Cusp bifurcation in a metastatic regulatory network.

Understanding the potential for cancers to metastasize is still relatively unknown. While many predictive methods may use deep learning or stochastic processes, we highlight a long standing mathematical concept that may be useful for modeling metastatic breast cancer systems. Ordinary differential equations (ODEs) can model cell state transitions by considering the pertinent environmental variables as well as the paths systems take over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. Many studies have applied concepts in one-parameter bifurcation theory to model biological network dynamics, and cell division. However, studies of two-parameter bifurcations are much more rare. Two-parameter bifurcations have not been studied in metastatic systems. Here we show how a specific two-parameter bifurcation phenomenon called a cusp bifurcation separates two qualitatively different metastatic cell state transitions modalities and propose a new perspective on defining such transitions based on mathematical theory. We hope the observations and verification methods detailed here may help in the understanding of metastatic potential from a basic biological perspective and in clinical settings.

Evolutionary potential of the monkeypox genome arising from interactions with human APOBEC3 enzymes.

APOBEC3, an enzyme subfamily that plays a role in virus restriction by generating mutations at particular DNA motifs or mutational 'hotspots', can drive viral mutagenesis with host-specific preferential hotspot mutations contributing to pathogen variation. While previous analysis of viral genomes from the 2022 Mpox (formerly Monkeypox) disease outbreak has shown a high frequency of C>T mutations at TC motifs, suggesting recent mutations are human APOBEC3-mediated, how emerging monkeypox virus (MPXV) strains will evolve as a consequence of APOBEC3-mediated mutations remains unknown. By measuring hotspot under-representation, depletion at synonymous sites, and a combination of the two, we analyzed APOBEC3-driven evolution in human poxvirus genomes, finding varying hotspot under-representation patterns. While the native poxvirus molluscum contagiosum exhibits a signature consistent with extensive coevolution with human APOBEC3, including depletion of TC hotspots, variola virus shows an intermediate effect consistent with ongoing evolution at the time of eradication. MPXV, likely the result of recent zoonosis, showed many genes with more TC hotspots than expected by chance (over-representation) and fewer GC hotspots than expected (under-representation). These results suggest the MPXV genome: (1) may have evolved in a host with a particular APOBEC GC hotspot preference, (2) has inverted terminal repeat (ITR) regions-which may be exposed to APOBEC3 for longer during viral replication-and longer genes likely to evolve faster, and therefore (3) has a heightened potential for future human APOBEC3-meditated evolution as the virus spreads in the human population. Our predictions of MPXV mutational potential can both help guide future vaccine development and identification of putative drug targets and add urgency to the task of containing human Mpox disease transmission and uncovering the ecology of the virus in its reservoir host.

Evolutionary potential of the monkeypox genome arising from interactions with human APOBEC3 enzymes.

APOBEC3, an enzyme subfamily that plays a role in virus restriction by generating mutations at particular DNA motifs or mutational "hotspots," can drive viral mutagenesis with host-specific preferential hotspot mutations contributing to pathogen variation. While previous analysis of viral genomes from the 2022 Mpox (formerly Monkeypox) disease outbreak has shown a high frequency of C>T mutations at T C motifs, suggesting recent mutations are human APOBEC3-mediated, how emerging monkeypox virus (MPXV) strains will evolve as a consequence of APOBEC3-mediated mutations remains unknown. By measuring hotspot under-representation, depletion at synonymous sites, and a combination of the two, we analyzed APOBEC3-driven evolution in human poxvirus genomes, finding varying hotspot under-representation patterns. While the native poxvirus molluscum contagiosum exhibits a signature consistent with extensive coevolution with human APOBEC3, including depletion of T C hotspots, variola virus shows an intermediate effect consistent with ongoing evolution at the time of eradication. MPXV, likely the result of recent zoonosis, showed many genes with more T C hotspots than expected by chance (over-representation) and fewer G C hotspots than expected (under-representation). These results suggest the MPXV genome: 1) may have evolved in a host with a particular APOBEC G C hotspot preference, 2) has inverted terminal repeat (ITR) regions -which may be exposed to APOBEC3 for longer during viral replication- and longer genes likely to evolve faster, and therefore 3) has a heightened potential for future human APOBEC3-meditated evolution as the virus spreads in the human population. Our predictions of MPXV mutational potential can both help guide future vaccine development and identification of putative drug targets and add urgency to the task of containing human Mpox disease transmission and uncovering the ecology of the virus in its reservoir host.