Phase response approaches to neural activity models with distributed delay.

In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson-Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks.

Co-targeting MCL-1 and ERK1/2 kinase induces mitochondrial apoptosis in rhabdomyosarcoma cells.

The RAS/MEK/ERK genetic axis is commonly altered in rhabdomyosarcoma (RMS), indicating high activity of downstream effector ERK1/2 kinase. Previously, we have demonstrated that inhibition of the RAS/MEK/ERK signaling pathway in RMS is insufficient to induce cell death due to residual pro-survival MCL-1 activity. Here, we show that the combination of ERK1/2 inhibitor Ulixertinib and MCL-1 inhibitor S63845 is highly synergistic and induces apoptotic cell death in RMS in vitro and in vivo. Importantly, Ulixertinib/S63845 co-treatment suppresses long-term survival of RMS cells, induces rapid caspase activation and caspase-dependent apoptosis. Mechanistically, Ulixertinib-mediated upregulation of BIM and BMF in combination with MCL-1 inhibition by S63845 shifts the balance of BCL-2 proteins towards a pro-apoptotic state resulting in apoptosis induction. A genetic silencing approach reveals that BIM, BMF, BAK and BAX are all required for Ulixertinib/S63845-induced apoptosis. Overexpression of BCL-2 rescues cell death triggered by Ulixertinib/S63845 co-treatment, confirming that combined inhibition of ERK1/2 and MCL-1 effectively induces cell death of RMS cells via the intrinsic mitochondrial apoptotic pathway. Thus, this study is the first to demonstrate the cytotoxic potency of co-inhibition of ERK1/2 and MCL-1 for RMS treatment.