Tatonetti Lab at Columbia University Medical Center

Adapted mean first passage time (MFPT)

Measurement of the proximity of node $i$ to node $j$

$$S_{j}=\dfrac {\dfrac {\sum\limits_{i\not \subset C}\big \langle T_{ij}\big \rangle }{\left| C'\right| }-\dfrac {\sum\limits_{i\subset C}\big \langle T_{ij}\big \rangle }{\left| C\right| }}{\dfrac {\sum\limits_{i}\big \langle T_{ij}\big \rangle }{\left| C\right| +\left| C'\right| }}$$

where $T_{ij}$ refers to the average number of steps a random walker takes to reach node $j$ beginning at node $i$.

Adapted betweenness centrality (BC)

Measurement of the fraction of shortest paths containing a node of interest $j$.

$$S_{j}=\dfrac {\dfrac {\sum\limits_{s\subset C}\dfrac {\sigma \left( s,t\mid j\right) }{\sigma \left( s,t\right) }}{\left( \left| C\right| -\mathbb1_C \begin{cases}1 \textrm{ if } j\subset C \\0 \textrm{ if } j\not \subset C\end{cases} \right) }-\dfrac {\sum\limits_{s\not \subset C}\dfrac {\sigma \left( s,t\mid j\right) }{\sigma \left( s,t\right) }}{\left( \left| C'\right| -\mathbb1_{C'} \begin{cases}0 \textrm{ if } j\subset C \\1 \textrm{ if } j\not \subset C\end{cases} \right) }}{\dfrac {\sum\limits_{s}\dfrac {\sigma \left( s,t\mid j\right) }{\sigma \left( s,t\right) }}{\left( \left| C\right| +\left| C'\right| - 1\right) }}$$

where $\sigma\left(s, t\right)$ is the number of shortest paths (smallest number of edges) between $s$ and $t$, and $\sigma \left( s,t\mid j\right)$ is the number of shortest paths between $s$ and $t$ passing through $j$.

Adapted shared neighbors (SN)

Measurement of the fraction of shared adjacent nodes (Tanimoto coefficient, $T_c$) between two nodes of interest

$$S_{j}=\dfrac {\dfrac {\sum\limits_{i\subset C}T_c\left( i,j\right) }{\left| C\right| }-\dfrac {\sum\limits_{i\not \subset C}T_c\left( i,j\right) }{\left| C'\right| }}{\dfrac {\sum\limits_{i}T_c\left( i,j\right) }{\left| C\right| +\left| C'\right| }} =\dfrac {\dfrac {\sum\limits_{i\subset C}\dfrac {\left| n_i \cap n_j\right|}{\left| n_i \cup n_j\right| }}{\left| C\right| }-\dfrac {\sum\limits_{i\not \subset C}\dfrac {\left| n_i \cap n_j\right|}{\left| n_i \cup n_j\right| }}{\left| C'\right| }}{\dfrac {\sum\limits_{i}\dfrac {\left| n_i \cap n_j\right|}{\left| n_i \cup n_j\right| }}{\left| C\right| +\left| C'\right| }}$$

where $n_i\textrm{ = \{neighbors of }i\}$ and $n_j = \{\textrm{neighbors of } j\}$.

Adapted inverse shortest path (ISP)

Measurement of the shortest path length connecting two nodes of interest

$$S_{j}=\dfrac {\dfrac {\sum\limits_{i\subset C}\dfrac {1}{\ell_s\left( i,j\right) }}{\left| C\right| }-\dfrac {\sum\limits_{i\not \subset C}\dfrac {1}{\ell_s\left( i,j\right) }}{\left| C'\right| }}{\dfrac {\sum\limits_{i}\dfrac {1}{\ell_s\left( i,j\right) }}{\left| C\right| +\left| C'\right| }}$$

where $\ell_s\left( i,j\right)$ is the smallest number of edges between $i$ and $j$.

MADSS: Modular Assembly of Drug Safety Subnetworks

Source code available on GitHub.

MADSS (Modular Assembly of Drug Safety Subnetworks) is a network analysis framework that predicts drug safety by scoring every protein in a human protein-protein interaction network (interactome) on its connectivity to a "seed" set of proteins with a genetic link to a phenotype of interest (e.g. disease, adverse drug reaction). Proteins receiving high connectivity scores constitute a neighborhood within the interactome; drugs targeting proteins within this neighborhood are predicted to be involved in mediating the phenotype of interest.

To build these neighborhoods, MADSS uses four adapted pairwise connectivity functions to score every protein in the interactome on its connectivity to the seed set (click for formula):

Each of these functions is adapted to the following formulation:

where C refers to the seed set, C' refers to the complementary set of proteins, and S_j is the metric connectivity score. M_ij represents the pairwise connectivity between protein j and protein i. If M_ij is higher for seeds than non-seeds, then S_j will be positive, and the protein is more connected to the seeds than the rest of the network.

Proteins receiving high connectivity scores thus constitute a subnetwork of the global interactome, which we call a neighborhood. We then assign drugs the connectivity score of their most highly connected target.

Citation

We created and validated MADSS in Lorberbaum, et al., Systems Pharmacology Augments Drug Safety Surveillance. Clinical Pharmacology & Therapeutics (2015) using four clinically relevant adverse events (AEs). We created a model for each of these AEs by training a random forest classifier using the drug connectivity scores as features and a gold standard from a Medication-wide association study as training labels.

Adverse event neighborhood visualizations are available for acute myocardial infarction, upper gastrointestinal bleeding, acute liver failure, and acute kidney failure.