We formulate a Lagrangian (individual-based) model to investigate the spacing of individuals in a social aggregate (e.g., swarm, flock, school, or herd). Mutual interactions of swarm members have been expressed as the gradient of a potential function in previous theoretical studies. In this specific case, one can construct a Lyapunov function, whose minima correspond to stable stationary states of the system. The range of repulsion (r) and attraction (a) must satisfy r < a for cohesive groups (i.e., short range repulsion and long range attraction). We show quantitatively how repulsion must dominate attraction ( Rr(d+1) > cAa(d+1) where R, A are magnitudes, c is a constant of order 1, and d is the space dimension) to avoid collapse of the group to a tight cluster. We also verify the existence of a well-spaced locally stable state, having a characteristic individual distance. When the number of individuals in a group increases, a dichotomy occurs between swarms in which individual distance is preserved versus those in which the physical size of the group is maintained at the expense of greater crowding.
IntroductionA substantial number of therapeutic drugs for Alzheimer's disease (AD) have failed in late-stage trials, highlighting the translational disconnect with pathology-based animal models.MethodsTo bridge the gap between preclinical animal models and clinical outcomes, we implemented a conductance-based computational model of cortical circuitry to simulate working memory as a measure for cognitive function. The model was initially calibrated using preclinical data on receptor pharmacology of catecholamine and cholinergic neurotransmitters. The pathology of AD was subsequently implemented as synaptic and neuronal loss and a decrease in cholinergic tone. The model was further calibrated with clinical Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-Cog) results on acetylcholinesterase inhibitors and 5-HT6 antagonists to improve the model's prediction of clinical outcomes.ResultsAs an independent validation, we reproduced clinical data for apolipoprotein E (APOE) genotypes showing that the ApoE4 genotype reduces the network performance much more in mild cognitive impairment conditions than at later stages of AD pathology. We then demonstrated the differential effect of memantine, an N-Methyl-D-aspartic acid (NMDA) subunit selective weak inhibitor, in early and late AD pathology, and show that inhibition of the NMDA receptor NR2C/NR2D subunits located on inhibitory interneurons compensates for the greater excitatory decline observed with pathology.ConclusionsThis quantitative systems pharmacology approach is shown to be complementary to traditional animal models, with the potential to assess potential off-target effects, the consequences of pharmacologically active human metabolites, the effect of comedications, and the impact of a small number of well described genotypes.
Despite tremendous advances in understanding the neurobiology of schizophrenia, no real therapeutic breakthrough in terms of novel antipsychotics has been made since the serendipitous discovery of chlorpromazine. We describe a computer-based mechanistic disease simulation model of biophysically realistic neurons that captures most of the subcortical neuromodulatory processes important in the pathophysiology of schizophrenia and calibrate this with a large retrospective clinical database for Positive and Negative Symptoms Scale in Schizophrenia (PANSS total) and extrapyramidal symptoms (EPS) liability. Additionally we make this platform more actionable for practical use in central nervous system drug discovery by introducing a synaptic receptor competition model that accurately captures clinical target exposures. The model accounts for threefold more variance than the simple dopamine D2 receptor occupancy rule and is also superior in a number of independent clinical data sets. As such, the model is a first step in a better understanding of the human neurobiology of schizophrenia. Using human pharmacology and a positron emission tomography target engagement study as input, the model can estimate a value for the clinical efficacy on PANSS total and EPS side effect liability for the clinical doses of a new investigative compound. This Quantitative Systems Pharmacology platform, by simulating the effect of co-medications and genotypes in a clinical setting, represents a useful addition to psychiatric drug discovery efforts. Drug Dev Res 73 : 196-213, 2012.
BackgroundDespite a tremendous amount of information on the role of amyloid in Alzheimer’s disease (AD), almost all clinical trials testing this hypothesis have failed to generate clinically relevant cognitive effects.MethodsWe present an advanced mechanism-based and biophysically realistic quantitative systems pharmacology computer model of an Alzheimer-type neuronal cortical network that has been calibrated with Alzheimer Disease Assessment Scale, cognitive subscale (ADAS-Cog) readouts from historical clinical trials and simulated the differential impact of amyloid-beta (Aβ40 and Aβ42) oligomers on glutamate and nicotinic neurotransmission.ResultsPreclinical data suggest a beneficial effect of shorter Aβ forms within a limited dose range. Such a beneficial effect of Aβ40 on glutamate neurotransmission in human patients is absolutely necessary to reproduce clinical data on the ADAS-Cog in minimal cognitive impairment (MCI) patients with and without amyloid load, the effect of APOE genotype effect on the slope of the cognitive trajectory over time in placebo AD patients and higher sensitivity to cholinergic manipulation with scopolamine associated with higher Aβ in MCI subjects. We further derive a relationship between units of Aβ load in our model and the standard uptake value ratio from amyloid imaging.When introducing the documented clinical pharmacodynamic effects on Aβ levels for various amyloid-related clinical interventions in patients with low Aβ baseline, the platform predicts an overall significant worsening for passive vaccination with solanezumab, beta-secretase inhibitor verubecestat and gamma-secretase inhibitor semagacestat. In contrast, all three interventions improved cognition in subjects with moderate to high baseline Aβ levels, with verubecestat anticipated to have the greatest effect (around ADAS-Cog value 1.5 points), solanezumab the lowest (0.8 ADAS-Cog value points) and semagacestat in between. This could explain the success of many amyloid interventions in transgene animals with an artificial high level of Aβ, but not in AD patients with a large variability of amyloid loads.ConclusionsIf these predictions are confirmed in post-hoc analyses of failed clinical amyloid-modulating trials, one should question the rationale behind testing these interventions in early and prodromal subjects with low or zero amyloid load.
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