Although studies have implicated variants in active chromatin regions and eQTLs as contributing significantly to complex traits (2, 8, 10, 23),
the importance of splicing remains unclear. We
therefore wondered what role common sQTLs
might play in complex diseases.
Owing to the extensive sharing of QTLs across
cell types (2, 24), we reasoned that QTLs identified
in LCLs should be informative about the relative
contribution of different regulatory mechanisms
to complex traits, in particular to immune-related
diseases (8). We thus compiled genome-wide
summary statistics for rheumatoid arthritis, multiple sclerosis, Alzheimer’s disease, schizophrenia,
height, and body mass index (16). Using two tests
with different underlying statistical models, we
searched for functional annotations that are associated with GWAS signals (16, 23).
As expected, eQTLs and haQTLs are predicted
to contribute to rheumatoid arthritis, multiple
sclerosis, and height according to one or both
methods (Fig. 4). Consistent with the notion that
disease SNPs in histone modification peaks are
mediated through the SNPs’ effect on chromatin,
haQTLs are more enriched in risk loci than are
variants that lie within H3K27ac peaks overall
(Fig. 4C and fig. S14).
sQTLs appear to have effects of similar or even
larger magnitude than eQTLs. For instance, there
is an enrichment of sQTLs with low P values in
the multiple sclerosis GWASs, even when compared to eQTLs (Fig. 4C and fig. S15). These enrichments are robust to the eQTL and sQTL
detection cutoffs, suggesting that they are not
simply due to the power of detection (fig. S16).
We also found similar patterns when we compared the effect of sQTLs on multiple sclerosis
to the effects of eQTLs identified in three purified immune cell types (fig. S17).
In conclusion, three main pathways mediate
the impact of genetic variation on gene regulation
with phenotypic and pathogenic consequences.
Of these, our work uncovers an unexpectedly
important role of RNA splicing in modulating
phenotypic traits (Fig. 4D). These findings indicate that RNA splicing should be a focal point
in future work on connecting genetic variation to
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We thank S. Prabhakar for early access to the H3K27ac data;
J. Blischak for technical assistance with the 4sU experiments;
the anonymous reviewers for helpful comments; and A. Battle,
A. Pai, N. Banovich, A. Fu, X. Lan, A. Harpak, and other members
of the Pritchard/Gilad Labs for helpful discussions. This work
was supported by NIH grants R01MH084703, RO1MH101825,
U01HG007036, and U54CA149145; by a Center for Computational,
Evolutionary and Human Genomics Fellowship; and by the Howard
Hughes Medical Institute. The 4sU-seq data have been deposited
in the Gene Expression Omnibus ( www.ncbi.nlm.nih.gov/geo/)
under accession no. GSE75220; other accession numbers can be
found in table S8.
Materials and Methods
Figs. S1 to S18
Tables S1 to S8
Data Table S1
24 November 2015; accepted 25 March 2016
Broken detailed balance at
mesoscopic scales in active
Christopher Battle,1,2 Chase P. Broedersz,2,3,4 Nikta Fakhri,1,2,5 Veikko F. Geyer,6
Jonathon Howard,6 Christoph F. Schmidt,1,2† Fred C. MacKintosh2,7†
Systems in thermodynamic equilibrium are not only characterized by time-independent
macroscopic properties, but also satisfy the principle of detailed balance in the
transitions between microscopic configurations. Living systems function out of
equilibrium and are characterized by directed fluxes through chemical states, which
violate detailed balance at the molecular scale. Here we introduce a method to probe for
broken detailed balance and demonstrate how such nonequilibrium dynamics are
manifest at the mesosopic scale. The periodic beating of an isolated flagellum from
Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes.
With a model, we show how the breaking of detailed balance can also be quantified in
stationary, nonequilibrium stochastic systems in the absence of periodic motion.
We further demonstrate such broken detailed balance in the nonperiodic fluctuations of
primary cilia of epithelial cells. Our analysis provides a general tool to identify
nonequilibrium dynamics in cells and tissues.
When a system reaches thermodynamic equilibrium, its properties become sta- tionary in time, which requires a net balance between rates of transitions into and out of any particular microstate of the system. Systems in thermodynamic equilib- rium, however, are known to be balanced in an even stronger way. They obey detailed balance, in which transition rates between any two micro- states are pairwise balanced (Fig. 1A). This means
there can be no net flux of transitions anywhere
in the phase space of system states. This principle
was identified and used by Ludwig Boltzmann
in his pioneering development of statistical mechanics, the microscopic basis for thermodynamics (1). In contrast, living systems operate
far from equilibrium, and molecular-scale violations of detailed balance lie at the heart of their
dynamics. For instance, metabolic and enzymatic
processes drive closed-loop fluxes through the
system’s chemical states (Fig. 1B) (2).
Nonequilibrium driving can boost intracellular transport (3–5), the fidelity of transcription (6), chemotaxis (7, 8), and the accuracy of
sensory perception (9, 10). To understand cell
1Drittes Physikalisches Institut, Georg-August-Universität,
37077 Göttingen, Germany. 2The Kavli Institute for
Theoretical Physics, University of California, Santa Barbara,
CA 93106, USA. 3Arnold-Sommerfeld-Center for Theoretical
Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333
München, Germany. 4Lewis–Sigler Institute for Integrative
Genomics and Joseph Henry Laboratories of Physics,
Princeton University, Princeton, NJ 08544, USA.
5Department of Physics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA. 6Department of
Molecular Biophysics and Biochemistry, Yale University, New
Haven, CT, USA. 7Department of Physics and Astronomy,
Vrije Universiteit, Amsterdam, Netherlands.
*These authors contributed equally to this work. †Corresponding
author. Email: email@example.com (F.C.M.); christoph.schmidt@