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Chromatin remodelers as active Brownian dimers
R. Blossey, H. Schiessel
To cite this version:
R. Blossey, H. Schiessel. Chromatin remodelers as active Brownian dimers. Journal of Physics A:
Mathematical and Theoretical, IOP Publishing, 2019, 52 (8), pp.085601. �10.1088/1751-8121/aafea0�.
�hal-02344788�
Chromatin remodelers as active Brownian dimers
R. Blossey
1
and H. Schiessel
2
1
University of Lille, UGSF CNRS UMR8576, 59000 Lille, France.
2
Institute Lorentz for Theoretical Physics, Leiden University, Niels Bohrweg 2, 2333
CA Leiden, The Netherlands.
E-mail: ralf.blossey@univ-lille.fr
Abstract. Chromatin remodelers are molecular motors which actively displace
nucleosomes on chromatin. Recent results on the structural properties of these motors
indicate that the displacement of nucleosomal DNA corresponds to an inchworm motion
induced by the generation and propagation of twist defects. Here we show that this
basic action mechanism can be described by a coarse-grained active Brownian dimer
(ABD) model, thereby quantitatively rationalizing the notion of inchworm motion.
The model allows for extensions to more microscopic as well towards more macroscopic
descriptions of chromatin hydrodynamics.
Keywords: nucleosome, chromatin remodeler, helicase, active Brownian dimer
Submitted to: J. Phys. A: Math. Gen.
Chromatin remodelers as active Brownian dimers 2
Introduction. Active systems currently are one of the most intensive fields of
research within the statistical physics community. Built on a large body of work
dealing with individual motors (see, e.g. [1]), the field has turned towards studies of the
collective behaviour of ‘active’ constituents, see, e.g. [2]. Here we are concerned with
chromatin remodeling motors which actively displace and remove nucleosomes from
the chromatin fiber, which have so far received only little attention in the statistical
physics or biophysics literature [1]. The number of modeling attempts of individual
remodeler dynamics has been rather limited so far; see, e.g., the references [3, 4, 5, 6]; but
also the collective behaviour of chromatin remodelers is beginning to attract attention
[7, 8, 9, 10].
This lack of attention may in part be explained by the structural complexity
and size of remodelers which has so far allowed to resolve only few and in particular
often partial structures; this also impeded studies of remodeler dynamics, except in
artificial constructs (see below). Very recently, the more widespread use of cryo-
electron microscopy and FRET-imaging techniques have led to numerous new results,
in particular on the (small) chromatin remodeler Chd1 [11, 12, 13, 14, 15].
Chromatin remodelers are built around evolutionarily conserved two-domain
ATPase units which belong to the helicase-related superfamily II (SF2), and can be
grouped into a small number of families which differ from each other by their accessory
subunits [16]. These molecular motors play crucial rules in numerous chromatin-based
processes such as the activation or the repression of transcription and DNA repair
[17, 18, 19]; their biological relevance is underscored by the recent understanding that
remodeler dysfunction is one source of regulatory diseases such as cancer [20]. A better
understanding of how the motors act on the nucleosomes is thus of key relevance.
In this paper we show that, at a coarse-grained level, the DNA displacement around
the nucleosome of a stripped-down version of chromatin remodeling enzymes can be very
well captured in terms of a different type of model, an active Brownian dimer model.
Such models were developed several years ago in the context of the simpler linear motors
[21].
Mapping of a chromatin remodeler to an active Brownian dimer. Our mapping
relies on recent structural biology results which we now briefly review. Liu et al. [22, 23]
have described the structure of a truncated version of a basic remodeler which they
call ScSnf2 in complex with a nucleosome core-particle with a 167-bp DNA fragment
containing the ‘601’ positioning sequence [24]. Cryo-electron microscopy of this fully
functional complex yielded a resolution of about 4
˚
A. From the observed populations
of the complex, the remodeler was found to bind at the nucleosome preferably in
different locations on DNA, i.e. either on superhelical location SHL 2, on SHL 6 and
simultaneously on both SHL 2 and SHL 6 [22]. We take this basic information as key
ingredients to be reflected in our model, which therefore should be able to describe a
basic chromatin remodeler without any further additional recognition domains.
Although precise dynamical information cannot directly be inferred from the cryo-
EM data, the following facts can be considered as established, also in conjunction with
Chromatin remodelers as active Brownian dimers 3
earlier work: (i) the remodeler structure consists of two lobes (also called ‘cores’, in
fact presumably properly folded protein domains), which form multiple contact surfaces
with both DNA turns; (ii) upon remodeling, the remodeler injects twist defects into the
DNA turns which are expelled at the end contact of the remodeler domains with the
DNA; (iii) the remodeler thus performs a spatially restricted rotation at the nucleosome
turns: its full rotation around the DNA is impeded by the presence of the histone core.
This limited rotary motion of the remodeler is a remainder of its helicase-like nature: a
helicase would fully rotate around a single DNA double-strand during its linear motion
along the DNA [25]. This rotation is represented in some models of helicases, but not by
the Brownian dimer model. In our case, this neglect is justified because of the specific
arrangement of the remodeler at the nucleosome. Figure 1 (left) displays a sketch of the
remodeler profile at the DNA turns around the nucleosome.
Core1&
2°&
1°&
Core2&
x
1
x
2
x
1
x
2
x
1
x
2
t
0
t
1
t
2
Figure 1. Two representations of the action of the remodeler on nucleosomal DNA.
Left: side-view of the engagement of the two remodeler lobes with the two turns of
DNA, following [22, 23]. Right: Mapping of the remodeler-DNA contacts on the two
remodeler footprints denoted by coordinates along the DNA centered at x
i
, i = 1, 2.
Each black bar represents the length of DNA along the nucleosome, with the red bars
indicating the footprints (contact surfaces) of the remodeler along the DNA. Top bar:
initial configuration at time t
0
. Middle bar: after a first step step t
1
, the left footprint
has moved to the right while the other is still unchanged. Lower bar: at time t
2
the
right footprint has also moved and the displacement step has been completed.
Turning to modeling this behaviour, condition (iii) allows to neglect the rotary
motion of the remodeler; conditions (i) and (ii) then allow to restrict the dynamics to
the footprints of the two lobes on DNA, which we denote as in [21, 26] as x
1
and x
2
. In
the course of the remodeler action, footprint x
1
is first shifted towards location x
2
via
twist defect injection; the displacement of footprint x
2
follows in due course leading to
twist defect ejection. The DNA length x ≡ x
1
− x
2
− x
0
where x
0
is the equilibrium
extension of the DNA around the nucleosome thus relaxes after one remodeler step
which is typically 1-2 bp large [27, 28, 29]; the variable x is therefore small, irrespective
of the location of x
1
and x
2
along the internucleosomal DNA. This mapping of the
displacement dynamics is illustrated in Figure 1 (right). The motion of the footprints
thus is indeed akin to an inchworm motion of DNA around the histone octamer [23].
Chromatin remodelers as active Brownian dimers 4
Modeling the inchworm. This inchworm motion can be rationalized in terms of
molecular motor models, for which there are two philosophies. The most common one
relies on Brownian ratchet models, where the key ingredient is the ratchet potential, a
potential with a sawtooth-profile, which controls motor motion in conjunction with the
ATP-consumption cycle. For chromatin remodelers such models have been developed for
the case of a remodeler from the ISWI family which is capable to position nucleosomes on
DNA; this could be demonstrated experimentally in single-molecule positioning assays
[4, 5]. For the present case in which the motion is that of a motor with two footprints, a
ratchet model has been discussed in the literature [33]. The other modeling philosophy
relies on active Brownian dimer models [21, 26], which is the approach we follow here.
In the overdamped case which we assume in the following, it is given by coupled
Langevin equations for the two footprint coordinates x
i
,
γ
i
(x) ˙x
i
(t) = −∂
i
U(x) + g
i
(x)ξ
i
(t) , (1)
where ξ
i
(t) is a Gaussian noise with zero mean hξ
i
(t)i = 0 and variance hξ
i
(t)ξ
j
(t)i =
δ
ij
δ(t −t
0
). Three key factors appear in this equation. The first is a spatially-dependent
friction term γ
i
(x) ≥ 0 which qualitatively models the remodeler-nucleosome interaction.
The second term is the potential U(x) which we ascribe to the interaction of the
remodeler domains between the two footprints. Both depend on the relative coordinate
x introduced before. Finally, the factor g
i
(x) describes the noise correlations. It is given
by
g
i
(x) ≡
p
2γ
i
(x)k
B
T + A
i
(2)
where the factor A
i
describes the contribution of non-equilibrium noise due to ATP-
consumption.
This active Brownian dimer model is obviously highly coarse grained, since the non-
equilibrium ATP-dependent driving force is not associated with particular configurations
of the remodeling-based ATP cycle (we comment on this further in the discussion).
Crucial in these kinds of models is the asymmetry in the spatially-dependent coupling
of the motor to the twist-stretched DNA: neglecting the spatial dependence destroys
the propagation mode in the model.
The dynamics of the two footprints can be decoupled into a center of mass motion
and the relative coordinate. Due to the dependence of γ
i
(x) and U(x) on only the rel-
ative coordinate x the equation of the center of mass coordinate x
cm
is a function of
the relative coordinate and the noise, while the equation for the relative coordinate is
independent from the center of mass coordinate. The dynamics of the latter can be cast
into a Fokker-Planck equation for the probability distribution of the relative coordinate
P (x, t) which reads as [26]
∂
t
P (x, t) = −∂
x
[a(x)P (x, t)] +
1
2
∂
x
[b(x)∂
x
[b(x)P (x, t)]] (3)
![Figure 1. Two representations of the action of the remodeler on nucleosomal DNA. Left: side-view of the engagement of the two remodeler lobes with the two turns of DNA, following [22, 23]. Right: Mapping of the remodeler-DNA contacts on the two remodeler footprints denoted by coordinates along the DNA centered at xi, i = 1, 2. Each black bar represents the length of DNA along the nucleosome, with the red bars indicating the footprints (contact surfaces) of the remodeler along the DNA. Top bar: initial configuration at time t0. Middle bar: after a first step step t1, the left footprint has moved to the right while the other is still unchanged. Lower bar: at time t2 the right footprint has also moved and the displacement step has been completed.](/figures/figure-1-two-representations-of-the-action-of-the-remodeler-2gocw1i8.webp)