Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erd\H{o}s-R\'enyi (ER) networks in detail. Depending on the degree distribution exponent ($\gamma$) of SF networks and phase-frustration parameter, the population undergoes from first order transition (explosive synchronization (ES)) to second order transition and vice versa. In ER networks transition is always second order irrespective of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self consistent equations considering the vanishing order parameter limit.Comment: 8 pages, 6 figure

Structural Basis for Rab8a Recruitment of RILPL2 via LRRK2 Phosphorylation of Switch 2

Rab8a is associated with the dynamic regulation of membrane protrusions in polarized cells. Rab8a is one of several Rab GTPases that are substrates of leucine-rich repeat kinase 2 (LRRK2), a serine/threonine kinase that is linked to Parkinson's disease. Rab8a is phosphorylated at T72 (pT72) in its switch 2 helix and recruits the phospho-specific effector RILPL2, which subsequently regulates ciliogenesis. Here, we report the crystal structure of phospho-Rab8a (pRab8a) in complex with the RH2 (RILP homology) domain of RILPL2. The complex is a heterotetramer with RILPL2 forming a central α-helical dimer that bridges two pRab8a molecules. The N termini of the α helices cross over, forming an X-shaped cap (X-cap) that orients Arg residues from RILPL2 toward pT72. X-cap residues critical for pRab8a binding are conserved in JIP3 and JIP4, which also interact with LRRK2-phosphorylated Rab10. We propose a general mode of recognition for phosphorylated Rab GTPases by this family of phospho-specific effectors.</p

Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation

We investigate transition to synchronization in Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage ($f$) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution namely Lorenz distribution. The effects of variation of $f$ and phase frustration parameter $\alpha$ on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength ($\lambda_c$) and group angular velocity ($\Omega_c$) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation we considered SK model on scale-free as well as Erd\H{o}s-R\'{e}nyi (ER) networks. Interestingly explosive synchronization (ES) has been observed in both the networks for different ranges of values of $\alpha$ and $f$. For scale-free networks, as the value of $f$ is set within $10\% \leq f \leq 70\%$, the range of the values of $\alpha$ for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case. On the other hand, for random networks, ES observed in a narrow window of $\alpha$ when the value of $f$ is taken within $30\% \leq f \leq 50\%$. In all the cases critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results.Comment: 7 pages, 5 figure

Perfect synchronization in networks of phase-frustrated oscillators

Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we show, constructively, how to strategically select the optimal frequency set, capturing the natural frequencies of all oscillators, for a given network and phase-lags, that will ensure perfect synchronization. We find that high levels of synchronization are sustained in the vicinity of the optimal set, allowing for some level of deviation in the frequencies without significant degradation of synchronization. Demonstrating our results on first and second order phase-frustrated Kuramoto dynamics, we implement them on both model and real power grid networks, showing how to achieve synchronization in a phase frustrated environment.Comment: To appear in Europhysics Letters, 7 pages, supplementary informatio

Transition to synchronization in adaptive Sakaguchi-Kuramoto model with higher-order interactions

We investigate the phenomenon of transition to synchronization in Sakaguchi-Kuramoto model in the presence of higher-order interactions and global order parameter adaptation. The investigation is done by performing extensive numerical simulations and low dimensional modeling of the system. Numerical simulations of the full system show both continuous (second order) as well as discontinuous transitions. The discontinuous transitions can either be associated with explosive (first order) or with tiered synchronization states depending on the choice of parameters. To develop an in depth understanding of the transition scenario in the parameter space we derive a reduced order model (ROM) using the Ott-Antonsen ansatz, the results of which closely matches with that of the numerical simulations of the full system. The simplicity and analytical accessibility of the ROM helps to conveniently unfold the transition scenario in the system having complex dependence on the parameters. Simultaneous analysis of the full system and the ROM clearly identifies the regions of the parameter space exhibiting different types of transitions. It is observed that the second order continuous transition is connected with a supercritical pitchfork bifurcation (PB) of the ROM. On the other hand, the discontinuous teired transition is associated with multiple saddle-node (SN) bifurcations along with a supercritical PB and the first order explosive transition involves a subcritical PB alongside a SN bifurcation.Comment: 11 pages, 11 figure

Emergent dynamics in delayed attractive-repulsively coupled networks

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory states (OS) we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states (IHSS) from the homogeneous steady state (HSS) sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state i.e. OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS) and (3) Emergence of OD state from oscillatory state (OS) without passing through AD i.e. OS-OD. The dynamics of each node in the network is assumed to be governed either by identical limit cycle Stuart-Landau system or by chaotic Rossler system. Based on clustering behavior observed in oscillatory network we derive a reduced low-dimensional model of the large network. Using the reduced model, we investigate the effect of time delay on these transitions and demarcate OS, AD and OD regimes in the parameter space. We also explore and characterize the bifurcation transitions present in both systems. The generic behavior of the low dimensional model and full network are found to match satisfactorily.Comment: Accepted for publication in Chao

Potential Role of Brain-Derived Neurotrophic Factor and Dopamine Receptor D2 Gene Variants as Modifiers for the Susceptibility and Clinical Course of Wilson's Disease

Wilson's disease (WD), an inborn error of copper metabolism caused by mutations in the ATPase copper transporting beta (ATP7B) gene, manifests variable age of onset and different degrees of hepatic and neurological disturbances. This complex phenotypical outcome of a classical monogenic disease can possibly be explained by modifier loci regulating the clinical course of the disease. The brain-derived neurotropic factor (BDNF), critical for the survival, morphogenesis, and plasticity of the neurons, and the dopamine receptor D2 (DRD2), one of the most abundant dopamine receptors in the brain, have been highlighted in the pathophysiology of various neuropsychiatric diseases. This study aims to identify the potential association between BDNF and DRD2 gene polymorphisms and WD and its clinical characteristics. A total of 164 WD patients and 270 controls from India were included in this study. Two BDNF polymorphisms [p.Val66Met (c.G196A) and c.C270T] and the DRD2 Taq1A (A2/A1 or C/T) polymorphism were examined for their association with WD and some of its clinical attributes, using polymerase chain reaction, restriction fragment length digestion, and bidirectional sequencing. The C allele and CC genotype of BDNF C270T were significantly overrepresented among controls compared to WD patients. In addition, a significantly higher proportion of the allele coding for Val and the corresponding homozygous genotype of BDNF Val66Met polymorphism was found among WD patients with age of onset later than 10 years. Furthermore, the A1A1 genotype of DRD2 Taq1A polymorphism was significantly more common among WD patients with rigidity. Our data suggest that both BDNF and DRD2 may act as potential modifiers of WD phenotype in the Indian context.</p

Deciphering the LRRK code: LRRK1 and LRRK2 phosphorylate distinct Rab proteins and are regulated by diverse mechanisms

Autosomal dominant mutations in LRRK2 that enhance kinase activity cause Parkinson s disease. LRRK2 phosphorylates a subset of Rab GTPases including Rab8A and Rab10 within its effector binding motif. Here, we explore whether LRRK1, a less studied homolog of LRRK2 that regulates growth factor receptor trafficking and osteoclast biology might also phosphorylate Rab proteins. Using mass spectrometry, we found that in LRRK1 knock-out cells, phosphorylation of Rab7A at Ser72 was most impacted. This residue lies at the equivalent site targeted by LRRK2 on Rab8A and Rab10. Accordingly, recombinant LRRK1 efficiently phosphorylated Rab7A at Ser72, but not Rab8A or Rab10. Employing a novel phospho-specific antibody, we found that phorbol ester stimulation of mouse embryonic fibroblasts markedly enhanced phosphorylation of Rab7A at Ser72 via LRRK1. We identify two LRRK1 mutations (K746G and I1412T), equivalent to the LRRK2 R1441G and I2020T Parkinson s mutations, that enhance LRRK1 mediated phosphorylation of Rab7A. We demonstrate that two regulators of LRRK2 namely Rab29 and VPS35 [D620N], do not influence LRRK1. Widely used LRRK2 inhibitors do not inhibit LRRK1, but we identify a promiscuous inhibitor termed GZD-824 that inhibits both LRRK1 and LRRK2. The PPM1H Rab phosphatase when overexpressed dephosphorylates Rab7A. Finally, the interaction of Rab7A with its effector RILP is not affected by LRRK1 phosphorylation and we observe that maximal stimulation of the TBK1 or PINK1 pathway does not elevate Rab7A phosphorylation. Altogether, these findings reinforce the idea that the LRRK enzymes have evolved as major regulators of Rab biology with distinct substrate specificity.</p