The jumping gene or "Sleeping Beauty" transposon is "Molecule of the Year 2009". This was announced by Professor Isidro T. Savillo, President of the International Society for Molecular and Cell Biology and Biotechnology Protocols and Researches (ISMCBBPR). The transposon was generated by Dr. Zsuzsanna Izsvák, Dr. Zoltán Ivics and Dr. Lajos Mátés of the Max Delbrück Center for Molecular Medicine in Berlin-Buch. According to the jury, it was selected out of 15 molecules nominated in the contest because "this molecule holds great promise for gene therapy". The jury pointed out that it can stably transfer genes even to stem or progenitor cells and is safer than a viral vector. It is the first time that the Molecule of the Year has been awarded to major recipients outside the USA in Europe.
Transposable elements are molecular parasites that propagate themselves in genomes. But at the same time they provide plasticity to the genome that clearly contributed to the evolution of gene function across the tree of life. About half of the human genome is derived from ancient transposable element sequences.
However, due to mutations, the vast majority of the transposons became inactivated. Based on transposons in fish that are presumed to have been active approximately 20 million years ago, Dr. Ivics and Dr. Izsvák resurrected a jumping gene more than ten years ago. They named the transposon Sleeping Beauty, because they literally awakened it after a long evolutionary "sleep".
The scientists modified the originally reconstructed transposon so that it acquired a highly elevated potency in gene transfer. In its award citation, the jury noted that this hyperactive transposon promises to be a revolutionary technology platform for genetic engineering in vertebrates.
With their new tool, Dr. Izsvák and Dr. Ivics were able to introduce genes into cells of vertebrates at efficiencies previously seen only with viral vector systems. This was impossible before, as researchers previously lacked efficient transposon technologies to do so. Therefore, Sleeping Beauty was referred to as a breakthrough at the European Society of Gene and Cell Therapy Conference in Hannover, Germany in November 2009.
Since 2002 the Molecule of the Year has been awarded by the ISMCBBPR, which was founded in 2000. Prior to 2002 the award was conferred by the journal Science.
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text:
\section{Introduction}
The binding of proteins to DNA or chromatin is at the basis of gene regulation, as for instance transcription factors stick to a gene along the DNA to promote or inhibit the subsequent binding of RNA polymerases, and hence to down or upregulate its transcription~\cite{Alberts,Voituriez,Voituriez2}.

In 1970 Riggs found that the association rate of the {\it lac}-repressor
in {\it E.coli} is ~$10^{10}M^{-1}s^{-1}$, two orders of magnitude larger
than it would be if the reaction time were dominated by the 3-dimensional (bulk)
diffusion of the proteins through cytoplasm~\cite{Riggs}.
How can proteins move around so quickly in the cell?
An intriguing mechanism, alternative to bulk diffusion, was proposed by Berg and von Hippel
in~\cite{Berg_I}. They conjectured that proteins may bind non-specifically to DNA and diffuse along it -- the linear portion $l_s$ of DNA which is explored before the protein detaches from it is known as the {\it sliding length}.
DNA looping may also allow hops and jumps of the protein between different sites on the DNA~\cite{metzler,def_jump_hop}. The expression {\it facilitated diffusion} indicates all the different mechanisms through which proteins exploit the presence of DNA in the cell in order to reduce
the {\it mean search time} (hereon MST), namely the average time that one protein needs to reach its target.
By considering a protein performing a very large number of slides, attachments and detachments, it is possible to theoretically estimate the value of the MST as a function of the sliding length $l_s$  (see e.g.~\cite{Marko,Voituriez,Voituriez2}).
The theory leads to the intriguing result that there should be an optimal
sliding length for which the mean search time is minimum, and
significantly smaller than in the bulk diffusion case, which provides an
explanation for Riggs' experimental results.

There are to date very few direct dynamical numerical simulations of facilitated diffusion (for an up-to-date theoretical review see~\cite{Voituriez}). Ref.~\cite{Furini} simulated detailed protein-DNA interactions with molecular dynamics, focussing on a small, unconfined, DNA loop, while Refs.~\cite{Lang_I,Lang_II,Lang_III,Kafri1,Florescu} focused on few selected isotropic geometries and on a single protein diffusing inside the cell. Our aim here is to extend the study of facilitated diffusion in a number of ways, with a view to bridge the gap towards more realistic conditions. We start from the observation that DNA is strongly confined {\it in vivo}~\cite{jpcmreview}, and consider both isotropic and anisotropic containers, which are relevant for eukaryotic nuclei and bacterial cells respectively. Secondly, to assess the role of DNA conformations, we simulate different persistence lengths: this is important in eukaryotes as the persistence length of chromatin varies in the 40-200 nm range and is thought to be activity-dependent~\cite{jcb}. Finally, we extend our investigation to the case in which ${\cal O}(10)$ identical proteins simultaneously search for their target -- this is a more realistic scenario given e.g. the typical copy numbers of transcription factors inside a bacterium such as {\it E. coli}~\cite{Kafri2,Xie}. As we shall show, each of these realistic add-ons leads to important qualitative differences in the physics of facilitated diffusion.

Specifically, we find that the confining geometry and the DNA elasticity affect the mean search time in a major way: our simulations show that anisotropy slows down facilitated diffusion, while flexible conformations lead to a larger speed-up around the optimal sliding length with respect to semiflexible ones. These differences are much more pronounced for short chains.
Our main result is that considering a cell with multiple copies of a protein looking for their target, as is the case in nature, leads to a very different view on facilitated diffusion with respect to the standard one, based on single protein models. Instead of displaying a well-defined minimum as a function of the sliding length, the MST for multiple proteins (i.e. the time {\it one} protein first hits the target) is remarkably flat, so that facilitated diffusion offers a robust way to speed up the search, not relying on any optimisation linked to fine tuning of the parameters controlling the intracellular protein dynamics.
This trend holds for the chain lengths considered here, which are more than one order of magnitude larger than the sliding length: however, very long chains, which we have not simulated, may again display a different behaviour.

\section{Method}
Our approach is based on direct Monte-Carlo simulations of the whole facilitated diffusion process.
For the DNA, we use a coarse-grained bead-spring model where beads are joined by FENE springs and interact via a shifted and cut-off Lennard-Jones (LJ) potential.
This provides a hard-core for the beads, hence capturing the polymer self-avoidance. The cut-off is at $2^{\frac{1}{6}}\sigma$, while the energy scale associated with the LJ potential is  $\epsilon=\frac{2}{5}k_B T$.
Within this setting the natural length scale in our simulations is provided by the size of the
chain beads, $\sigma$. We chose to simulate confining geometries with sizes of $\sim$ 10$\sigma$ - 30$\sigma$ as detailed below, and chains with contour length $L_c$ ranging from $60\sigma$ to $200\sigma$.
Such relatively short polymers allow us to more stringently test the theories
which typically rely on the existence of many unbinding and binding events and hence implicitly assume long polymers.
Moreover conditions similar to our simulations may be designed experimentally by using
naked DNA ($\sigma=2.5$ nm) of length 150-500 nm confined in vesicles of size ~50 nm -- a set-up which should be realisable with single molecule experiments {\it in vitro}. An intriguing alternative mapping is to yeast chromatin {\it in vivo}, where the appropriate coarse graining entails a value of $\sigma\sim 30$ nm (containing $\sim$ 3 kilo-base pairs of DNA), and typical chromosome length is $\sim 10^6$ base pairs (or $L_c \sim$ 300$\sigma$).

The elasticity of the DNA is modelled by a standard Kratky-Porod potential,
$U_b=-K_b\sum_i \vec{t}_i \cdot \vec{t}_{i+1}$,
where $\vec{t}_i=\vec{r}_{i+1}-\vec{r}_i$, $\vec{r}_i$ being the position of the i-th monomer, and where the persistence length is determined in terms of $K_b$, the bending rigidity, via $l_p=K_b \sigma/k_B T$. We have considered the case of semiflexible ($l_p=20 \sigma$) and flexible ($K_b=0$) polymers, relevant to DNA and yeast active chromatin respectively~\cite{jcb}.
Equilibrium DNA configurations are grown and relaxed inside cylindrical or spherical containers. For the confining geometry, we used cylinders having a total length of 30$\sigma$ and radii $R_{cyl}$ going from 4$\sigma$ to 10$\sigma$ to provide different aspect ratios for the container.
Sphere radii $R_s$ range from 7$\sigma$ to 13$\sigma$ giving isotropic confining regions
with the same volumes of the cylindrical counterparts.
Rather than explicitly modelling polymer dynamics, the equilibrium DNA conformations
are kept frozen during single
diffusion processes. This quenched approximation for the DNA is in line with
most previous theoretical and numerical work~\cite{Marko},~\cite{Lang_I} and
can be justified by noting that the typical time needed by the polymer to change from one
conformation to a completely uncorrelated one (Rouse time $\tau_R$~\cite{Rouse}) is $\sim L_c^2$, and for the cases we consider is larger than the timescale associated with protein diffusion, $\sim R^2/D_3$.

\begin{figure}
\label{fig:1}
\includegraphics[width=7.2cm]{Fig1.png}
\caption{(Color online) Some simulation snapshots. A semiflexible polymer is confined inside a cylinder (a) or a sphere (b), while some proteins (red dots) diffuse in 3D or slide along it.}
\end{figure}

Proteins are modelled as pointlike and non-mutually-interacting particles, whose initial
positions are chosen to be uniformly distributed at the walls of the confining geometry.
In the bulk, proteins diffuse with a coefficient $D_3=0.021 \sigma^2/$~ns. We use reflecting boundary conditions at the surface of the sphere or cylinder.
Interaction with DNA is modelled as follows: whenever the new proposed position for the protein falls inside one of the DNA beads, this starts sliding with probability $p$.
During each time step spent sliding, the protein may hop either to the right or to the left DNA bead, or detach from the genome with a probability $1-p$.
Different choices of $p$ correspond to different values of the sliding length $l_s$, the key optimisation parameter in the theory of facilitated diffusion.
The duration of a sliding step, $\Delta t_s=48$~ns, was chosen in order to give a one-dimensional diffusion coefficient $D_1$ equal to $D_3$ in agreement with previous theoretical estimates~\cite{Marko}
and simulations~\cite{Lang_I} (even though most experimental results suggest $D_1 < D_3$~\cite{Xie,D_3}).
When the particle is at one of the two terminal beads of the chain it is
always reflected, as in~\cite{Lang_I}. Some snapshots of our simulations are shown in Fig.~1a and 1b respectively for cylindrical and spherical confinement for semiflexible chains.
The diffusion process for one protein stops as soon as it
reaches the target, here modelled as an internal DNA bead. The interaction radius between the protein and the target, $r_b$ was equal to $r_b=0.35\sigma$ (which corresponds to about 1 nm for facilitated diffusion on naked DNA).
For a fixed DNA equilibrium configuration the MST is estimated by averaging the
time needed by one particle to reach the target over 100 initial conditions. A second
average is then performed over $\sim 50$ different DNA configurations equilibrated in the
confined region.

\section{Results}

\subsection{Comparison with theoretical results}

\begin{figure}
\label{fig:2}
\includegraphics[width=6.7cm]{Fig2.pdf}
\caption{(Color online) Dependence of the MST on $l_s$ is the case of a cylinder having radius $R_{cyl}=9\sigma$ and $L_c=200\sigma$ according to our data and to the theoretical predictions made in \cite{Marko} ($\tau_M$) and in \cite{Lang_I} ($\tau_K$). The case shown in the inset refers to short chains ($L_c=60\sigma$) and to very anisotropic confinement (cylinder with radius $R_{cyl}=4\sigma$ and side length
$L=30\sigma$).}
\end{figure}

We first compare our results to existing theoretical predictions by focusing on the
cylindrical confining geometry and on the facilitated diffusion of a single protein.
Empty circles in Fig.~2 correspond to the simulated dependence of the MST on $l_s$
in the case of $l_p=20\sigma$, and $L_c=200\sigma$ (error bars are smaller than symbols). These points are compared with theoretical curves (solid lines) predicted in~\cite{Marko} ($\tau_M$) and in~\cite{Lang_I} ($\tau_K$).
The latter gives a better estimate of the MST for small $l_s$, as well as of
the optimal sliding length. For large $l_s$, according to both theoretical
models, the MST should increase much faster than in our data, which instead tend to quickly saturate around a constant value.
This discrepancy is more dramatic for shorter DNAs (see inset of Fig.~2, corresponding to a volume
fraction of $\sim 2\%$ -- a similar albeit smaller effect is observed for spherical confinement, discussed below)
where it is more likely for the diffusing protein to reach the target in just a few slides.
Such extreme events violate the hypothesis, used to estimate the MST theoretically, that the
length scale over which the sliding mechanism occurs is much smaller than $L_c$~\cite{note}.

\subsection{Search time for ten proteins}

\begin{figure}
\label{fig:3}
\includegraphics[width=6.7cm]{Fig3-2.png}
\caption{(Color online) Comparison between the dependence on $l_s$ of the MST for one protein, scaled by 10 (mean field approximation) and for the first of ten particles (numerical data). Data refer to semiflexible DNA in a cylinder ($R_{cyl}=4\sigma$ and $L_c=200\sigma$).}
\end{figure}

So far we have considered the facilitated diffusion of a single protein. However in a cell there are typically more copies of the same protein which simultaneously search for the same target -- and a reaction is initiated once the first reaches it.

It is then natural to look at the time at which the first of several proteins finds the target.
In Fig.~3 we plot the MST of the first of ten non-interacting and simultaneously diffusing particles -- for comparison we also show the corresponding MST curve for a single protein, rescaled by a factor of 10 as expected from a naive mean-field argument (critically analysed in Ref.~\cite{Kafri2}, see also below). The simulated data largely deviate from this simple estimate.

\begin{figure}\label{fig:4}
\includegraphics[width=0.9\columnwidth]{Fig4.png}
\caption{(Color online) The normalised histogram of the number of particles
which have reached the target at a given time $t$,
in the case of $N_p=10$ (blue, top curve) and $N_p=1$ (red, bottom curve).
Both graphs refer to a semiflexible polymer with $L_c=60\sigma$ and to a cylindrical confinement with  $R_{cyl}=4\sigma$. }
\end{figure}

The ultimate reason for this deviation lies in the markedly non-exponential nature of the search time distributions, which suggests the existence of multiple timescales in the dynamics.
This can be appreciated by plotting the distribution of arrival times, (i.e. the time to first reach the target), $P(t)$, shown in Fig.~4 for both the case of one single particle and for that of ten particles.
From the linear-log plot in Fig.~5 it is apparent that neither distribution
is exponential -- a better fit is provided by a streched exponential
distribution (data not shown).

We note that, as our ten proteins are non-interacting,
the probability that one of the
$N_p$ diffusing particles  reaches the target at time $t$,
$R_{N_p}(t)=\int_0^t P(t^\prime)dt^\prime$, is given by
\begin{equation}
R_{N_p}(t)=1-(1-R(t))^{N_p},
\end{equation}
where $R(t)$ is the corresponding single protein probability
(see e.g. \cite{Kafri1}).
While directly considering the trajectories of 10 proteins in our
simulations, we have verified that this formula holds for our data.
If $P(t)$ were a simple exponential, this formula shows that there
would simply be a factor of
$N_p$ between the MST of a single diffusing particle and the one where $N_p$ are
simultaneously diffusing in the system.

\begin{figure}\label{fig:5}
\includegraphics[width=0.49\columnwidth]{Fig5a.png}
\includegraphics[width=0.49\columnwidth]{Fig5b.png}
\caption{(Color online) These graphs show the same data as Fig.~4 ($L_c=60\sigma$, semiflexible configurations confined in a cylinder with  $R_{cyl}=4\sigma$), but in a log-linear plot to stress the non exponential
behavior of the distributions and they refer to the case of one particle (left) and of ten independent particles diffusing simultaneously (right).
}
\end{figure}

Importantly, we also find that the $l_s$ dependence of the MST of the first of ten proteins does {\em not} display a clear minimum anymore. This  suggests that, when more than one protein are searching for the target,  there is effectively no optimal sliding length!
In other words, while facilitated diffusion is still faster than bulk diffusion, there is no need for the protein to fine tune the sliding length on the DNA to optimize the search process; rather, the advantages due to facilitated diffusion are robust and largely independent of the protein-DNA affinity.
While this holds up to the longer chain length simulated here, we cannot rule out that very long chains may display a different behaviour.

\subsection{Effect of confining geometry and DNA elasticity}

To further bridge the gap between simulations and biologically relevant conditions, it is important to address the effect of the aspect ratio of the confining geometry and of DNA elasticity. As mentioned in the introduction, there is a range of naturally occurring values for these parameters, and it is interesting to explore what impact tuning these has on the dynamics of facilitated diffusion. For instance, is there a difference in the efficiency of facilitated diffusion within eukaryotic nuclei, which are roughly spherical, and inside elongated bacterial cells? Do proteins search faster for a target inside euchromatin regions of the chromosomes, which are more flexible than inactive, heterochromatic ones~\cite{jcb}? To address these questions, we systematically analysed different confining conditions and polymer elasticities, and report below some typical results for the MST as a function of $l_s$.

\begin{figure}
\includegraphics[width=0.98\columnwidth]{Fig6.png}
\caption{(Color online) Dependence of the MST on $l_s$ for different geometries and DNA elasticity. Data refer to a single protein, $R_{cyl}=4\sigma$ and correspondingly $R_s=7\sigma$, when $L_c=60\sigma$ (a) and $L_c=200\sigma$ (b). (c) shows the MST for the first of ten particles for the same values of $R_s$ and $R_{cyl}$, when $L_c=200\sigma$.}
\label{fig:6}
\end{figure}

We have considered ten different cylindrical geometries, of aspect ratio $L/(2R_{\rm cyl})$ ($L$ and $R_{\rm cyl}$ are cylinder height and radius respectively, $L$ is kept fixed) variable between 3/2 and 15/4 -- we only report results on the MST for the most anisotropic case, as the difference with respect to the case of spherical confinement is more readily appreciable there. As anticipated, we also compare the cases of flexible ($l_p=0$) and semiflexible ($l_p=20$ $\sigma$) polymers.
In the Appendix we provide more details on the conformations of the polymer on which proteins perform their search for the target, and in particular discuss how they change with elasticity and confining geometry. Here we focus on the results for the MST.
Each panel of Fig.~\ref{fig:6} (from a to c) shows the $l_s$ dependence of the MST for four different cases:
semiflexible and flexible DNA inside a cylinder, and semiflexible and flexible DNA inside a sphere  with the same volume. Note that to better highlight the effect of anisotropy on the MST, we focused on the most anisotropic cylindrical geometry, namely the one with aspect ratio $L/2R_{cyl}= 15/4$.

For the smallest chains considered ($L_c=60\sigma$, Fig.~6a) we observe major effects both of geometry and polymer elasticity, especially for small $l_s \stackrel{<}{\sim} 2\sigma$.
In particular, in constrast to what happens when $l_p=20\sigma$ in a cylinder (Fig.~2 inset), in all other cases a well-defined optimal sliding length exists, and, more importantly, the MST is much smaller. This points out how both isotropy and flexibility can play an important role in enhancing the facilitated diffusion. Our results suggest that, at least for short chains, the search is faster within a sphere and on a flexible polymer.

Fig.~\ref{fig:6}b shows the same plots as in Fig.~\ref{fig:6}a, but relative to the case of $L_c=200\sigma$.
Here the effects of the confining geometry and DNA conformations are less significant.
This is due to the fact that the volume fraction occupied by the DNA now increases, so that even the stiffest conformations develop loops and local contacts, as they need to bend several times to fit in.  Moreover, long polymers are more homogeneously distributed in the cell than short ones, which renders the local environment of a DNA segment
less sensitive to the overall confining geometry, or polymer elasticity.
Finally, Fig.~\ref{fig:6}c shows the MST for the first of ten proteins to reach the target, for $L_c=200\sigma$. The data confirm the lack of an optimal sliding length.
Interestingly, we also find that, as for the case of a single diffusing protein, the search is quicker within a sphere. The effect of flexibility is still present but milder than for a single protein.

An analysis of the statistics of 3D excursions in between slides, given below, sheds more light on these results.

\subsection{Statistics of jumps and hops}

Here we provide an analysis of how the occurence probability of different 3D-diffusion mechanisms such as ``jumps'' and ``hops'' is affected by DNA elasticity and confinement geometry, with a view of explaining our results in Fig.~\ref{fig:6} on the influence of these factors on the MST.

``Hops'' and ``jumps''  are 3D-diffusion events that take place between two slides. In a hop the distance along the DNA between the take-off (detachment) and landing (re-attachment) point is ``small'', while in a jump it is ``large''. In our treatment we consider the distance ``small'' if it is less than 10 beads, and ``large'' otherwise.

\begin{figure}
\includegraphics[width=0.98\columnwidth]{Fig7.png}
\caption{(Color online) Histograms describing the average number (a, b) duration (c, d) and the average distance between the takeoff and landing points ('length', e, f) for jumps and hops. Blue (left) columns refer to $L_c=60\sigma$, while orange (right) columns refer to $L_c=200\sigma$. Numbers on the horizontal axis refer to different geometries and elasticities: (1) and (2) are for semiflexible DNA confined in a cylinder and in a sphere respectively, (3) and (4) refer to flexible DNA in a cylinder and in a sphere respectively. All data refer to the case of $R_{cyl}=4\sigma$ ($L/(2R_{cyl})=15/4$) -- and correspondently $R_s=7\sigma$.}
\label{fig:7:new}
\end{figure}

The key features of the statistics of jumps and hops are shown in Fig.~\ref{fig:7:new}.
The absolute numbers of jumps and hops give the clearest signal. As these quantities depend on the sliding length, we plot their value at the minimum MST (as a function of $l_s$) in Fig.~\ref{fig:7:new}a,b. For $L_c=60\sigma$, both quantities are largest in the case of a semiflexible DNA in cylindrical confinement, which correlates well to a larger MST in this situation. Furthermore, still for $L_c=60\sigma$, in the case of spherical confinement a smaller number of jumps is required on a flexible DNA (case 4 in Fig.~\ref{fig:7:new}) than on a semiflexible one (case 2 in Fig.~\ref{fig:7:new}), to reach the target, again in agreement with the MST trends in Fig.~\ref{fig:6}. Facilitated diffusion on a flexible DNA inside a cylindrical container would require the smallest number of jumps, which does not match the fact that the MST in this case is not optimal. This is because in this situation the number and duration of hops also plays a role: these are relatively numerous, and, more importantly, each of these lasts about $50\%$ longer, with respect to the average of the other cases (see Fig.~\ref{fig:7:new}d).

It is also interesting to monitor the ratio between the number of jumps and the number of hops, which instead does {\it not} depend on the sliding length. This ratio is once again affected by the polymer elasticity, more so in the case of a cylindrical confinement, where for a semiflexible DNA it is equal to 0.11, almost twice as large as for a flexible DNA (0.06). In the case of spherical confinement the ratio between hops and jumps is again equal to 0.11 for semiflexible polymers, and rises to 0.09 for flexible ones.
These differences are related to the average backbone distance between the takeoff and landing points, in both jumps and hops: as can be seen in Fig.~\ref{fig:7:new}e and f, particles perform longer jumps along a semiflexible than along a flexible polymer. In contrast, hops are shorter when performed along semiflexible configurations. This is evidence of the fact that stiffness favours either very short or very long range (in terms of chemical distance) three-dimensional displacements, while flexibility allows intermediate-range displacements, due to enhanced local bending. Short-range 3D displacements are advantageous for short DNA chains, as witnessed by our MST data in Fig.~\ref{fig:6}.

When longer polymers are considered ($L_c=200\sigma$), though, the trends are less clearcut.
On the one hand, for very low values of $l_s$, the MST in a cylinder is again larger with respect to that in a sphere, and once more this is in line with the trends in the total number of jumps.
On the other hand, now the semiflexible DNA inside cylindrical confinement no longer gives the slowest search, especially for larger values of $l_s$, where the MST is largest for a flexible chain inside a cylinder.
This is in part because the frequent intermediate-range displacements performed on flexible polymers confined in cylinders make a less efficient strategy in longer chains, as this wastes time in sampling nearby (in terms of chemical distance) DNA regions.
At the same time, it is interesting to note that jumps always take (slightly) longer along flexible than along semiflexible chains. We ascribe this to the fact that in flexible polymers most of the nearby beads are also adjacent along the chain, and it is less likely for a protein to find a closeby bead which is very far along the DNA. This is a disadvantage especially in the case of long polymers, where jumps are expected to play an important role in favouring a better sampling of DNA.
As a result the MST inside a cylinder is slightly longer in the flexible case.

We finally note that in all cases isotropic confinement reduces the MST, for both small and long polymers. This can be explained by noting that in a sphere any two points are on average closer together than inside a cylinder. This is quantified via  Fig.~11 (see Appendix), showing the mutual distance distribution function, $\Pi(r)$~\cite{note2}.
This distribution is much more spread for cylinders than for spheres, which allows a particle in a sphere to reach its target after a considerably smaller number of 3D-diffusion events.

To summarise, in this section we have analysed the statistics of jumps and hops with a view of understanding more deeply the results in Fig.~\ref{fig:6} on the effect of geometry and elasticity on the MST trends.
Firstly, we have seen that, especially for short polymers, the MST trends can be rationalised by looking at the total number of jumps and hops needed to get to the target. This may be viewed as a consequence of the fact that the mutual distance distribution function goes to  zero at a much shorter distance in an isotropic geometry.
Secondly, we have shown that in a cylinder, 3D-displacements along a flexible chain usually take longer than in the presence of semiflexible DNA. This increases the MST of long polymers, where the search requires several such jumps.

\section{Summary and Conclusions}

In summary, we have presented detailed Monte Carlo direct dynamical simulations of the facilitated
diffusion of one or several proteins inside a cylindrical or spherical cell in presence of
equilibrated DNA configurations. We have compared our simulation results with theoretical
predictions for the mean search time, the time needed for one protein to first reach its target, for instance a promoter along the genome.
For short DNA chains we find a large discrepancy, which we attribute to the fact that proteins can reach the target with no or few sliding steps
along the genome. This discrepancy attenuates as the contour length of the DNA increases.
Our main result is that the average search time needed for the first of several copies of the same protein looking for their target simultaneously shows a qualitatively different dependence on physical parameters: most notably, there is no longer an optimal sliding length leading to the fastest search.
This is important biologically, as in bacterial or eukaryotic cells the typical copy numbers of e.g. transcription factors is low but larger than unity (typically $\sim$10~\cite{Xie}).
This fact may then be interpreted as a way to ensure that the search for the specific target of a protein is not crucially dependent on the precise value of its non-specific affinity with DNA.
Interestingly, we have also found that polymer elasticity and the confining geometry may both affect the mean search time: facilitated diffusion is most effective inside spherical cells and in presence of flexible polymers.
We find it intriguing to note that these advantages may be exploited for facilitated diffusion inside the spherical nuclei of eukaryotic cells such as yeast, where an enrichment in local gene activity is thought to correlate with an enhanced chromatin flexibility~\cite{jcb}. Finally, we hope that our results may stimulate {\it in vitro} single molecule experiments on facilitated diffusion of proteins on DNA molecules of different contour lengths and under different confining geometries.

\section{Acknowledgements}
The work was carried out under the HPC-EUROPA2 project (project number: 228398) with the support of the European Commission - Capacities Area - Research Infrastructures.

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Bankruptcy and Financial Distress Litigation Clients have retained Cornerstone Research in matters involving fraudulent conveyance and preferential transfer, valuation of distressed firms and their securities and assets, securities fraud, ERISA, lender and auditor liability, change of control, and piercing the corporate veil, among other complex topics.
We work with a broad network of testifying experts, including prominent faculty and industry practitioners, in a distinctive collaboration. Our staff consultants contribute expertise in economics, finance, accounting, and marketing, as well as business acumen, familiarity with the litigation process, and a commitment to produce outstanding results.


Fight, also known as Fight: A Stikfas Film, is an award-nominated 2007 action film by Errol Elumir. It follows the story of a woman martial artist who fights off several opponents. It was made with Stikfas figurines and not any type of construction toy. While it is not technically a brickfilm (though LEGO baseplates do appear), it was nominated for several Brick Award for Film Arts awards.
The Lady wakes up suddenly. She is in the middle of a black voice, standing atop large gray baseplates. As she moves about, more baseplates fold upward to expand the area. Two opponents, Green and Red, jump down from above. Green and Red rush the Lady, who fights them off expertly. Lady punches Green off the edge of the area, and shortly kicks off Red as well.
Suddenly, the Lady is surrounded by more Red and Green opponents. She fights them all off. Finally, a black ninja appears, rushing at the Lady with a sword. The Lady detaches her hair and smacks the ninja out cold.


text:
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text:
Refuse/Resist é o quarto single da banda brasileira de heavy metal Sepultura, foi lançada em 1993 e também está presente no álbum Chaos A.D., cujo também foi lançado em 1993.

Singles de 1993

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Careers | Air Control Mechanical Contracting, Inc.
Air Control Mechanical Contracting, Inc.
Please email or fax your resume to pdamato@acmci.com along with the info below.
Copyright © Air Control Mechanical Contracting, Inc.


text:
Q: A is a square matrix and given that $A^3 = 2\mathbb{I}$, then show $A-\mathbb{I}$ is invertible and find its inverse Could anyone guide along with this question?
I was trying $(A−I)(A−I)^{−1} = I$ and was figuring if there's a way out to expand $(A−I)^{−1}$. I also tried $(A−I)x=0$ but to no avail.

A: For excercises like this it is always a good idea to start with the classical expansions. In this case: $$
A^3-I=(A-I)(A^2+A+I)
$$
We can then write: $$
(A-I)(A^2+A+I)=A^3-I=2I-I=I
$$
By comparison with $(A-I)(A-I)^{-1}=I$ we can find that $$
(A-I)^{-1}=(A^2+A+I)
$$

A: See from the relation you have given.
$f (x)=x^3-2$ is a polynomial that annihilates the operator.hence the minimal polynomial must divide this polynomial .and hence as you can see that the eigenvalues are.cube root of 2....i hope this hepls...proceed on these lines

A: Of course, in this case, we can just immediately see the inverse after using the factorization of $x^3-1$.
But I think it is good to know the general method:
Let $A$ be a matrix with $f(A)=0$ for some polynomial $f$ and $g$ some other polynomial, which is co-prime to $f$. The euclidean algorithm (so you actually have a general method at hand to compute it!) yields polynomials $a,b$ with
$$af+bg=1,$$
hence we have $$\mathbb I=a(A)f(A)+b(A)g(A)=b(A)g(A).$$
We have shown: $g(A)$ is invertible and the inverse is $b(A)$.

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Just getting back from Milwaukee, Wisconsin where I grew up, and still have family. The colors of the season there were maize, grey, and blue, and happened to perfectly match the palette of my collection lately.
We're jumping right in for some great holiday markets starting this weekend. 1 on the west side of LA, and 1 on the east side. Truly hope to see you at one of these. We'll be selling festive treats such as dip dyed napkins and hand towel sets, one of a kind silk scarves, and holiday dresses.
The Westside Holiday Market at UCLA's Fowler Museum event Sunday Dec 6th will have California made goods, and organic Spanish inspired food and coffee. So excited for this beautiful venue.
Both events have easy street, or lot parking.
If you're reading this from outside of Los Angeles, check the webstore for recent additions. And more to come in the next week.
My career took a turn in September, when a former professor asked me to teach fashion at Woodbury University in Burbank. Design, trend forecasting, merchandising, storytelling through imagery, and illustration were all part of this class called LA Fashion. I had no idea what I was getting into! It's been a rad journey to be on the other side of instruction....since I tend to see myself as the student. Working with LA's future fashion designers has been a challenging, rewarding, eye opening experience. Many thanks to the mentors that coached me.


For the past year I have had these how to make cheesecloth ghosts appearing on my Pinterest feed. I won't lie, they are pretty awesome. Plus they are very easy to make which means even little ones can get involved.
Make sure that you follow my Halloween board on Pinterest for more ideas. Don't forget to save the pin for later.
* We used hard cotton balls from Hobby craft, but you could just use a scrunched up bit of tin foil.
To start with you will need to make a frame for your ghost. Place your ball on top of the kebab stick and attach some arms. We cut a straw up and taped them onto the kebab stick. If you have pipe cleaners they would probably be easier to use as you simple wrap them around rather than tape them on.
It will take a few hours for your ghost to fully dry; therefore you will need somewhere to put your frame. We stuck ours into pots of play doh to keep them upright.
In a bowl mix together some water and PVA glue.
Next cut some cheesecloth and stick it in your glue mix. Squeeze any excess glue out and place it over your frame. Make sure that your get the fabric in the position that you want.
After a few hours your ghost should have completely hardened.
Carefully peel it off of the frame.
Finally add some thread to the top of the ghost and then hang it up somewhere for a truly awesome Halloween decoration.
EC made a wonderful observation that the finished product actually looked rather like a Dementor from Harry Potter! Of course after such a fabulous idea I had to give it a go and make one for him.
All you need to do is add a little bit of black paint to the glue and water mix. To make it a bit more realistic I added a couple of layers of cheesecloth to it rather than just one. The finished product is actually rather scary. They are perfect for any Harry Potter themed party.
My Dementor with our Harry Potter themed pumpkins.
If you liked this how to make cheesecloth ghosts decoration be sure to check out my ghost leaves and hanging bats.
10 Halloween Inspired Pieces You Can Wear Everyday!


text:
About Us, Our Mission and Belief
NAMI BI – Board of Directors
Half Year Report, July – November 2018
Annual Report 2017- 2018
Mental Health, Mental Illness, on Block Island
bringing services and support for those who are ill and education for mental health to all on Block Island
BI Wellness
Be Well Block Island
Videos/Articles
Letters on the Opioid Crisis
The National Alliance on Mental Illness, Block Island
NAMI Block Island is a 501c3 organization affiliated with NAMI Rhode Island and NAMI, the National Alliance on Mental Illness, the nation's largest grassroots mental health organization dedicated to building better lives for the millions of Americans affected by mental illness.
Mission Statement: NAMI BLOCK ISLAND is a nonprofit organization whose purposes are to bring mental health services to the island, to educate the public about mental illness in order to reduce stigma, and to provide support for families of persons with mental illness.
Our vision has three strands: advocacy for services on-island; education; and support for friends and families.
We are a non-profit organization whose purposes are to bring mental health services to the island, to educate the public about mental illness in order to reduce stigma, and to provide support for families with mental illness. NAMI Block Island is now able to provide programs for islanders, and donations can be tax deductible.
We believe in Recovery as well as in support.
Recovery is a Journey
It may not mean returning to the same life as before the onset of a mental illness. However, with services tailored to their needs, many people can significantly reduce the impact of their illness and live satisfying lives. Recovery is a process. It needs patience.
One of the biggest impediments to recovery, wellness and return to a working world is social STIGMA, hence our programs to offer information and a forum for sharing experience.
We look forward to a day when openness replaces shame and secrecy, when the signs of illness are seen with sympathy. This is doubly important as with effective and timely care, relapses can often be prevented.
Bylaws governing our non-profit status and affiliation to NAMI can be seen here.
All are welcome to attend Board meetings, Contact any member of the Board of Directors to get the time and place of the next meeting.
Any comments about this page - you can tell us here Cancel reply
Do you want to another language??
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Unresolved Endings – Shutter Island Barney's Version
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1.1 ABSTRACT
In this essay, I will focus on the relationship between empathy and reader's choice of ending. In order to do this I have chosen two narrative texts – Mordecai Richler's Barney's Version (1997) and Dennis Lehane's Shutter Island (2003), both of which have open endings. "The most commonly nominated feature of narrative fiction to be associated with empathy is character identification" (Keen 2006: 214) and so in this essay the word 'empathy' is used in the context of empathy for fictional characters within the text.
The two novels used in this case deal with Alzheimer's disease and Schizophrenia as being central to the plot, thus introducing empathy for the character. Since these are disclosed only towards the end I will analyse whether empathy for the character undergoes any strong change and whether or not this affects the reader's choice of ending.
Since empathy is an emotional process and has no linguistic marker, I have chosen extracts[1] that struck me as triggers for empathy and labelled them 'implicit markers'. I have also mentioned how the film adaptations of these narrative texts influence the reader. Owing to the word limit I have included only what I have thought relevant and important to my analysis of empathy in resolving the ending.
1.2 EMPATHISING WITH THE UNRELIABLE PROTAGONIST
Narrative theorists and critics have pointed out a set of narrative techniques like "first person narration and the interior representation of characters' consciousness and emotional states – as devices supporting character identification" (Keen 2006:213). These narrative techniques are said to create empathetic responses and experiences. While Barney's Version is a first person narrative dealing with the emotional states of characters and their consciousness, Shutter Island, though a third person narrative, also deals with emotional states and character consciousness. What brings the reader closer to both the narrative texts is that they are written in the form of an autobiography and a journal respectively. Lodge acknowledges the view that by modelling a narrative text on "the discourse of personal witness: the confession, the diary, the autobiography, the memoir, the disposition", it creates "an illusion of reality" (Lodge 2002).
Character identification is seen as a form of empathy that occurs in the reader as a consequence of reading (Keen 2006). In the present case, the reader might begin to empathise further (or identify) with the character of Barney Panofsky only after he is diagnosed with Alzheimer's disease. Keen suggests that this is likely because negative situations (death, pain, suffering, and illness) evoke empathy more readily in a reader as opposed to positive situations (achievement, success, joy) (Keen 2006).
Barney's Version is Barney's attempt to reflect on the various aspects of his way of life – his innermost insecurities, failures, the humiliations and also his vanities. As we enter Barney's world, the reader very often encounters Barney's creation of a "galaxy of ebullient, perverse, and obsessed characters, all of whom are portrayed as posing an imminent threat to his shady and irreverent personality" (Branko, 1999:149). The reader also learns the possibility that Barney drove his first wife to commit suicide. Up until the diagnosis in the novel, we feel no strong sense of empathy[2] towards Barney except of course when he talks of Miriam, his third wife and the only one he truly ever loved. "Miriam Miriam, my heart's desire" (Barney's Version 1997: 19), this sentence reoccurs in the novel every time Barney talks of his third wife. Barney seems indifferent to everyone in his life except to his children and his third wife, Miriam (Brzezinski, 1999: 105). The novel is divided into three parts – the three Panofsky wives. Miriam is his third wife and hence rightly belongs to the last part of the novel; nevertheless, she appears constantly throughout the novel. Despite how despicable Barney seems through most of the book, he can be hysterical, but the love he has for Miriam and his children breathes a little kindness into his character. Barney has only loved Miriam truly and this seems rather obvious to the reader because the reader is able to contrast his feelings for Miriam with that of his other wives.
The fictional autobiography ends on a cheerless note, where Barney picks up the phone to call Miriam but realises he can't remember her number. Throughout the novel we see and feel Barney's love for Miriam, and to a reader that empathises with those feelings, this can be quite anguishing. In the afterword written by his son, Mike, you learn more about Barney post diagnosis. Owing to the narrative situation, wherein Barney knows that the disease is going to eat him wholly very soon he decides to tie the loose ends of his life.
Twenty-five thousand dollars for Benoit O'Neil, who had been caretaker of the cottage in the Laurentians for years.
The estate was obliged to settle John Hughes-McNoughton's monthly bar bill at Dink's for as long as he lived.
There was also a surprise, considering how often our father joked about schvartzes, a two-hundred-thousand dollar trust fund was to be set up to establish a scholarship at McGill University for a black student who excelled in arts; the aforesaid scholarship in memory of Ismail Ben Yussef aka. Cedric Richardson, who had died of cancer on November 18, 1995.
[Barney's Version 1997: 399]
He was to be buried, as he had already arranged, in the Protestant cemetery at the foot of Mont Groulx, but there should be a Star of David on his stone, and the adjoining plot had been reserved for Miriam.
These extracts that appear in the afterword written by Mike, paint a very different picture of Barney and strikes me as an implicit marker for empathy. "When you are facing the end, everything that's not real is stripped away. You're the most real you'll ever be, more real than you have ever been before". ( Schels and Lakotta 2007). This is a common belief and can be seen even in Barney's Version. Barney's dislike for Cedric Richardson and his mocking of schvartzesis very evident throughout the novel and yet he decides to set up a two-hundred-thousand dollar trust fund dedicated to Cedric.
His gestures, as seen in the above extracts, evoke a strong sense of empathy, especially character empathy. My hypothesis is that if the reader does not in fact empathise with Barney during the course of the story, he/she most certainly does when Barney is diagnosed and more so, when he/she learns about Barney in the afterword narrated by Mike.This kind of character empathy evokes a certain level of reader involvement.
Also crucial to the story is the disappearance of Barney's friend Boogie. Barney's second wife is caught having an affair with his friend, Boogie, at their cottage. The second Mrs Panofsky drives away in rage leaving Barney and Boogie arguing over the issue. In the course of this argument Barney threatens to kill Boogie with his gun. Boogie disregards the threat and insists on going for a swim over Barney's warning that he is too drunk to swim. Boogie ignores Barney's plea and proceeds towards the lake and never returns.
During his interrogation, when inspector O'Hearne asks him about Boogie, sarcastically, Barney tells him that he shot Boogie through the heart. This is used as Barney's acceptance of murder and following this he is also arrested and convicted for murder but later acquitted as no body is found (though many people remain convinced of his guilt).
"Did you really murder that guy all those years ago?
I think not, but some days I'm not so sure. No, I didn't. I couldn't have."
As readers we are led to believe that Barney has murdered Boogie. Barney playfully fires a warning shot over Boogie's head and the last we see of Boogie in the novel is him tumbling into the water. His explanation to O'Hearne coupled with the above example leaves the reader with little choice but to believe that Barney has murdered his friend. The murder has a motive – Barney's second wife is having an affair with Boogie but what we also know is that Barney was never in love with the second Mrs Panofsky and that since the night of his wedding to her (the first time he met Miriam), he has been in love with Miriam and has been wanting to divorce his wife and marry Miriam. In his conversation with Boogie after the incident at the cottage he asks Boogie to be his co-respondent for the divorce. It can be gathered that though he had a motive, it did not mean much because he was never in love with the second Mrs Panofsky and in fact he was happy she was having an affair because that alluded to an effortless divorce. In spite of all this the narrator's unreliability as seen in example 1 does not help the reader to make a decision.
The mystery behind Boogie's death is given a plausible ending in the novel. Mike, in the final page, while in the porch of Barney's cottage, sees a water bomber lowering on to the lake, scooping gallons of water and dumping it on the mountain. It is left to the readers to fill the gap and choose what we believe to be the cause of Boogie's death (Gavins 2007; Emmott 1998; Ryan 1998; Gerrig and Rapp 2004).
Owing to the third person narration in Dennis Lehane's novel, the reader is not invited to form a close relationship with the main character as in the case of Barney's Version, which is a first person narrative but nonetheless it does not affect the empathetic experience because of the content and situation that the novel poses to the reader(Keen 2006).As the text progresses the reader empathises with the characters for several reasons. To begin with, his love for his wife, Dolores Chanal, who he believes died in a fire. He dreamed of her repeatedly and every little object would somehow trigger a memory of her.
"Dolores had been dead for two years, but she came to life at night in his dreams, and he sometimes went full minutes into a new morning thinking she was out in the kitchen or taking her coffee on the front stoop of their apartment on Buttonwood. This was a cruel trick of the mind, yes, but Teddy had long ago accepted the logic of it – waking after all was an almost natal state. You surfaced without a history, then spent the blinks and yawns reassembling the past, shuffling the shards into chronological order before fortifying yourself for the present."
[Shutter Island 2003: 36]
This extract strikes me as an implicit marker for empathy not only because of the content but also because of the language that is used. There is a connection between language and emotions and as the story progresses you empathise more owing to the situation we believe Teddy is caught up in and the language that is used to explain it (Kovecses 1990). Readers identify with Teddy's fear and wish for Teddy to escape from the island. When we reach the final chapter we encounter the plot twist that goes completely against reader expectation.
The reader feels as though he/she is caught in a web of deceit, not knowing whom to believe. If the reader empathises with the character of Teddy, he/she wishes that Teddy is not a patient and as per his claims in the narrative text, he is speaking the truth. The reader hopes that everyone else around Teddy is lying. Similar to the situation in Barney's Version, our choice of reality depends on how much we empathise with the character of Teddy. As the novel moves ahead from this point, the reader is left with no choice but to believe that Teddy is indeed a patient at Shutter Island. At this moment the reader almost feels as though the rug has been pulled from under their feet. On my reading of the novel, I continued hoping that Teddy's fictional reality was the true reality.
The narrative technique is such that throughout the novel, you proceed with the main character on his journey thus being persuaded to believe his thoughts and views only. Since the story world is that of mental illnesses, the reader not only revels in the horror but also empathises with the disturbed characters. When at the end of the novel, it is revealed that Teddy is himself a patient at Shutter Island, the reader empathises with him further. Alan Palmer's "theory of mind" can be used to understand Teddy's frame of mind (Palmer 2004). Rachael Solando, the missing patient according to Teddy is purely fictitious. What is really interesting here is how at the end of the novel we learn that Rachel Solando is in fact his wife Dolores Chanal. Through the novel we see how he feels about the patient Rachel Solando, which only goes to show us how he really feels about the his wife, Dolores Chanal. All these serve as implicit markers embedded within the text for character empathy – a reader is moved by Teddy's present state of affairs, his love for his wife, the need to create a fictitious life in order to escape reality, and of course the recurrent dreams.
The novel after what is called its 'plot twist' further leaves the reader with an unresolved end. The reader is previously warned about Andrew/Teddy's mental health and the doctors' failed attempts to cure him.
"It's been decided that if we can't bring you back to sanity – now, right now – permanent measures will be taken to make sure you never hurt anyone again. Do you understand what I'm saying to you?"
[Shutter Island 2003: 371]
The readers' expectation at this point is that Teddy is brought back to sanity for the reader is aware that if this is not the case, Teddy will have to undergo a lobotomy. It seems to the reader that Teddy has accepted the reality because when he is examined by Dr Cawley, Teddy accepts that he is in fact Andrew Laeddis and that he invented this story as way of escaping from reality (the truth).
1.3 CONCLUSION – AN EXTENSION OF MY STUDY
In this essay I have tried to elucidate the fact that empathy plays a vital function in trying to reach a conclusive end. This essay is an analysis based on my experience of reading both, Mordecai Richler's Barney's Version and Dennis Lehane's Shutter Island. Based on their research, Gerrig and Rapp in their 'Psychological processes underlying literary impact' have mentioned that readers assimilate propositions in a way that it has an impact on their judgements and similar to how readers expect what happens, I am convinced that when there is an unresolved issue they tend to incline their belief to what they hope is the truth. This hope is largely governed by empathy.
An empirical study similar to that achieved by Gerrig and Rapp should be carried out to assess and record whether or not there is a pattern between empathy and readers' expectation and whether or not this pattern influences the final choice of endings. The hypothesis is that it does and this can be further influenced by the film adaptations. Both the movie adaptations of these narrative texts seem to incline towards a definite ending.
Additionally an empirical study recording readers' choice of endings can be studied and a pattern can be drawn between choice of endings and character empathy. Further, the extracts that I have labelled implicit markers of empathy can be excluded from the text and a different set of readers can be asked to read the edited narrative text and their results can be studied. If it is that the readers who have read the edited version are void of empathy towards the main character resulting in them choosing the alternate endings, it can be concluded that character empathy does play a key role in resolving endings.
Based on the film adaptations, a third empirical study can be effectuated where readers are divided into two groups – one group containing readers who have only read the book and the other containing readers who have read the book and watched the movie. Through this it seems likely that we can study whether or not film adaptations influence readers when deciding on a culmination.
Branko, G. (1999), Barney's Version. World Literature Today (73:1) pp 149.
Brzezinski, S. Antioch Review (57:1) Winter 1999, 104-105.
Emmott, C. (2003b), 'Reading for pleasure: A Cognitive Poetic Analysis of "Twists in the Tale" and Other Plot Reversals in Narrative Texts', in J. Gavins and G. Steen (eds) (2003), Cognitive Poetics in Practice, London: Routledge, pp 145-59.
Gavins, J. (2007), Text World Theory: An Introduction. Edinburgh: Edinburgh University Press.
Gerrig, R. (1993), Experiencing Narrative Worlds: On the Psychological Activities of Reading, New Haven and London: Yale University Press.
Gerrig, R and Rapp, D. (2004), Psychological Processes Underlying Literary Impact. Poetics Today, 25(2): 265-281.
Keen, S. (2006), A Theory of Narrative Empathy. Narrative, 14(3): 207-236.
Keen, S. (2007), Empathy and the Novel. pp. xxix, 242 pp.
Kovecses, Z. (1990), Emotion Concepts, New York: Springer.
Kuiken, D. Miall, D, and Sikora, S. (2004), Forms of Self Implication in Literary Reading. Poetics Today, 25(2): 171-203.
Lehane, D. (2010), Shutter Island, United States: William Morrow.
Lodge, D. (2002), Consciousness & the Novel: Connected Essays, pp. xii, 320 pp.
Miall, D, Kuiken, D. (2002), 'A Feeling for Fiction: Becoming what we Behold', Poetics 30: 221-41.
Oatley, K. (1995), A Taxonomy of the Emotions of Literary Response and a Theory of Identification in Fictional Narrative.Poetics :Journal for Empirical Research on Literature, the Media and the Arts, 23(1-2): 53-74.
Palmer, A. (2004), Fictional Minds, pp. vi, 275 pp.
Richler, M. (1998), Barney's Version, London : Vintage.
Ryan, M. (1998), 'The Text as World versus Text as Game: Possible World Semantics and Postmodern Theory', Journal of Literary Semantics 27(3): 137-63.
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