\TRONCO{
Motivation: We introduce \TRONCO{ (TRanslational ONCOlogy), an open-source \R{ package that implements the state-of-the-art algorithms for the inference of cancer progression models from (epi)genomic mutational profiles. \TRONCO{ can be used to extract population-level models describing the trends of accumulation of alterations in a cohort of cross-sectional samples, e.g., retrieved from publicly available databases, and individual-level models that reveal the clonal evolutionary history in single cancer patients, when multiple samples, e.g., multiple biopsies or single-cell sequencing data, are available. The resulting models can provide key hints in uncovering the evolutionary trajectories of cancer, especially for precision medicine or personalized therapy. Availability: \TRONCO{ is released under the GPL license, it is hosted in the Software section at \href{http://bimib.disco.unimib.it/{http://bimib.disco.unimib.it/ and archived also at \href{http://www.bioconductor.org/{bioconductor.org. % and \href{https://github.com/BIMIB-DISCo/TRONCO{https://github.com/BIMIB-DISCo/TRONCO. Contact: \href{tronco@disco.unimib.it{tronco@disco.unimib.it
main.tex
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\begin{document}

\title{\TRONCO{}: an \R{} package for the inference of cancer progression models from heterogeneous genomic data}

\author[1]{Luca De Sano\footnote{Equal contributors}$\,$,}
\author[1,2]{Giulio Caravagna$^{\ast}$,}
\author[1]{Daniele Ramazzotti$^{\ast}$,}
\author[1,3]{Alex Graudenzi}
\author[1]{Giancarlo Mauri}
\author[4]{Bud Mishra}
\author[1,5]{Marco Antoniotti}

\affil[1]{Department of Informatics, Systems and Communication, University of Milano-Bicocca, Milan, Italy.}
\affil[2]{School of Informatics, University of Edinburgh, Edinburgh, UK.}
\affil[3]{Institute of Molecular Bioimaging and Physiology of the Italian National Research Council (IBFM-CNR), Milan, Italy.}
\affil[4]{Courant Institute of Mathematical Sciences, New York University, New York, USA.}
\affil[5]{Milan Center for Neuroscience, University of Milan-Bicocca, Italy.}

\date{}

\maketitle

\begin{abstract}

  \textbf{Motivation:} We introduce \TRONCO{} (TRanslational
  ONCOlogy), an open-source \R{} package that implements the
  state-of-the-art algorithms for the inference of cancer progression
  models from (epi)genomic mutational profiles. \TRONCO{} can be used
  to extract population-level models describing the trends of
  accumulation of alterations in a cohort of cross-sectional samples,
  e.g., retrieved from publicly available databases, and
  individual-level models that reveal the clonal evolutionary history
  in single cancer patients, when multiple samples, e.g., multiple
  biopsies or single-cell sequencing data, are available.  The
  resulting models can provide key hints in uncovering the
  evolutionary trajectories of cancer, especially for precision
  medicine or personalized therapy.



  \textbf{Availability:} \TRONCO{} is released under the GPL license,
  it is hosted in the Software section at
  \href{http://bimib.disco.unimib.it/}{http://bimib.disco.unimib.it/}
  and archived also  at
  \href{http://www.bioconductor.org/}{bioconductor.org}.

  % and \href{https://github.com/BIMIB-DISCo/TRONCO}{https://github.com/BIMIB-DISCo/TRONCO}. 

  \textbf{Contact:} \href{tronco@disco.unimib.it}{tronco@disco.unimib.it} 

\end{abstract}

\section{Introduction}
\label{sec:introduction}

\begin{figure*}[!ht]
  \begin{center}
    \includegraphics[width=1.00\textwidth]{tronco-tool}
  \end{center}
  \vspace*{.05in}
  \caption{\textbf{(A)} \texttt{TRONCO} can process either alterations
    (e.g., somatic mutations or wider chromosomal lesions) in a cohort
    of independent samples (top lolliplot diagram), or a set of
    multiple snapshots from a unique patient (e.g., multi-region or
    single-cell, bottom panel).  \textbf{(B)} \emph{Oncoprints} allow the
    user to visualize the data that the tool is processing.
    Regardless of the source, each row represents a certain
    alteration - at a custom resolution depending on the cancer under study  - and each column a sample. \textbf{(C)} A model inferred
    with the tool might outline  cancer evolution occurring in a population 
     ensemble or in an individual patient. \rev{Graphically, alterations are
     represented as nodes with different colors (e.g., green mutations
     and blue homozygous deletions). Algorithms such as CAPRI 
     allow describing  alterations with logical formulas, in an attempt to
     find their role as a ``group''  (see  \cite{Ramazzotti15092015}
     for details); we picture such groups  with dashed lines.} In the panel, we show a
    hypothetical ensemble-level model predicting a selection pressure
    on two genes mapped to  17p13, \textsc{tp53} and \textsc{hic1}, as
    it may be inferred by analyzing  samples  harbouring either
    \textsc{tp53}/\textsc{hic1} mutations or homozygous deletions in
    the cytoband where any of these two genes map, i.e., here for
    purely explanatory cases we suppose just \textsc{tp53}, which maps
    to 17p13.1. The model suggests a trend of selection  towards
    mutations in gene \textsc{y}, which shall be interpreted as a  set
    of preferential  clonal expansions characteristic of the population of analyzed samples,  involving
    alterations of the functions mapped to 17p13 and \textsc{y}.
    \rev{\textbf{(D)} \texttt{TRONCO} supports  three data types. Custom data, which is supposed
    to be provided as a {\em binary input matrix} storing the presence (1) or absence (0) of a certain alteration
    in a sample. Or, standard data formats such as the \emph{Mutation Annotation
   Format} (MAF) for  somatic mutations, as well as the \emph{Genomic
   Identification of Significant Targets in Cancer}  (GISTIC) format for focal Copy Number Variations.
   Data can be generated by custom experiments, or collected - along with other ``omics'' - 
   from public databases such as TCGA and cBio portal. For the latter, cBio portal, \texttt{TRONCO} implements a query
    system to fetch data with minimal effort. The tool engine can then be used to manipulate  genomic
    profiles -- regardless of their source -- and  run progression inference  algorithms.
	}
    }
\label{fig:XXX}
\end{figure*}

Cancer develops through the successive expansions of clones, in which 
certain (epi)genomic alterations, called \emph{drivers}, confer a
\emph{fitness} advantage and progressively accumulate, in a context of
overall scarcity of resources \cite{nowell1976clonal}. \rev{Specifically, in Nowell's seminal work, tumor evolution is described in terms of stepwise genetic variation such that growth advantage is the key for the survival and prorogation of the clones.} Therefore, one can define \emph{cancer progression models}, in terms of
\emph{probabilistic causal graphical models}, where the conditional
dependencies and the temporal ordering among these alterations are described, revealing the evolutionary trajectories of cancer at the
(epi)genome level.

We further distinguish \cite{Caravagna2015:_pipeline}. $(i)$
\emph{ensemble-level} progression models, describing the statistical
trends of accumulation of genomic alterations in a cohort of distinct
cancer patients. \rev{Such models describe the temporal partial orders of fixation and accumulation of such alterations and represent population-level trends;} and $(ii)$  \emph{individual-level} models, thus
accounting for the specific evolutionary history of cancer clones in
individual tumors. \rev{Such models thus impute the ancestry relations of the observed clones.} 

Even if the inference of such models is further complicated by a
series of theoretical and technical hurdles, such as, e.g.,
\emph{intra-} and \emph{inter-tumor heterogeneity} and the effective
detection of drivers, it can benefit from the increasing amount of
\emph{next-generation sequencing} (NGS) data, currently available
through public projects such as The Cancer Genome Atlas (TCGA,
\url{https://tcga-data.nci.nih.gov}).
%\cite{tcga}.
Usually, such databases provide \emph{cross-sectional} (epi)genomic
profiles retrieved from single biopsies of cancer patients, which can
be used to extract ensemble-level models; but higher resolution data
such as \emph{multiple-biopsies}, or even \emph{single-cell} sequencing
data are becoming more accessible and reliable, which
can be used to infer individual-level models.

Here we introduce \TRONCO{} (TRanslational ONCOlogy), an \R{} package
built to infer cancer progression models from heterogeneous genomic
data (in the form of alterations persistently present along tumor
evolution.)  Currently, \TRONCO{}  provides the implementation of two 
algorithms: $(i)$  \texttt{CAPRESE} (CAncer PRogression
Extraction with Single Edges \cite{Loohuis:2014im}), and $(ii)$
\texttt{CAPRI} (CAncer PRogression Inference
\cite{Ramazzotti15092015}), both based on Suppes' theory of
\emph{probabilistic causation} \cite{suppes1970probabilistic}, but
with distinct goals and properties (see  Software Implementation).


\TRONCO{}, in its current form and perspective, should be thought
of as a tool that provides the implementation of up-to-date solutions
to the progression inference problem.  At the time of the writing it 
can be effectively used as the final stage of a modular
pipeline for the extraction of ensemble-level cancer progression
models from cross-sectional data \cite{Caravagna2015:_pipeline}. In
such a pipeline input data are pre-processed to $(i)$ stratify samples
in tumor subtypes, $(ii)$ select driver alterations and $(iii)$
identify groups of fitness-equivalent (i.e., mutually exclusive)
alterations, prior to the application of the \texttt{CAPRI} algorithm.
% 
The resulting ensemble-level progression models depict the evolutionary dynamics of cancer, with 
translational impacts on diagnostic and therapeutic processes, especially in
regard to precision medicine and personalized drug development. 

From the complementary perspective, \texttt{TRONCO} can also exploit
the \texttt{CAPRESE} algorithm to infer the clonal evolutionary
history in single patients when multiple samples are available, as in
the case of multiple biopsies and/or single-cell sequencing data, as
long as the set of driver events is selected; see
\cite{Caravagna2015:_pipeline}.


\section{Software Implementation}
\label{sec:algorithms}

\TRONCO{} implements a set of \R{} functions to aid the user  to
extract a cancer progression model from genomic data. At a high-level,
these function shall help to import, visualize and manipulate  genomic
profiles -- regardless of their source -- eventually allowing
the implemented algorithms to run and assess the
confidence in a model.

\rev{The basics steps of \TRONCO{}'s usage are shown in Figure \ref{fig:XXX}. 
In panel $(a)$ we show multiple  input  alterations (e.g., somatic mutations or copy number alterations) either from a cohort of patients, or a unique patient (e.g., multi-region or single-cell sequencing); in panel $(b)$ we show an oncoprint visualization from the tool, i.e., a matrix whose columns represent  samples and rows the  alterations and their presence per sample; panel $(c)$ shows an inferred  graphical Bayesian progression model    obtained with one of the available algorithms; finally, in panel $(d)$ we show data supported for processing in the tool. For a more detailed explanation of the implementation of the package see \cite{antoniotti2015design}.}

% descrivere oncoprint, descrivere provenienza dati, togliere pipeline, indicare che i modelli sono grafi

\paragraph{Data loading and manipulation.} Common  formats to store
data used to extract progression models can be natively imported. 
These include, for instance, the  \emph{Mutation Annotation
  Format} (MAF) for  somatic mutations, as well as the \emph{Genomic
  Identification of Significant Targets in Cancer}  (GISTIC) format to
store focal Copy Number Variations. The tool can exploit the cBio
portal for Cancer Genomics, which collects among others TCGA projects,
to access freely available instances of such data
\cite{cerami2012cbio}.

% ref al pannello D quando ci sarà

\TRONCO{} provides functions for data preprocessing to, e.g., select a certain subset of alterations, or samples
or any abstraction which might be appropriate according to the cancer being studied.


\paragraph{Visualization and interaction with other tools.} \TRONCO{}
implements an \emph{oncoprint} system to visualize the processed data. Datasets can be
exported for processing by other tools used to,
e.g., stratify input samples and detect groups of mutually exclusive
alterations, which include the \emph{Network Based Stratification}
\cite{hofree2013network} and \emph{MUTEX} \cite{babur2015systematic}
tools. \TRONCO{} allows the visualization of the inferred models.

\paragraph{Model inference and confidence.} \TRONCO{} provides two 
algorithms: $(i)$ \texttt{CAPRESE}, which uses a
\emph{shrinkage}-like estimator to infer \emph{tree}-models of
progression, and $(ii)$ \texttt{CAPRI}, which extracts more general
\emph{direct acyclic graphs (DAG)} - thus allowing for confluent
evolution and complex hypothesis testing -- by combining
\emph{bootstrap} and \emph{maximum likelihood estimation}. \rev{\texttt{CAPRESE} and \texttt{CAPRI} both rely on the same theory of \emph{probabilistic causation}, but with distinct goals and properties. The former reconstructs tree models of  progressions, while the latter  general directed acyclic graphs. Both methods are agnostic  to the type of input data (i.e., whether its an ensemble or an individual tumor), but shall be used in different contexts as they produce different types of models. Indeed, \texttt{CAPRESE} is better at extracting cancer evolution in a single individual as in that case trees capture branched evolution and trunk events, which shall suffice to describe clonal evolution. Instead, when heterogeneity might result in multiple evolutionary routes with common downstream alterations, the underlying true model is a graph, and \texttt{CAPRI} should be the tool of choice.} %In \cite{Caravagna2015:_pipeline} examples of the usage of the two algorithms on real data along with a deeper discussion on the interpratation of the models are provided.} 

% togliere ref a suppes / caprese si presta a ricostruire architetture clonali su singolo pz - capri visto che permette di...  togliere ref a caravagna&

Whatever a model is, \texttt{TRONCO} implements a set of functions to assess
its confidence   via $(i)$ non-parametric,
$(ii)$ parametric and $(iii)$ statistical bootstrap. 


\section{Discussion}
\label{sec:discussion}

% \TRONCO{} aims to become the bioinformatics reference tool of choice
% providing  the  community  with the implementation of up-to-date
% statistical routines to understand the evolutionary trajectories of
% any cancer. Indeed, in terms of computational speed, scalability with
% respect to sample size, predictive accuracy and robustness against
% noise in the input data, the algorithms implemented in the tool is
% demonstrably to be the current state-of-the-art for the inference
% problem.  The implementation in \R{} makes straightforward the
% interaction of \TRONCO{} with other common bioinformatics tools,
% possibly allowing the creation of a common suite of tools for cancer
% progression inference. The porting of the tool to other widely used
% bioinformatics platforms such as, e.g., Cytoscape
% \cite{shannon2003cytoscape} is under development.

\TRONCO{} provides up-to-date, theoretically well-founded, statistical
methods to understand the evolution of a cancer
(ensamble-level) or a single tumor (individual-level).
The implemented algorithms are demonstrably
the state-of-the-art for the progression inference problem, in
terms of computational cost, scalability with respect to sample size, 
accuracy and robustness against noise in the data.
The implementation makes straightforward the interaction of
\TRONCO{} with other common bioinformatics tools, possibly allowing
the creation of a common suite of tools for cancer progression
inference.

\rev{Finally, we refer to \cite{Caravagna2015:_pipeline} or the Supplementaty materials for a demonstration
of the usage of \TRONCO{} on real genomics data both at the ensemble-level
and individual-level progression models. In particular, this paper outlines the capability of the methods to reproduce much of the current knowledge
on the progression for a set of cancer types, as well as to suggest clinically relevant 
insights. Furthermore, we also provide users with detailed manuals, vignettes, and source code to replicate all the analysis presented in the paper plus others (case studies: colorectal cancer, clear cell renal cell carcinoma and acute chronic myeloid leukaemia) in the Supplementary Materials and at the \TRONCO{} official webpage (Software section at \href{http://bimib.disco.unimib.it/}{http://bimib.disco.unimib.it/}).}
 
\paragraph{\textbf{Financial support.}} MA, GM, GC, AG, DR acknowledge
Regione Lombardia (Italy) for the research projects RetroNet through
the ASTIL Program [12-4-5148000-40]; U.A 053 and Network Enabled Drug
Design project [ID14546A Rif SAL-7], Fondo Accordi Istituzionali 2009.
BM acknowledges founding  by the NSF grants CCF-0836649, CCF-0926166
and a NCI-PSOC grant.

\bibliographystyle{plain}
\bibliography{biblio}

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\includepdf[pages=-]{supplementary.pdf}

\end{document}

main.bbl
\begin{thebibliography}{1}

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\end{thebibliography}
