physical cues such as substrate geometry on protrusion growth and how this
directs cellular decision making.

Here, we construct a mechanistic model for geometry-sensitive protrusion
growth and force generation that describes how cells migrate on simple
confining substrates. The key aspect of our model is that the growth of
protrusions that direct cell movement is sensitive to the physical properties
of the confining substrate, such as adhesiveness or geometry. We demonstrate
and test our model by investigating how cell migration is guided by various
physical cues in frequently employed experimental assays. To show that our
model is applicable to unisotropic environments, we consider ”ratchet-like”
adhesive patterns. The migration bias predicted by our model describes
previous experiments [20, 22]. Subsequently, we consider a second central
aspect of physiological cell migration: lateral confinement, where our model
provides mechanistic insight into the previously observed stimulation of
protrusion growth through lateral confinement [18, 28]. Finally, we illustrate
the generalizability of our model by showing that it correctly describes the
impact of protrusion confinement on cellular decision making, which we explore
experimentally using cells on micro-patterns.

Figure 1:  Components of the migration model. A. Side view showing the key
molecular components of the model. B. Top view of a cell on an unisotropic
substrate. Confinement-induced actin alignment stimulates protrusion growth,
resulting in increased membrane tension and retrograde flow.

As a starting point, we build on previously developed models for one-
dimensional mesenchymal migration of cells that can form protrusions on both
sides of the nucleus [25, 26, 27]. These models account for actin
polymerization against a membrane of surface tension $\tau$ with a
polymerization rate $r_{p}$ at both sides of the cell (Fig. 1A). This induces
a retrograde flow with velocity $v_{\mathrm{r}}$ of actin towards the center
of the cell. This flow is opposed by so-called focal adhesions, which
mechanically connect actin filaments across the membrane to the substrate.
These adhesions are typically modeled as elastic bonds that stochastically
bind to actin filaments, resulting in a friction force opposing the retrograde
flow [27]. To account for the observed coupling between retrograde flow
velocity and cell polarity [11], the retrograde flow is assumed to advect a
generic polarity cue. The local concentration of this cue controls actin
polymerization rates [25, 26]. Protrusion growth is opposed by myosin
contractility and membrane tension. In previous work the resulting restoring
force was modeled in terms of the effective (visco-)elastic material
properties of the cell, which were assumed to be independent of the
environment [27, 26]. Hence, the migration dynamics predicted by these models,
do not couple to the physical micro-environment of the cell, which restricts
their applicability to the case of migration on homogeneous substrates.

To broaden the scope of such models, we note that the geometry and
adhesiveness of the environment can determine the shape of the protrusions
during migration. To understand how structured substrates impact cell
migration, we thus derive the force produced by protrusions as a function of
their dimensions. We first consider the force balance at the front of a
protrusion, where the actin retrograde flow velocity,
$v_{r}=\zeta_{a}^{-1}(f_{c}+f_{\tau})$, is assumed to be driven by the sum of
the myosin generated contractile force $f_{c}$ and the membrane force
$f_{\tau}$ (Fig. 1B), and $\zeta_{a}$ is the effective friction coefficient
associated to the actin filaments 111See Supplemental Material at [URL will be
inserted by publisher] for details on the derivation and implementation of the
model, the experimental methods as well as the derivation of an approximate
model that only accounts for a single protrusion coordinate. The Supplemental
Material contains Refs. [48, 49, 50]. Myosin motors generate a contractile
force by traversing counter-oriented actin filaments inside a network in the
crossover region between the protrusion and the cell body, where actin
filaments associated with the nucleus and the protrusion overlap [30]. The
generated contractile force is, in general, governed by the myosin force-
velocity relation [31]. In our case, the myosin velocity is set by $v_{r}$.
Since typical nuclear velocities observed in mesenchymal cell migration
($<30\mathrm{nm/s}$ [16, 12, 32]) are at least an order of magnitude below the
unloaded velocity of myosin motors ($200-800\mathrm{nm/s}$ [33]), we
approximate the force generated by a myosin motor by the stall force $f_{s}$.
The total number of actin filaments of diameter $\ell_{a}$ extending from the
protrusion with width $w_{p}$ is set by $w_{p}v_{r}/(r_{d}\ell_{a}^{2})$, a
balance between the influx due to retrograde flow and the loss due to
depolymerization with rate $r_{d}$ (see ††footnotemark: ). The myosin number
contributing to contractility is then
$w_{p}v_{r}/(r_{d}\ell_{a}^{2})r_{m}\rho_{m}$, where $r_{m}$ is an interaction
radius and $\rho_{m}$ is the myosin line density. Together with the force
balance driving retrograde flow, we obtain

$f_{c}=\frac{w_{p}r_{m}\rho_{m}f_{s}}{\ell_{a}^{2}r_{d}}v_{r}=\ell_{a}^{-2}\frac{w_{p}r_{m}\rho_{m}f_{s}}{\zeta_{a}r_{d}-w_{p}r_{m}\rho_{m}f_{s}}f_{\tau}.$
(1)

Physically, larger membrane forces increase retrograde flow. This results in a
higher actin density in the crossover region and consequently an increased
myosin driven contractility (Fig. 1B), which leads to a coupling between
myosin contractility and the membrane force.

To obtain an expression for the membrane tension $f_{\tau}$, we consider the
formation of a protrusion of length $L_{p}$, height $h_{p}$, and width
$w_{p}\gg h_{p}$ [34, 35], which may be constrained by the confining micro-
environment. The resulting increase in surface area is opposed by the membrane
force $f_{\tau}=2(h_{p}+w_{p})\tau\approx 2w_{p}\tau$. Note, for a constant
surface tension $\tau$ the contractile force in Eq. (1) would be independent
of the protrusion length, which is incompatible with protrusion-guided
migration. However, the surface tension of the cell can vary with a change in
surface area [36, 37, 38]. We account for this up to linear order, by
$\tau=\tau_{0}+2\tau_{1}L_{p}/h_{p}$, with parameters $\tau_{0}$ and
$\tau_{1}$. The membrane force is then given by

$f_{\tau}=2w_{p}\tau_{0}+\frac{4\tau_{1}}{h_{p}}w_{p}L_{p}.$ (2)

The first term is due to the baseline tension of the membrane, which should be
balanced by the internal pressure of the cytosol, such that only the second
term contributes to the mechanical coupling between the nucleus and the
protrusion in terms of the contractile force (see Eq. (1))

$f_{c}=\frac{4\tau_{1}w_{p}r_{m}\rho_{m}f_{s}}{(\zeta_{a}r_{d}-w_{p}r_{m}\rho_{m}f_{s})h_{p}\ell_{a}^{2}}w_{p}L_{p}=k_{c}L_{p}.$
(3)

Note, we defined a linear elastic coupling (spring constant $k_{c}$) between
the nucleus and the protrusion, which has been used as a key component of
several migration models [18, 26, 27]. In our model, this elastic coupling
emerges from the interplay between an increased membrane tension, retrograde
flow and myosin contractility.

Next, we combine this result with the polymerization driven motion of the
protrusion edges to derive an equation of motion for the protrusion growth on
both sides of the cell. Using that the velocity of the front of the
protrusions is given by the difference between the projected actin
polymerization velocity $\ell_{a}S_{\ell/r}r_{p}(x_{\ell/r})$ and the
retrograde flow velocity, we obtain a dynamical equation for the two
protrusion positions $x_{\ell/r}$

$\dot{x}_{\ell/r}=-\frac{k_{\ell/r}(x_{\ell/r})}{\zeta_{a}(x_{\ell/r})}(x_{\ell/r}-x_{n})\mp\ell_{a}S_{\ell/r}r_{p}(x_{\ell/r}),$
(4)

where
$k_{\ell/r}(x_{\ell/r})=k_{c}(x_{\ell/r})+4\tau_{1}w_{p}(x_{\ell/r})/h_{p}$
and the order parameter $S_{\ell/r}=\langle|\cos(\vartheta_{\ell/r})|\rangle$
measures the average orientation of actin filaments in the direction of
protrusion growth (Fig. 1B). The friction coefficient $\zeta_{a}(x_{\ell/r})$
accounts for the binding dynamics of the focal adhesions [27]. Since cells can
form more adhesions on wider or more densely coated patterns, $\zeta_{a}$
generally depends on the position of the protrusion on the substrate
††footnotemark: . Eq. (4) thus illustrates one aspect induced by the confining
geometry on protrusion dynamics: while a wider protrusion can produce larger
contractile forces (Eq. (3)), it is bound to the substrate through more
adhesive bonds. Consequently, on a substrate with a homogeneous adhesiveness,
$k_{\ell/r}/\zeta_{a}$ is independent of the width of the protrusions and thus
identical on both sides of the cell ††footnotemark: .

The dynamics of the nucleus are given by the balance of contraction forces
generated by the two protrusions

$\dot{x}_{n}=\frac{k_{c}(x_{\ell})}{\zeta_{n}(x_{n})}(x_{\ell}-x_{n})+\frac{k_{c}(x_{r})}{\zeta_{n}(x_{n})}(x_{r}-x_{n}).$
(5)

Since the nucleus is indirectly connected to the substrate through focal
adhesions, the nuclear friction coefficient $\zeta_{n}$ accounts for viscous
drag within the cytosol and adhesion-induced stochastic friction (see
††footnotemark: ).

To complete the model, we require an expression for the polymerization rate
$r_{p}$ (Eq. (4)), which depends on the local concentration of polarity cues
in the cytosol [39, 40]. As the cell polarizes, it builds up a gradient in
polarity cues. Here, we account for this by considering the concentration of a
generic back-polarity cue that accumulates in the rear of a polarized cell and
inhibits actin polymerization (Fig. 1). The difference in the average
concentration in the two halves of the cell is $\Delta c=c_{r}-c_{\ell}$, with
$c_{\ell/r}$ representing the concentration to the left/right of the nucleus
and the polarity cue binds to and unbinds from actin filaments with rates
$\kappa^{c}_{\mathrm{on}}$ and $\kappa^{c}_{\mathrm{off}}$, respectively.
Following previous work [11], we assume the polarity cue to be advected with
the retrograde flow. The advective flux between the two parts of the cell is
then given by $\Delta v_{r}n_{c}c_{0}$, where $\Delta
v_{r}=v_{r}(x_{r})-v_{r}(x_{\ell})$,
$n_{c}=\kappa^{c}_{\mathrm{off}}/(\kappa^{c}_{\mathrm{on}}+\kappa^{c}_{\mathrm{off}})$
is the bound fraction of the polarity cue and $c_{0}$ denotes the polarity cue
concentration around the cell mid-plane. The polarity cue flux between the two
parts of the cell can thus be written as

$J(x,t)=-(1-n_{c})\tilde{D}\partial_{x}c(x,t)-\Delta
v_{r}n_{c}c_{0}+\tilde{\sigma}\xi(t),$ (6)

with diffusion constant $\tilde{D}$. We assume the polarity to be the
dominating source of noise in the migratory dynamics of the cell, and account
for this in Eq. (6) by adding Gaussian white noise $\xi(t)$ of strength
$\tilde{\sigma}$.

Treating the overall concentration of the polarity cue $c_{0}$ in the cell as
conserved, we write the concentration in the two parts of the cell as
$c_{\ell/r}=c_{0}\mp\Delta c/2$. The gradient of the concentration profile can
then be approximated as $\partial_{x}c(x,t)\approx\Delta c/L_{c}$, where
$L_{c}$ is the length of the cell. The left and right end of the cell are
treated as no-flux boundaries, and the dynamics of $\Delta c$ can then be
approximated by ††footnotemark:

$\partial_{t}\Delta c(t)\approx-D\Delta c(t)-\frac{4n_{c}c_{0}}{L_{c}}\Delta
v_{r}(\Delta c)+\frac{4\tilde{\sigma}}{L_{c}}\xi(t),$ (7)

with $D=4(1-n_{c})\tilde{D}L_{c}^{-2}$. Importantly, for a protrusion at
steady state, the retrograde flow is equal to the projected polymerization
velocity (see Eq. (4)). Expanding $\Delta v_{r}$ in terms of $\Delta c$ on
both sides of the cell (see ††footnotemark: ), then allows us to derive an
equation for the dynamics of the polarity $P(t)\equiv-P_{0}\Delta c(t)$ as

$\dot{P}=-\alpha P-\beta
P^{3}+\delta\left(S_{r}-S_{\ell}\right)+\sigma\xi(t),$ (8)

with $\sigma=4P_{0}\tilde{\sigma}L_{c}^{-1}$,
$\alpha=D-4n_{c}c_{0}L_{c}^{-1}\ell_{a}r_{1}\left(S_{r}+S_{\ell}\right)$,
$\beta=4P_{0}^{-2}n_{c}c_{0}L_{c}^{-1}\ell_{a}r_{3}(S_{r}+S_{\ell})$, and
$\delta=4P_{0}n_{c}c_{0}L_{c}^{-1}\ell_{a}r_{p}(c_{0})$. The coefficients
$r_{\mathrm{1/3}}>0$ stem from the leading order expansion of $\Delta v_{r}$.
To couple Eq. (8) to Eq. (4), we note that we can relate the polarization rate
to the polarity to leading order as
$r_{p}(t)=r_{p}(c_{0})+r_{1}P_{0}^{-1}P(t)$. The resulting mechanistic model
given by the closed set of equations (4), (5) and (8) describes protrusion
driven 1D confined migration behavior of cells in structured micro-
environments. To test this model and investigate what new insights it can give
into migration on structured substrates, we apply our model to a variety of
different experimentally studied migration assays.

_Migration on Directed Patterns.–_ Cell migration can be biased due to
unisotropic adhesiveness of the micro-environment [20, 21, 22].
Experimentally, this is realized through directed, ”ratchet-like” adhesive
patterns (Fig. 2A), which induce biased migration, a phenomenon known as
”ratchetaxis”. The direction of this migration bias depends on the geometry of
the micro-pattern. To demonstrate how to capture such asymmetry theoretically,
we first consider a cell located on a triangular pattern with two symmetric,
rectangular neighboring patterns that its protrusions can engage with (Fig.
2A, left). The triangular shape of the pattern allows the cell to form wider
protrusions on the blunt end compared to the pointed end of the triangle. The
key mechanism of geometry sensing in our model here follows from Eq. (3):
Wider protrusions have an increased effective spring constant and thus
$k_{c}(x_{\ell})>k_{c}(x_{r})$. Since the boundaries of the pattern are not
parallel to the direction of migration, we assume $S_{\ell}=S_{r}$. Hence, the
asymmetry of $k_{c}$ leads to a higher pulling force on the nucleus in the
direction of the wider side of the pattern ($-$-direction) and consequently we
find a migration bias towards the $-$-direction (Fig. 2B).

Figure 2:  Modeling cell migration on directed substrates. A. Migration on
different directed micro-patterns (ratchetaxis). Triangular patterns lead to
protrusions of different protrusion widths $w_{p}$ on both sides of the
nucleus (left, center) but can also result in different densities of adhesive
bonds $\rho_{b}$ at the front of the two protrusions (center). B. First-step
migration biases obtained from simulations of our model on different micro-
patterns. C. Effect of pattern spacing on the migration bias
$p=(N_{+}-N_{-})/(N_{+}+N_{-})$ on periodic patterns, with the number of steps
in the $+/-$-direction $N_{+/-}$.

For cells migrating on a periodic triangular pattern (Fig. 2A, center)
however, a second mechanism becomes relevant: due to the tapering of the
pattern, the protrusion in the $-$-direction overlaps with non-adhesive
regions. This reduces the density of adhesion bonds $\rho_{b}$ and thus
$k_{\ell}>k_{r}$, resulting in a migration bias in the $+$-direction in our
simulations (Fig. 2B, Fig. S3 ††footnotemark: ). Bigger gaps between the
patterns lead to a stronger asymmetry in the adhesion density below the two
protrusions. This reinforces the imbalance between $k_{\mathrm{l}}$ and
$k_{\mathrm{r}}$ increasing the migration bias (Fig. 2C and S3 ††footnotemark:
). Overall, the predicted migration biases on the different geometries agree
well with experimental observations [20, 22].

_Lateral Confinement.–_ _In vivo_ , cells frequently migrate under conditions
of lateral confinement. Experimentally, the effect of confinement is often
studied by using micro-patterns [9, 10, 41, 11, 42], and this lateral
confinement can induce intricate nonlinear migration dynamics [16, 18]. To
provide mechanistic insight into these findings, we apply our model to cells
migrating through confining channels on adhesive stripes. Actin branching [43]
and random fluctuations in the orientations of the actin filaments lead to a
range of filament orientations in unconfined cells [44, 30]. We expect the
distribution of filament orientations relative to the direction of migration
to be narrowed by the confinement (Fig. 3A). This could be either due to
direct constraints of the orientations for fibers longer than the width of the
pattern or propagation of a preferred orientation over a correlation length
scale into the bulk through alignment interactions, as in nematic and polar
liquid crystals [45, 46, 47].

Figure 3:  Modeling cell migration in lateral confinement. A. Lateral
confinement of the protrusion leads to alignment of actin filaments. B. Fit of
the analytical expression for $\alpha$ on dumbbell-shaped patterns to the
values reported in [18]. C. and D. Lateral confinement induces spontaneous
polarization of the cell. For homogeneous confinement (C.), both polarization
directions are equally likely, while for asymmetric confinement (D.), the
polarization is biased in the direction of stronger confinement.

We account for such boundary-induced alignment by assuming that the order
parameter $S$ increases with increasing confinement of the protrusion as
$S=1-sw_{p}^{2}$, where $s>0$ is a parameter that accounts for the strength of
the alignment interactions between actin filaments. This gives us the
following expression for $\alpha$ (see Eq. (8)) as a function of the
protrusion width:

$\alpha(w_{p,\ell},w_{p,r})=D-2n_{c}c_{0}l_{a}r_{1}(2-sw_{p,r}^{2}-sw_{p,\ell}^{2}).$
(9)

Note, if the protrusions are sufficiently confined, $\alpha$ becomes negative
inducing a self-reinforcement of the polarity and consequently protrusion
growth.

Figure 4:  Cellular decision making in lateral confinement. A. Time series of
a cell migrating on a chain of adhesive islands that are connected by adhesive
bridges of increasing width (scale bar: 35µm). B. Predicted migration bias for
cells encountering different bridge widths on both sides. $p_{r/\ell}$ denotes
the probability that the cell migrates into the right/left channel. C.
Experimentally observed together with theoretically predicted migration
biases.

The polarity feedback parameter $\alpha(w_{\rm cell},w_{c})$ for cells on a
pattern wider than the width of the cell $w_{\rm cell}$ entering a confining
channel of width $w_{c}$ with their leading protrusion (see Fig. 1B) is shown
in Fig. 3B, and agrees well with a similar inferred model constrained by
experimental data [18]. In uniform confinement, both directions of
polarization are equally likely, since the bias term in Eq. (8) vanishes (Fig.
3C). However, in a scenario where only one side of the cell is confined (Fig.
3D), our model predicts a bias for the cell to polarize in the direction of
the confinement. For migration on dumbbell-shaped micro-patterns we find the
same qualitative behavior that was reported in [18] (see ††footnotemark: ) our
approach does however present a biophysical mechanism underlying the geometry
adaptation of protrusion and polarity dynamics reported there: the sign of
$\alpha(w_{p,\ell},w_{p,r})$ is set by the competition between advection and
diffusion of the polarity cue. Confinement-induced protrusion growth leads to
an increases in the advection of the polarity cue towards the rear of the
cell. As a consequence, differences in the polarity concentration profile get
reinforced under confinement.

Further, our model can be generalized to various other confining geometries,
as opposed to prior approaches [20, 27, 18]. In particular, our model predicts
that confinement can have opposing effects on the preferred direction of
migration. On the one hand, confinement-induced actin alignment stimulates
polarization in the direction of reduced channel width. On the other hand, the
contractile force decreases with stronger confinement (Eq. (3)), leading to a
net force on the nucleus away from the confinement. To put this in context,
consider a cell that can choose between two channels of different width (Fig.
4B). Interestingly, our model then predicts a non-monotonic dependence of the
migration bias on the two bridge widths. To test this prediction, we perform
micro-pattern experiments with cells migrating on a series of square-shaped
adhesive islands connected by bridges of increasing width (Fig. 4A)
††footnotemark: . Our model predicts a transition from a bias towards the
wider channels at narrow bridge widths to a bias towards the narrower channel
at wider bridge width, which agrees well with the experimentally observed
behavior (Fig. 4C). The observed transition in the migration bias yields new
insights into the decision making of cells that migrate through confining
environments with heterogeneous pore sizes.

To summarize, we developed a generalizable model for directed mesenchymal cell
migration in structured micro-environments from basic biophysical principles.
At the core of our model is the coupling between substrate-controlled
protrusion formation and cellular migration behavior. Here, it would be
insightful to further investigate how the micro-environment affects membrane
tension locally and globally. We demonstrated that our model explains the
emergence of directed migration in response to different external cues such as
asymmetric adhesion densities and the geometry sensing of polarity dynamics
[18] in lateral confinement. This model of confined cell migration broadens
the scope of cell migration models to more physiological conditions, where
cells are simultaneously exposed to different physical migration cues and
could form the basis for more complex approaches in the future that also
integrate detailed biochemical signaling pathways.

We thank Daniel Riveline, Tom Brandstätter, Janni Harju, David Brückner and
Bram Hoogland for helpful discussions. This project was funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation), Project No.
201269156— SFB 1032 (Projects B01 and B12).

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