Prenatal exposure to valproic acid causes allodynia associated with spinal microglial activation.

Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by deficits in social communication and social interaction and the presence of restricted, repetitive behaviors. Additionally, difficulties in sensory processing commonly occur in ASD. Sensory abnormalities include heightened or reduced sensitivity to pain, but the mechanism underlying sensory phenotypes in ASD remain unknown. Emerging evidence suggests that microglia play an important role in forming and refining neuronal circuitry, and thus contribute to neuronal plasticity and nociceptive signaling. In the present study, we investigated the age-dependent tactile sensitivity in an animal model of ASD induced by prenatal exposure to valproic acid (VPA) and subsequently assessed the involvement of microglia in the spinal cord in pain processing. Pregnant ICR (CD1) mice were intraperitoneally injected with either saline or VPA (500 mg/kg) on embryonic day 12.5. Male offspring of VPA-treated mothers showed mechanical allodynia at both 4 and 8 weeks of age. In the spinal cord dorsal horn in prenatally VPA-treated mice, the numbers and staining intensities of ionized calcium-binding adapter molecule 1-positive cells were increased and the cell bodies became enlarged, indicating microglial activation. Treatment with PLX3397, a colony-stimulating factor 1 receptor inhibitor, for 10 days resulted in a decreased number of spinal microglia and attenuated mechanical allodynia in adult mice prenatally exposed to VPA. Additionally, intrathecal injection of Mac-1-saporin, a saporin-conjugated anti-CD11b antibody to deplete microglia, abolished mechanical allodynia. These findings suggest that prenatal VPA treatment causes allodynia and that spinal microglia contribute to the increased nociceptive responses.

Asymptotic stability of a modified Lotka-Volterra model with small immigrations.

Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.

Multi-species coexistence in Lotka-Volterra competitive systems with crowding effects.

Classical Lotka-Volterra (LV) competition equation has shown that coexistence of competitive species is only possible when intraspecific competition is stronger than interspecific competition, i.e., the species inhibit their own growth more than the growth of the other species. Note that density effect is assumed to be linear in a classical LV equation. In contrast, in wild populations we can observed that mortality rate often increases when population density is very high, known as crowding effects. Under this perspective, the aggregation models of competitive species have been developed, adding the additional reduction in growth rates at high population densities. This study shows that the coexistence of a few species is promoted. However, an unsolved question is the coexistence of many competitive species often observed in natural communities. Here, we build an LV competition equation with a nonlinear crowding effect. Our results show that under a weak crowding effect, stable coexistence of many species becomes plausible, unlike the previous aggregation model. An analysis indicates that increased mortality rate under high density works as elevated intraspecific competition leading to the coexistence. This may be another mechanism for the coexistence of many competitive species leading high species diversity in nature.