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Título
Statistical methodology and software to analyse oscillatory signals with applications to biology
Director o Tutor
Año del Documento
2020
Titulación
Doctorado en Matemáticas
Resumo
Many physiological and biological phenomena, such as menstrual cycles
(Draper et al. (2018)), reproductive activity (Simonneaux and Bahougne (2015),
Caba et al. (2018)), cell cycle (Liu et al. (2017)) or circadian biology (Hughes
et al. (2009), Zhang et al. (2014), Andreani et al. (2015), Seney et al. (2019)),
are governed by oscillatory systems consisting of numerous signals that exhibit
rhythmic patterns over time. For example, the circadian clock is a molecular
pacemaker that orchestrates daily functional activity including metabolic state,
endocrine activity or neural excitability. Genes involved in those processes that
exhibit rhythmic expression patterns along ~24-hour periods are called circadian
genes. The study of such signals with temporal rhythmic patterns, and
how these patterns change under different conditions, is called chronobiology.
Chronobiology has been an active area of research during the past two
decades, with major impact on treating cardiovascular disorders like hypertension
(Halberg et al. (2013)), detecting genes associated with neurodegenerative
disorders (Li et al. (2013)) or depression (Chauhan et al. (2017)), and improving
the effectiveness of cancer treatments (Chan et al. (2017)). For instance, Haus
(2009) demonstrated that the timing of radiation according to host and/or tumour
rhythms improves the toxic/therapeutic ratio of the treatment. These and
other findings in biomedical sciences have increased interest in chronobiological
experiments.
From a statistical point of view, the analysis of rhythmic signals ( ) in
chronobiology has several challenges because of: (a) displays a wide variety
of rhythmic patterns over time, which are not exactly sinusoidal or even symmetric
(Koren£i£ et al. (2012), Zhang et al. (2014), Rueda et al. (2019)); (b)
the density of the time points and the number of periods of data is usually very
small (Panda et al. (2002), Hughes et al. (2007, 2009), Yang and Su (2010));
(c) the intrinsic circular nature of data from oscillatory systems; (d) the vari-
1
ability in time course expression data due to noisy nature of the data; (e) in
some applications, the temporal order among samples may be unknown. For
these reasons, standard time series or Fourier models are not convenient for the
analysis of chronobiological rhythms (Elkum and Myles (2006), Wijnen et al.
(2006), Leise (2013)). Models based on parametric functions of time, such as
Cosinor, have been proposed in chronobiology to model these patterns (Tong
(1976), Cornelissen (2014)). The main drawback of these approaches is that
such parametric functions are too rigid, as signals in oscillatory systems very
often exhibit asymmetric patterns.
There are several commonly encountered problems in chronobiology. The
main problem to solve in this context is rhythmicity detection as not all patterns
observed in an oscillatory system display rhythmic patterns. For a given signal
; rhythmicity detection can be formulated as the following hypothesis test:
H0 : is a flat signal (1.1)
H1 : is rhythmic signal.
This problem has been studied extensively in literature, existing a wide
variety of procedures to address it including, among others, those based on sinusoidal
curve fitting (Liu et al. (2004), Straume (2004), Cornelissen (2014)),
autocorrelation (Levine et al. (2002)) or Fourier analyses (Wichert et al. (2004)).
Some non-parametric approaches, such as JTK_Cycle (JTK) (Hughes et al.
(2010)) and RAIN (Thaben and Westermark (2014)), based on Jonckheere-
Terpstra test and Kendall's tau correlation, are widely employed by biologists.
However, these two latter approaches do not detect asymmetric rhythmic patterns
properly.
A fundamental assumption made in the above discussion is that the time
corresponding to each biological sample is known. However, in many instances,
such as when dealing with samples obtained from human cadavers (Li et al.
(2013), Seney et al. (2019)) or human organ biopsies, (Lamb et al. (2011), Bossé
et al. (2012)), the exact time corresponding to each biological sample may be
unknown. In such cases, one needs to first estimate or determine the time associated
with each sample before investigating rhythmicity. This problem, known
as temporal order estimation, is other crucial issue in chronobiology. Some recent
procedures to cope with this problem are Oscope (Leng et al. (2015)) and
CYCLOPS (Anafi et al. (2017)). Oscope was specifically designed to recover
cell cycle dynamic, and it is only applicable in single cell RNA-Seq experiments.
CYCLOPS is far from a mathematical close-fitting formulation. It is based on a
neural network framework (which is like a black box) and uses additional rhythmicity
information which is not always available.
In addition to the major rhythmicity issues mentioned above, other interesting
questions related to the analysis of oscillatory signals, such as peak time
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estimation or rhythm-pattern comparisons, deserve consideration. For instance,
when dealing with circadian genes, time peak estimation reveals crucial information
for biologists about the timings at which genes' biological function is
carried out.
The main motivation of this thesis was to solve appealing rhythmicity questions
specifically related to the analysis of circadian gene expression. In particular,
the starting problem of this thesis was to identify among the several
thousand of genes registered in a genetic study, those that display rhythmic
expression patterns.
Materias (normalizadas)
Metodología estadística
Materias Unesco
12 Matemáticas
Departamento
Departamento de Estadística e Investigación Operativa
Idioma
eng
Tipo de versión
info:eu-repo/semantics/publishedVersion
Derechos
openAccess
Aparece en las colecciones
- Tesis doctorales UVa [2275]
Arquivos deste item
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