Mathematical modeling of transdermal delivery of topical drug formulations in a dynamic microfluidic diffusion chamber in health and disease.

Mathematical models of epidermal and dermal transport are essential for optimization and development of products for percutaneous delivery both for local and systemic indication and for evaluation of dermal exposure to chemicals for assessing their toxicity. These models often help directly by providing information on the rate of drug penetration through the skin and thus on the dermal or systemic concentration of drugs which is the base of their pharmacological effect. The simulations are also helpful in analyzing experimental data, reducing the number of experiments and translating the in vitro investigations to an in-vivo setting. In this study skin penetration of topically administered caffeine cream was investigated in a skin-on-a-chip microfluidic diffusion chamber at room temperature and at 32°C. Also the transdermal penetration of caffeine in healthy and diseased conditions was compared in mouse skins from intact, psoriatic and allergic animals. In the last experimental setup dexamethasone, indomethacin, piroxicam and diclofenac were examined as a cream formulation for absorption across the dermal barrier. All the measured data were used for making mathematical simulation in a three-compartmental model. The calculated and measured results showed a good match, which findings indicate that our mathematical model might be applied for prediction of drug delivery through the skin under different circumstances and for various drugs in the novel, miniaturized diffusion chamber.

Exchange-only virial relation from the adiabatic connection.

The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength λ at λ = 0. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on v-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit (λ ↘ 0) involving the exchange-correlation potential vxcλ, which exists by assumption of v-representability. On the other hand, a local-exchange potential vx is not warranted to exist as such a limit.

Exchange energies with forces in density-functional theory.

We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.

A Kinetic Finite Volume Discretization of the Multidimensional PIDE Model for Gene Regulatory Networks.

In this paper, a finite volume discretization scheme for partial integro-differential equations (PIDEs) describing the temporal evolution of protein distribution in gene regulatory networks is proposed. It is shown that the obtained set of ODEs can be formally represented as a compartmental kinetic system with a strongly connected reaction graph. This allows the application of the theory of nonnegative and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, it is straightforward to show the existence, uniqueness and stability of equilibria. Moreover, the computation of the stationary probability distribution can be traced back to the solution of linear equations. The discretization scheme is presented for one and multiple dimensional models separately. Illustrative computational examples show the precision of the approach, and good agreement with previous results in the literature.

The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just one-body particle density. In this Part II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some nonstandard alternatives. For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, nondifferentiability of the density functional can be mitigated through Moreau-Yosida regularization. Interesting insights can be drawn from both Maxwell-Schrödinger DFT and quantum-electrodynamic DFT, which are also discussed here.

S-Diagnostic─An a Posteriori Error Assessment for Single-Reference Coupled-Cluster Methods.

We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+. Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T1, D1, max T2, and D2 diagnostics as well as different indices of multideterminantal and multireference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T1, D1, max T2 and D2 diagnostics and is comparable to the indices of multideterminantal and multireference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multireference regimes. The S-diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+, which have been known to be misdiagnosed by T1 and D1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.

Persistence and stability of generalized ribosome flow models with time-varying transition rates.

In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.

Upregulated expression of oncomodulin, the beta isoform of parvalbumin, in perikarya and axons in the diencephalon of parvalbumin knockout mice.

The calcium-binding proteins parvalbumin, calbindin D-28k, calretinin and calcineurin are present in subsets of GABAergic gigantic calyciform presynaptic terminals of the reticular thalamic nucleus (RTN). Previously it was hypothesized that GABA and calcium-binding proteins including parvalbumin are not only colocalized in the same neuron subpopulation, but that GABA synthesis and parvalbumin expression could be also genetically regulated by a common mechanism. Moreover, parvalbumin expression levels could influence GABA synthesis. For this, we analyzed GABA immunoreactivity in RTN gigantic calyciform presynaptic terminals of parvalbumin-deficient (PV-/-) mice. With respect to GABA immunoreactivity we found no differences compared to wild-type animals. However, using a polyclonal parvalbumin antibody raised against full-length rat muscle parvalbumin on brain sections of PV-/- mice, we observed paradoxical parvalbumin immunoreactivity in partly varicose axons in the diencephalon, mainly in the lamina medullaris externa surrounding the thalamus. A detailed immunohistochemical, biochemical and molecular biological analysis revealed this immunoreactivity to be the result of an upregulation of oncomodulin (OM), the mammalian beta isoform of parvalbumin in PV-/- mice. In addition, OM was present in a sparse subpopulation of neurons in the thalamus and in the dentate gyrus. OM expression has not been observed before in neurons of the mammalian brain; its expression was restricted to outer hair cells in the organ of Corti. Our results indicate that the absence of parvalbumin has no major effect on the GABA-synthesizing system in RTN presynaptic terminals excluding a direct effect of parvalbumin on this regulation. However, a likely homeostatic mechanism is induced resulting in the upregulation of OM in selected axons and neuronal perikarya. Our results warrant further detailed investigations on the putative role of OM in the brain.

Distribution of oxytocin-immunoreactive neuronal elements in the rat spinal cord.

We investigated the distribution of oxytocin in rat spinal cord using immunocytochemistry and radioimmunoassay (RIA). Each segment of the spinal cord from cervical to coccygeal contained oxytocin-immunoreactive fibers. The Rexed laminae I and II of the dorsal horn showed moderate to intense immunoreactivity. A dense network was found around the central canal where some fibers apposed the ependyma. The autonomic centers of the spinal cord at the thoracolumbar and sacral segments were heavily innervated. Few fibers were found around the motoneurons. In the white matter, the immunoreactivity was localized mainly in the dorsal part of the lateral funiculus, in the pars funicularis of the nucleus intermediolateralis and in a longitudinal network of the lateral funiculus below the spinal cord surface. Some fibers from this network entered the pia mater. RIA measurements revealed that the cervical spinal cord had lower oxytocin content than that found in either the thoracic, lumbar, sacral or coccygeal region. Our results show that the distribution of oxytocin-immunoreactive fibers in the spinal cord correlates with anatomic locations related to nociceptive, autonomic and motor functions. We assume that oxytocin-containing axons play a role in secreting oxytocin directly into the liquor space of the spinal cord.

Modification of ionotropic glutamate receptor-mediated processes in the rat hippocampus following repeated, brief seizures.

The seizure-induced molecular and functional alterations of glutamatergic transmission in the hippocampus have been investigated. Daily repeated epileptic seizures were induced for 12 days by intraperitoneal administration of 4-aminopyridine (4-AP; 4.5 mg/kg) in adult Wistar rats. The seizure symptoms were evaluated on the Racine's scale. One day after the last injection, the brains were removed for in vitro electrophysiological experiments and immunohistochemical analysis. The glutamate receptor subunits NR1, NR2A, NR2B, GluR1, GluR1(flop), GluR2, and KA-2 were studied using the histoblotting method. The semi-quantitative analysis of subunit immunoreactivities in hippocampal layers was performed with densitometry. In the hippocampus, increase of GluR1, GluR1(flop) and NR2B immunostaining was observed in most of the areas and layers. The significant decrease of GluR2 staining intensity was observed in the CA1 and dentate gyrus. Calcium permeability of hippocampal neurons was tested by a cobalt uptake assay in hippocampal slices. The uptake of cobalt increased in the CA1 area and dentate gyrus, but not in the CA3 region following 4-AP treatment. Effects of AMPA and NMDA (N-methyl-d-aspartate) glutamate receptor antagonists (1-(4-aminophenyl)-4-methyl-7,8-methylenedioxy-5H-2,3-benzodiazepine hydrochloride (GYKI 52466) and D-APV respectively) were measured in hippocampal slices using extracellular recording. Analysis of the population spikes revealed the reduced effectiveness of the AMPA receptor antagonist GYKI 52466, while the effect of the NMDA receptor antagonist d-(2R)-amino-5-phosphonovaleric acid was similar to controls. The results demonstrated that repeated convulsions induced structural and functional changes in AMPA receptor-mediated transmission, while NMDA and kainate receptor systems displayed only alterations in receptor subunit composition.

The kynurenate analog SZR-72 prevents the nitroglycerol-induced increase of c-fos immunoreactivity in the rat caudal trigeminal nucleus: comparative studies of the effects of SZR-72 and kynurenic acid.

Administration of nitroglycerol in a migraine model results in an increased number of c-fos-expressing secondary sensory neurons in the caudal trigeminal nucleus. Since synapses between first- and second-order trigeminal neurons are mediated by excitatory amino acids, NMDA receptors are inhibited by kynurenic acid, though this crosses the blood-brain barrier only poorly. Systemic treatment of rats with SZR-72, a newly synthetized kynurenic acid analog, diminished the nitroglycerol-induced increase of c-fos immunoreactivity in the brain stem highly significantly, while treatment with kynurenic acid resulted in a significantly smaller decrease, proving that SZR-72 is much more effective than kynurenic acid.

Long-lasting dephosphorylation of connexin 43 in acute seizures is regulated by NMDA receptors in the rat cerebral cortex.

Gap junctions consisting of connexin 43 subunits provide intercellular communication between astrocytes, contributing to their function of maintaining the central nervous system (CNS) microenvironment. Magnetic resonance imaging (MRI) studies demonstrate prolonged astrocyte swelling related to seizures, while in vitro studies show the disruption of intercellular coupling and the cytotoxic swelling of astrocytes in seizure-equivalent environments. We examined the relation between astrocyte swelling and connexin 43 regulation using an in vivo seizure model. Generalised tonic-clonic convulsions were induced in adult rats using intraperitoneally (i.p.)-administered 4-aminopyridine (4-AP). The expression of connexin 43 mRNA and protein at 1, 3 and 24 h after seizure induction was measured. Astrocytic swelling was assessed at the same time points using transmission electron microscopy. mRNA and protein levels remained unaltered at all time periods. However, a significant (≈50%) reduction was found in the amount of phosphorylated (P1, P2) to unphosphorylated (NP) forms of connexin 43 at 3 h. The amount increased thereafter, but was still significantly lower than in the controls at 24 h post-seizure. Simultaneously, marked astrocytic swelling was measured in the neocortex. Pre-treatment with N-methyl-D-aspartate (NMDA) receptor antagonist dizocilpine maleate (MK-801) resulted in the amelioration of seizure symptoms and the prevention of connexin 43 dephosphorylation, as well as significantly reduced astrocytic swelling. Dephosphorylation of connexin 43 was shown to reduce astrocytic gap junction (GJ) permeability. Our results therefore suggest that, during acute seizures, a prolonged inhibition of intercellular coupling develops in the astrocyte network. This accounts for the long-lasting astrocyte swelling observed, and potentially impairs buffering function. The results also imply that this uncoupling is regulated through neuronal and/or glial NMDA-type glutamate receptors.

Kinetics of the cellular immune response following closed head injury.

BACKGROUND: The contribution of brain edema to brain swelling in cases of traumatic brain injury (TBI) remains a critical problem. We believe that inflammatory reactions may play a fundamental role in brain swelling following a head injury. Although possible roles of microglia activation and the release of mediators have been suggested, direct evidence of cellular immune reactivity in diffuse brain injury following closed head trauma is lacking. Accordingly, the objective of this study was to assess the temporal pattern of microglia activation and lymphocyte migration in an experimental model of TBI. METHOD: An impact acceleration TBI model was utilized to induce diffuse brain damage in adult Wistar rats. The animals were separated into three groups: unoperated controls, sham-operated controls and trauma group. At various times after TBI induction (5 min-24 h), rats were perfused transcardially. Sagittal brain sections were analyzed with immunohistochemical markers of CD3 to reveal the presence of T-lymphocytes, and by immunochemistry for the detection of CD11b to reveal microglia activation within the brain parenchyma. FINDINGS: In the control groups, scattered T-cells were found in the brain parenchyma. In the trauma group, TBI induced microglia activation and a transient biphasic T-cell infiltration of the brain parenchyma in all regions was found, beginning as early as 30 min post injury and reaching its maximum values at 45 min and 3 h after trauma induction. CONCLUSION: These results lead us to suggest that the acute response to severe head trauma with early edema formation is likely to be associated with inflammatory events which might be triggered by activated microglia and infiltrating lymphocytes. It is difficult to overestimate the clinical significance of these observations, as the early and targeted treatment of patients with severe head injuries with immunosuppressive medication may result in a far more favorable outcome.

Kynurenine in combination with probenecid mitigates the stimulation-induced increase of c-fos immunoreactivity of the rat caudal trigeminal nucleus in an experimental migraine model.

Nitroglycerin, often used as a migraine model, results in increased number of c-fos immunoreactive secondary sensory neurons in the caudal trigeminal nucleus. Since synapses between first- and second-order trigeminal neurons are mediated by excitatory amino acids, NMDA receptors are presumably inhibited by kynurenic acid, the only known endogeneous NMDA receptor antagonist. Although kynurenic acid does not cross the BBB, its precursor, kynurenine, if combined with probenecid, crosses it readily. Systemic kynurenine + probenecid treatment significantly diminishes nitroglycerin-induced increase of c-fos immunoreactivity in the brainstem.

Structural and functional MRI following 4-aminopyridine-induced seizures: a comparative imaging and anatomical study.

Structural and functional MRI was used in conjunction with computerized electron microscopy morphometry to study changes 2 h, 24 h and 3 days after 4-aminopyridine-induced seizures lasting 2 h in rats. T2 (relaxation time) values showed changes throughout the cerebral cortex, hippocampus, amygdala and medial thalamus, with a different temporal progression, showing a complete recovery only after 3 days. Two hours after seizures, the apparent diffusion coefficient was decreased throughout the brain compared to control animals, and a further decrease was evident 24 h after seizures. This was followed by a complete recovery at 3 days post-seizures. Functional MRI was performed using regional cerebral blood volume (rCBV) maps. The rCBV was increased shortly after convulsions (2 h) in all structures investigated, with a significant return to baseline values in the parietal cortex and hippocampus, but not in the medial thalamic nuclei, 24 h after seizure onset. No rCBV alterations were detected 3 days after seizures. Electron microscopy of tissue samples of parietal neocortex and hippocampus revealed prominent astrocytic swelling 2 h post-convulsions which decreased thereafter gradually. In conclusion, this experiment reports for the first time structural and functional brain alterations, lasting several hours, in 4-aminopyridine-treated rats after seizure onset. MRI approach combined with histological and ultrastructural analysis provided a clarification of the mechanisms involved in the brain acute response to ictal activity.

Somato-dendritic synapses in the nucleus reticularis thalami of the rat.

In the reticular nucleus of the rat thalamus, about 30% of the synapses are brought about by the perikarya of parvalbumin-immunopositive neurons, which establish somato-dendritic synapses with large dendrites of nerve cells of specific thalamic nuclei. Although the parvalbumin-immunopositive presynaptic structures bear resemblance to goblet-like or calyciform axonal endings, electron microscopic immunocytochemistry and in situ hybridization revealed that these structures are parts of the perikaryal cytoplasm studded with synaptic vesicles. In about 15% of the somato-dendritic synapses, axons are seen to be in synaptic contact with the parvalbumin-immunoreactive perikaryon. Double immunohistochemical staining revealed that the parvalbumin immunoreactive presynaptic perikarya and dendrites contained GABA. It is assumed that the peculiar somato-dendritic synaptic complexes subserve the goal of filtration of impulses arriving at the reticular nucleus from various thalamic nuclei, thus processing them for further sampling.

Time-dependent distribution and neuronal localization of c-fos protein in the rat hippocampus following 4-aminopyridine seizures.

The immunohistochemical localization of c-fos protein in the CNS neurons was studied in a model of generalized epilepsy induced by the intraperitoneal injection of 4-aminopyridine to adult Wistar rats. This specific blocker of the voltage-dependent potassium channels proved to be suitable for use in the investigation of epileptogenesis. Following the treatment of adult rats with 5 mg kg of 4-aminopyridine, the animals experienced generalized seizures. At the end of the experiment, the rats were briefly anesthetized and perfused with fixative. Frozen coronal plane sections were cut and processed for immunohistochemistry, using polyclonal c-fos antibody. The number and distribution of immunostained cell nuclei in the hippocampus were analyzed in detail with the help of a digital microscope camera and a morphometry program. The highest level of immunostaining was detected in most of the structures at 3 h, but the level had decreased to the control level by 5 h following 4-aminopyridine injection. In the dentate fascia, immunostaining was highest at 1 h and then decreased slowly until 5 h post-injection. The activated neuronal assemblies were analyzed with the aid of parvalbumin c-fos double immunostaining. These countings revealed the highest inhibitory interneuronal activation in every part of the hippocampus (including the dentate fascia) at 3 h post-injection. The results indicate that systemic 4-aminopyridine induces limbic seizures, which are probably initiated in the entorhinal cortex.

Effects of eletriptan on the peptidergic innervation of the cerebral dura mater and trigeminal ganglion, and on the expression of c-fos and c-jun in the trigeminal complex of the rat in an experimental migraine model.

Nociceptive axons and terminals in the supratentorial cerebral dura mater display an intense calcitonin gene-related peptide (CGRP) immunoreactivity. In an experimental migraine model, it has been shown that electrical stimulation of the rat trigeminal ganglion induced an increase in the lengths of CGRP-immunoreactive axons, increased size and number of pleomorphic axonal varicosities in the dura mater, and an increased number of c-jun and c-fos protein-expressing nerve cells in the trigeminal complex. We demonstrate the effect of the highly specific and moderately lipophilic serotonin agonist eletriptan (Pfizer) which prevents the effects of electrical stimulation in the dura mater. Eletriptan also affected the caudal trigeminal complex; it markedly reduced the numbers of the oncoprotein-expressing cells, mainly after stimulation and to some extent also in nonstimulated animals. Eletriptan also affected expression of CGRP in perikarya of trigeminal ganglion cells, insofar as the number of small nerve cells exhibiting a compact CGRP immunoreaction was decreased to one quarter of the original value. In all these respects, eletriptan acted in a similar way to sumatriptan, with the notable exception that eletriptan also blocked the stimulation-induced effects in the nucleus caudalis trigemini and the upper cervical spinal cord (trigeminal complex), whereas sumatriptan did not. It is concluded that eletriptan, acting on perikarya and both the peripheral and the central axon terminals of primary sensory neurons, exerts its antimigraine effect by an agonist action on 5-HT1B/1D receptors throughout the entire trigeminal system, probably by passing the blood-brain-barrier because of its lipophilic character.