Papers

We introduce the Random Walk Approximation (RWA), a new method to approximate the stationary solution of master equations describing stochastic processes taking place on graphs. Our approximation can be used for all processes governed by non-linear master equations without long-range interactions and with a conserved number of entities, which are typical in biological systems, such as gene regulatory or chemical reaction networks, where no exact solution exists. For linear systems, the RWA becomes the exact result obtained from the maximum entropy principle. The RWA allows having a simple analytical, even though approximated, form of the solution, which is global and easier to deal with than the standard System Size Expansion (SSE). Here, we give some theoretically sufficient conditions for the validity of the RWA and estimate the order of error calculated by the approximation with respect to the number of particles. We compare RWA with SSE for two examples, a toy model and the more realistic dual phosphorylation cycle, governed by the same underlying process. Both approximations are compared with the exact integration of the master equation, showing for the RWA good performances of the same order or better than the SSE, even in regions where sufficient conditions are not met.

Targeted Next Generation Sequencing is a common and powerful approach used in both clinical and research settings. However, at present, a large fraction of the acquired genetic information is not used since pathogenicity cannot be assessed for most variants. Further complicating this scenario is the increasingly frequent description of a poli/oligogenic pattern of inheritance showing the contribution of multiple variants in increasing disease risk. We present an approach in which the entire genetic information provided by target sequencing is transformed into binary data on which we performed statistical, machine learning, and network analyses to extract all valuable information from the entire genetic profile. To test this approach and unbiasedly explore the presence of recurrent genetic patterns, we studied a cohort of 112 patients affected either by genetic Creutzfeldt–Jakob (CJD) disease caused by two mutations in the PRNP gene (p.E200K and p.V210I) with different penetrance or by sporadic Alzheimer disease (sAD).

Unsupervised methods can identify functionally relevant sources of variation in the data, like haplogroups and polymorphisms that do not follow Hardy–Weinberg equilibrium, such as the NOTCH3 rs11670823 (c.3837 + 21 T > A). Supervised classifiers can recognize clinical phenotypes with high accuracy based on the mutational profile of patients. In addition, we found a similar alteration of allele frequencies compared the European population in sporadic patients and in V210I-CJD, a poorly penetrant PRNP mutation, and sAD, suggesting shared oligogenic patterns in different types of dementia. Pathway enrichment and protein–protein interaction network revealed different altered pathways between the two PRNP mutations.

Missense variants are among the most studied genome modifications as disease biomarkers. It has been shown that the “perturbation” of the protein stability upon a missense variant (in terms of absolute ΔΔG value, i.e., |ΔΔG|) has a significant, but not predictive, correlation with the pathogenicity of that variant. However, here we show that this correlation becomes significantly amplified in haploinsufficient genes. Moreover, the enrichment of pathogenic variants increases at the increasing protein stability perturbation value. These findings suggest that protein stability perturbation might be considered as a potential cofactor in diseases associated with haploinsufficient genes reporting missense variants.