Fendler and Atwal: Systematic deciphering of cancer genome networks 343 “interacting” encompasses chemical, syn- tenic, and indirect regulation of one gene on another via proteins and other factors such as non-coding RNAs. Underlying these analy- ses sits the hope that one could start from genome-wide experiments and let the aggre- gated results inform which genes are inter- acting in a network, not just correlated in a network. The important distinction here is in- teracting versus correlations. Correlations describe only a statistical relationship be- tween genes, returning a statistic that only in- forms from sampling the model distribution, whereas interactions return the model distri- bution itself (Note: we explicitly define in- teractions in the next section). Probabilistic models have thus been designed to build gene networks using, e.g., Bayesian Net- works [33], information-theoretic models [34], deterministic models [35], and sparse- network methods [36,37]. All of these mod- els are, in some way, attempting to construct or help construct a graph, i.e., an abstract construct that connects vertices (often genes) with edges (an interaction between those genes). Each method has its own set of ad- vantages and disadvantages in terms of ac- curacy and computational time, and each method invokes its own set of assumptions about the nature of the interactions [38]. For example, deterministic models commonly referred to as ODEs (ordinary differential equations) explicitly model the interactions in terms of relatively simple equations, with- out noise, but must be fit to a large number of biological parameters that are often un- known. Information-theoretic models, while successful in identifying transcription factors in cancer [39], cannot handle loops in net- works and suffer from noise from indirect in- teractions, which effectively removes information from the system. Bayesian net- works while successful are typically compu- tationally expensive. A Physics Approach … Going Backward Physicists traditionally make sense of natural phenomena by concocting a mathe- matical model while ensuring experimental agreement. For example, magnetic forces may be represented by a mathematical model constructed between particles and can generally be written in terms of energies or interactions between those particles. When dealing with statistical quantities, those in- teractions are put into the framework of the probabilistic model, which defines the prob- ability of being in a particular state. For ex- ample, the probability of being in the state with particle-1 up and particle-2 down, is a function of the interactions between the two particles. Recently, physicists have taken an interest in the inverse-problem, i.e., using experimental data to reverse-engineer the in- teractions typically a priori defined. Thus, back to the geneticist, rather than defining interactions and examining the resultant sta- tistical dynamics of altered gene states, we use the experimental probabilities of being in a particular expression or copy number state, for example, gene-1 deleted and gene- 2 amplified, to determine the interactions between the genes. As shown by Lezon et al. [40], one can take this approach and determine the explicit relationship between gene interactions and statistically measured quantities, such as a Pearson correlation. Fortuitously, the proba- bilistic model parallels the common Spin- Glass or Ising system physicists have investigated for decades. With the analogy that genes are interacting particles, Lezon et al. successfully showed that the gene inter- actions are not equal to the expression co- variance matrix as typically calculated from expression technologies, but equal to the in- verse of the covariance matrix. At first glance, this may be surprising, but these re- sults exemplify the fact that algorithms that supplement statistical correlations for gene interactions are incomplete, otherwise, the gene interactions would be equal to the co- variance matrix. Fortunately, this approach does not suf- fer from indirect correlations as some of the other approaches do, delivers the explicit forces one would typically a priori define between genes from measured data, may infer large interactions between genes even when those genes have low correlations [41], and it can be vastly improved upon through the use of dimension reduction al-