\documentclass[11pt]{article}
\usepackage[margin=1.2in,a4paper]{geometry} % try also "letterpaper" instead of "a4paper"
\usepackage{enumitem} % this package is used to generate the custom chapter prefix "[Chapter number].[Exercise Number]"

\begin{document}

%%%%%%%%%% header %%%%%%%%%%
\noindent {\sf\LARGE GENOME-SCALE ALGORITHM DESIGN} \\
\noindent {\sf by Veli M{\" a}kinen, Djamal Belazzougui, Fabio Cunial and Alexandru I. Tomescu}\\
\noindent {\sf Cambridge University Press, 2nd edition, 2023}\\
\noindent {\sf www.genome-scale.info}\\
\noindent\makebox[\linewidth]{\rule{\paperwidth}{0.4pt}}
%%%%%%%%%% header %%%%%%%%%%

\section*{Exercises for Chapter 1. Molecular biology and high-throughput sequencing}

\begin{enumerate}[label=1.\arabic*]
\item Write a program that lists all the DNA sequences that encode a given protein sequence.
\item In a given organism some codons are used more frequently than others to encode the same amino acid. Given the observed frequency of every codon in a species, normalize it into probabilities and write a program that, given a protein sequence, samples a random DNA sequence that encodes that protein under such codon usage probabilities.
\item In a given organism, some \emph{codons pairs} occur less frequently than others.
\begin{enumerate}
\item Given the set of all exons of an organism, write a program that computes the ratio $z(XY)$ between the observed and the \emph{expected} number of occurrences of every pair of consecutive codons $XY$. Note that the expected number of occurrences of pair $XY$ depends on the frequency with which $X$ and $Y$ are used to encode their corresponding amino acids.
\item Given a DNA sequence $S$ that encodes a protein $P$, let $f(S)$ be the average of $z(XY)$ over all consecutive pairs of codons $XY$ in $S$. Write a program that computes, if it exists, a permutation $S'$ of the codons of $S$, such that $S'$ still encodes $P$, but $f(S')<f(S)$. Such an \emph{artificially attenuated} version of $S$ has been shown to decrease the rate of protein translation: for more details, see \cite{coleman2008virus}.
\end{enumerate}
\end{enumerate}

\begin{thebibliography}{xx}

\bibitem{coleman2008virus} Coleman, J.~R., Papamichail, D., Skiena, S., Futcher, B., Wimmer, E.
  and Mueller, S.  (2008), `Virus
  attenuation by genome-scale changes in codon pair bias', {\em Science} {\bf
  320}(5884),~1784--1787.

\end{thebibliography}

\end{document}  
