Circadian oscillations are generated by the purified cyanobacterial clock proteins, KaiA, KaiB, and KaiC, through rhythmic interactions that depend on multisite phosphorylation of KaiC. However, the mechanisms that allow these phosphorylation reactions to robustly control the timing of oscillations over a range of protein stoichiometries are not clear. We show that when KaiC hexamers consist of a mixture of differentially phosphorylated subunits, the two phosphorylation sites have opposing effects on the ability of each hexamer to bind to the negative regulator KaiB. We likewise show that the ability of the positive regulator KaiA to act on KaiC depends on the phosphorylation state of the hexamer and that KaiA and KaiB recognize alternative allosteric states of the KaiC ring. Using mathematical models with kinetic parameters taken from experimental data, we find that antagonism of the two KaiC phosphorylation sites generates an ultrasensitive switch in negative feedback strength necessary for stable circadian oscillations over a range of component concentrations. Similar strategies based on opposing modifications may be used to support robustness in other timing systems and in cellular signaling more generally.circadian rhythms | allostery | mathematical modeling C ircadian clocks are biological timing systems that allow organisms to anticipate and prepare for daily changes in the environment. A hallmark of a circadian oscillator is its ability to drive self-sustained rhythms in gene expression and behavior with a period close to 24 h, even in the absence of environmental cues (1). A general challenge for the biochemical machinery that generates rhythms is to precisely define the duration of the day in the face of perturbations, including fluctuations in the cellular abundance of the molecular components. The importance of maintaining precise circadian timing is underscored by experiments showing that mismatch between the clock period and the rhythms in the external environment results in health problems and fitness defects (2, 3).Although circadian clocks are found across all kingdoms of life, the Kai oscillator from cyanobacteria presents a uniquely powerful model system to study the design principles inherent in the molecular interactions that generate rhythms. A mixture of the purified proteins KaiA, KaiB, and KaiC results in stable oscillations in the phosphorylation state of KaiC in vitro that persist for many days and share many of the properties of circadian clocks in vivo (4-6). In particular, the oscillator can successfully generate near-24-h rhythms over a range of concentrations of the clock proteins both in vivo and in vitro (7-9), so fine-tuning of gene expression is not needed to support a functional clock. Much has been learned about the behavior of the isolated Kai proteins, including the determination of high-resolution crystal structures of all three components (10-12). A critical challenge that remains is to understand how the properties of the Kai proteins are integrated together in the full...

While the link between amyloid β (Aβ) accumulation and synaptic degradation in Alzheimer's disease (AD) is known, the consequences of this pathology on population coding remain unknown. We found that the entropy, a measure of the diversity of network firing patterns, was lower in the dorsal CA1 region in the APP/PS1 mouse model of Aβ pathology, relative to controls, thereby reducing the population's coding capacity. Our results reveal a network level signature of the deficits Aβ accumulation causes to the computations performed by neural circuits. Alzheimer's disease (AD) is a progressive neurodegenerative disorder associated with cognitive decline that is thought to arise in part from the pathological accumulation of amyloid β (Aβ) plaques 1 throughout the neocortex and hippocampus. Plaques cause a constellation of changes in neural circuits including, but not limited to, degradation of dendritic spines 2 , reductions in synapse density 2,3 , and increases in the intrinsic excitability of neurons 3. Aβ pathology has been linked to various behavioral and cognitive changes 4,5 ; for example in mouse models, plaque burden correlates with degradation of place fields in the dorsal CA1 (dCA1) subfield of the hippocampus, and is associated with poor performance on spatial memory tasks 4. Such behaviors require the orchestration of activity across large groups of neurons, or ensembles, whose dynamics are governed by the structure of neural circuits 6. However, although Aβ pathology disrupts multiple features of these circuits 2,7,8 , the net effect of these changes on the structure of population activity and the resulting disruptions in neural computation remains unknown. To address this question, we performed electrophysiological recordings in the hippocampus of awake APP/ PS1 mice (model of Aβ pathology 9), where amyloid plaques can be seen at 12 months of age 10 and plaque burden corresponds to poor performance on spatial cognition and memory tasks, such as the T-maze alternation task 4,5. We found a reduction in the pair-wise correlations between neurons in APP/PS1 animals as compared to controls. Additionally, we identified a reduction in the entropy of population activity across a large array of ensemble sizes, suggesting that the coding vocabulary of populations of neurons in the dCA1 region of hippocampus is compromised in this mouse model of amyloid pathology. Materials and Methods Animals. All protocols and procedures were approved by the University Committee on Animal Resources (UCAR) at the University of Rochester and were performed in accordance with the guidelines of the Institutional Animal Care and Use Committee (IACUC) at the University of Rochester. 4 APP/PS1 double transgenic mice and 4 littermate control mice were used in this study. The APP/PS1 mice expressed chimeric mouse/human amyloid precursor protein (Mo/HuApp695swe) 11 and mutant human presenilin-1 (PS1-dE9) 12 under the control of the neuron-specific prion protein promotor element 9. All mice were males aged 11 to 13 months. By this age, amyl...

HIV-associated neurocognitive disorders (HAND) represent an important source of neurologic complications in individuals with HIV. The dynamic, often subclinical, course of HAND has rendered diagnosis, which currently depends on neuropsychometric (NP) evaluation, a challenge for clinicians. Here, we present evidence that functional brain connectivity, derived by large-scale Granger causality (lsGC) analysis of resting-state functional MRI (rs-fMRI) time-series, represents a potential biomarker to address this critical diagnostic need. Brain graph properties were used as features in machine learning tasks to 1) classify individuals as HIV + or HIV − and 2) to predict overall cognitive performance, as assessed by NP scores, in a 22-subject (13 HIV − , 9 HIV +) cohort. Over nearly all seven brain parcellation templates considered, support vector machine (SVM) classifiers based on lsGC-derived brain graph features significantly outperformed those based on conventional Pearson correlation (PC)-derived features (p < 0.05, Bonferroni-corrected). In a second task for which the objective was to predict the overall NP score of each subject, the lsGC-based SVM regressors consistently outperformed the PC-based regressors (p < 0.05, Bonferroni-corrected) on nearly all templates. With the widely used Automated Anatomical Labeling (AAL90) template, it was determined that the brain regions that figured most strongly in *

Visual Abstract

Functional connectivity analysis of functional MRI (fMRI) can represent brain networks and reveal insights into interactions amongst different brain regions. However, most connectivity analysis approaches adopted in practice are linear and non-directional. In this paper, we demonstrate the advantage of a data-driven, directed connectivity analysis approach called Mutual Connectivity Analysis using Local Models (MCA-LM) that approximates connectivity by modeling nonlinear dependencies of signal interaction, over more conventionally used approaches, such as Pearson's and partial correlation, Patel's conditional dependence measures, etcetera. We demonstrate on realistic simulations of fMRI data that, at long sampling intervals, i.e. high repetition time (TR) of fMRI signals, MCA-LM performs better than or comparable to correlation-based methods and Patel's measures. However, at fast image acquisition rates corresponding to low TR, MCA-LM significantly outperforms these methods. This insight is particularly useful in the light of recent advances in fast fMRI acquisition techniques. Methods that can capture the complex dynamics of brain activity, such as MCA-LM, should be adopted to extract as much information as possible from the improved representation. Furthermore, MCA-LM works very well for simulations generated at weak neuronal interaction strengths, and simulations modeling inhibitory and excitatory connections as it disentangles the two opposing effects between pairs of regions/voxels. Additionally, we demonstrate that MCA-LM is capable of capturing meaningful directed connectivity on experimental fMRI data. Such results suggest that it introduces sufficient complexity into modeling fMRI time-series interactions that simple, linear approaches cannot, while being data-driven, computationally practical and easy to use. In conclusion, MCA-LM can provide valuable insights towards better understanding brain activity.