The suprachiasmatic nucleus (SCN) of the hypothalamus is a multioscillator system that drives daily rhythms in mammalian behavior and physiology. Based on recent data implicating vasoactive intestinal polypeptide (VIP) as the key intercellular synchronizing agent, we developed a multicellular SCN model to investigate the effects of cellular heterogeneity and intercellular connectivity on circadian behavior. A 2-dimensional grid was populated with 400 model cells that were heterogeneous with respect to their uncoupled rhythmic behavior (intrinsic and damped pacemakers with a range of oscillation periods) and VIP release characteristics (VIP producers and nonproducers). We constructed small-world network architectures in which local connections between VIP producing cells and their 4 nearest neighbors were augmented with random connections, resulting in long-range coupling across the grid. With only 10% of the total possible connections, the small-world network model was able to produce similar phase synchronization indices as a meanfield model with VIP producing cells connected to all other cells. Partial removal of random connections decreased the synchrony among neurons, the amplitude of VIP and cAMP response element binding protein oscillations, the mean period of intrinsic periods across the population, and the percentage of oscillating cells. These results indicate that small-world connectivity provides the optimal compromise between the number of connections and control of circadian amplitude and synchrony. This model predicts that small decreases in long-range VIP connections in the SCN could have dramatic effects on period and amplitude of daily rhythms, features commonly described with aging. KeywordsSCN; circadian; graph theory; small world; intercellular communication; synchronization; senescence The suprachiasmatic nucleus (SCN) of the hypothalamus is the mammalian circadian pacemaker responsible for the temporal organization of a number of physiological and behavioral rhythms. Circadian rhythmicity is ensured not only by autonomous intracellular mechanisms within individual cells (Reppert and Weaver, 2002) but also by intercellular communication that coordinates functionally and structurally distinct cell types across the SCN (Low-Zeddies and Takahashi, 2001). Vasoactive intestinal polypeptide (VIP) is a critical neuropeptide responsible for the generation of circadian rhythms and the synchronization of individual oscillations (Aton et al., 2005). VIPergic cells appear to make connections with other VIPergic neurons (Daikoku et al., 1992) as well as with neurons within the dorsomedial 1To whom all correspondence should be addressed:

The suprachiasmatic nucleus (SCN) of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology. Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression. We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels.

Antibody drug conjugates (ADCs) represent novel anti-cancer modalities engineered to specifically target and kill tumor cells expressing corresponding antigens. Due to their large size and their complex kinetics, these therapeutic agents often face heterogeneous distributions in tumors, leading to large untargeted regions that escape therapy. We present a modeling framework which includes the systemic distribution, vascular permeability, interstitial transport, as well as binding and payload release kinetics of ADC-therapeutic agents in mouse xenografts. We focused, in particular, on receptor dynamics such as endocytic trafficking mechanisms within cancer cells, to simulate their impact on tumor mass shrinkage upon ADC administration. Our model identified undesirable tumor properties that can impair ADC tissue homogeneity, further compromising ADC success, and explored ADC design optimization scenarios to counteract upon such unfavorable intrinsic tumor tissue attributes. We further demonstrated the profound impact of cytotoxic payload release mechanisms and the role of bystander killing effects on tumor shrinkage. This model platform affords a customizable simulation environment which can aid with experimental data interpretation and the design of ADC therapeutic treatments.

We developed a multicellular model characterized by a high degree of heterogeneity to investigate possible mechanisms that underlie circadian network synchronization and rhythmicity in the suprachiasmatic nucleus (SCN). We populated a two-dimensional grid with 400 model neurons coupled via γ-aminobutyric acid (GABA) and vasoactive intestinal polypeptide (VIP) neurotransmitters through a putative Ca(2+) mediated signaling cascade to investigate their roles in gene expression and electrical firing activity of cell populations. As observed experimentally, our model predicted that GABA would affect the amplitude of circadian oscillations but not synchrony among individual oscillators. Our model recapitulated experimental findings of decreased synchrony and average periods, loss of rhythmicity, and reduced circadian amplitudes as VIP signaling was eliminated. In addition, simulated increases of VIP reduced periodicity and synchrony. We therefore postulated a physiological range of VIP within which the system is able to produce sustained and synchronized oscillations. Our model recapitulated experimental findings of diminished amplitudes and periodicity with decreasing intracellular Ca(2+) concentrations, suggesting that such behavior could be due to simultaneous decrease of individual oscillation amplitudes and population synchrony. Simulated increases in Cl(-) levels resulted in increased Cl(-) influx into the cytosol, a decrease of inhibitory postsynaptic currents, and ultimately a shift of GABA-elicited responses from inhibitory to excitatory. The simultaneous reduction of IPSCs and increase in membrane resting potential produced GABA dose-dependent increases in firing rates across the population, as has been observed experimentally. By integrating circadian gene regulation and electrophysiology with intracellular and intercellular signaling, we were able to develop the first (to our knowledge) multicellular model that allows the effects of clock genes, electrical firing, Ca(2+), GABA, and VIP on circadian system behavior to be predicted.