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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Topography and associations of luteinizing hormone-releasing hormone and neuropeptide Y-immunoreactive neuronal systems in the human diencephalon.

Neuropeptide Y (NPY) potentiates the effect of luteinizing hormone-releasing hormone (LHRH) on luteinizing hormone secretion in several species, including human. In addition to the pituitary sites, the interactions of the NPY and LHRH systems may involve diencephalic loci. However, the morphologic basis of this putative communication has not yet been elucidated in the human brain. To discover interaction sites, the distribution and connections of LHRH and NPY-immunoreactive (IR) neuronal elements in the human hypothalamus were investigated by means of light microscopic single- and double-label immunocytochemistry. NPY-IR perikarya and fibers were found to be widely distributed in the ventral diencephalon, with high densities in the preopticoseptal, periventricular, and tuberal regions. Small neuronal cell groups were infiltrated with a dense network of varicose NPY-IR fibers in the lateral preoptic area. The LHRH-IR perikarya were located mainly in the preopticoseptal region, diagonal band of Broca, lamina terminalis, and periventricular and infundibular nuclei. A few LHRH-IR neurons and fibers were scattered in the mamillary region. The overlap between the NPY and LHRH systems was apparent in the periventricular, paraventricular, and infundibular nuclei. Double-labeling immunohistochemistry showed NPY-IR axon varicosities in contact with LHRH-IR perikarya and main dendrites. The putative innervation of LHRH neurons by NPY-IR fibers was also seen in 1-microm-thick plastic sections and with confocal laser scanning microscope, thus further supporting the functional impact of NPY-IR terminals on LHRH-IR neurons. The present findings suggest that the hypophysiotropic LHRH-synthesizing neurons may be innervated by intrahypothalamic NPY-IR fibers. Confirmation by ultrastructural analysis would demonstrate that the LHRH system in the human hypothalamus is regulated by NPY, as has been demonstrated in nonhuman species.

A ventral approach to stereotaxy of the guinea pig brain.

The guinea pig (Cavia porcellus) is a species frequently used in neuromorphological and neurophysiological studies. Some experimental data suggest that the guinea pig might also be used to develop an animal model of Alzheimer's disease. These studies would require microsurgical manipulations of the nervous system. The present paper describes a method for ventral stereotaxic intrusions in the guinea pig brain through the oval foramen at the skull base. The topographic relationships of the bony landmarks to major parts of the central nervous system and the cranial nerves are analysed, and the results are tested by intrahippocampal injection of horseradish peroxidase.

Semiquantitative evaluation of histochemically detectable calcium binding in mammalian brain slices.

A method is described for the electron histochemical demonstration of Ca in the central nervous system, based on fixation on Ca-containing paraformaldehyde solution and the subsequent complexing of Ca by ammonium oxalate. The method resulted in highly electron-dense deposits, with good ultrastructural preservation. The Ca content of the deposits was proved by physico-chemical analysis. The high electron density permitted the counting of deposits and thereby an estimation of their numerical density, via planimetry of electron micrographs. Since pre- and postsynaptic localizations could be distinguished on the basis of ultrastructure, this procedure is regarded as a unique semiquantitative method for estimation of the tissue Ca binding of mammalian brain slices.

Stimulation-dependent calcium binding sites in the guinea pig hippocampal slice: an electrophysiological and electron microscopic study.

Transverse slices of the hippocampus of guinea pigs were prepared in order to investigate Ca2+ binding sites in CA1. Electrical stimulation (Schaffer collaterals and stratum oriens) combined with different aminopyridine compounds (AP) were used for neuronal activation. With histochemical methods Ca2+ binding sites were identified and localized at the electron microscopic level as electron dense deposits of granular or elongated shape. After electrical stimulation, electron dense deposits of 30-50 nm diameter were spread at low density over all layers of CA1. Electrical stimulation combined with application of aminopyridine compounds led to electron dense deposits of 60-400 nm diameter, mainly restricted to the activated input layers. Deposits were predominantly found at presynaptic sides, with few at dendrites and glial cells. Application of aminopyridine alone led to very few deposits, spread over the total CA1 area. The results indicate that aminopyridines, if combined with electrical stimulation, display a strong presynaptic action, which results in a remarkable Ca2+-translocation at the preterminal and terminal level. On the dendritic side aminopyridines in the concentrations used for the study weakly activate Ca2+ movements.

Immunohistochemical detection of raf protein kinase in cerebral cortical areas of adult guinea pigs and rats.

The raf protooncogenes are the cellular counterparts of the v-raf oncogene expressed by a murine sarcoma virus. The raf protooncogenes encode cytoplasmic serine/threonine-specific protein kinases which can be activated from different growth factor receptors by phosphorylation. The mRNAs of raf protooncogenes are found in a large variety of normal adult tissues, including the central nervous system. As concerns the distribution and localization of their protein products (the raf kinases), very few data are to be found in the literature. This is the first detailed description of their light microscopic localization in neocortical and allocortical areas of rodents. Preembedding immunohistochemical studies were performed on vibratome sections from the brains of adult guinea pigs and albino rats. The localizations of two isoenzymes, raf-1 kinase and B-raf kinase, were studied with the help of isoenzyme-specific polyclonal antibodies. Both of the antibodies detected raf protein-like immunoreactivity in many neurons and scattered glial cells of the sensory neocortex, and the cingular, pyriform, perirhinal and entorhinal allocortical areas. Pyramidal and non-pyramidal cells of Ammon's horn, granule cells of the dentate fascia and the large neurons in the hilar region were immunoreactive, too. The findings indicated that B-raf protein kinase and raf-1 kinase are present almost ubiquitously in the neurons of the investigated cortical structures. The intensity of staining obtained with serial dilutions of the antibodies indicated that the cytoplasmic concentration of B-raf kinase is tended to be higher than that of raf-1 kinase. The present findings suggested that the raf kinases are localized in postsynaptic structures, mainly in dendrites and cell bodies. Their cytosolic localization and their ability to undergo intracellular translocation during activation and phosphorylation raise the possibility that they play a pivotal role in the intracellular signaling of neurons.

Immunohistochemical localization of raf protein kinase in dendritic spines and spine apparatuses of the rat cerebral cortex.

The ultrastructural localization of raf protein (product of the raf protooncogene) in the neocortex, pyriform cortex and hippocampus of the rat has been investigated by means of pre-embedding immunohistochemistry. Specificity of the antiserum was tested with Western blotting. Besides the immunoreactivity of the dendrites, remarkably strong immunostaining of the dendritic spines and spine apparatuses was noted in each of the investigated areas. The postsynaptic densities were also stained. Since raf proteins are serine/threonine-specific protein kinases, our findings could be important steps toward the understanding of dendritic spine plasticity.

Parvalbumin- and calbindin-containing neurons express c-fos protein in primary and secondary (mirror) epileptic foci of the rat neocortex.

The present experiments aimed at the description and further immunocytochemical characterization of activated neocortical neurons expressing the c-fos gene. Focal seizures were induced by the topical application of isotonic, isohydric 4-aminopyridine solution to the frontal neocortex of adult anesthetized Wistar rats. The EEG of both hemispheres was recorded from the surface of the skull. The animals were perfused with fixative, coronal plane vibratome sections were cut and stained with cocktails containing polyclonal c-fos and monoclonal calbindin or parvalbumin antibodies. The polyclonal c-fos antibody was tested with Western blotting and the diffusion of 4-aminopyridine investigated with autoradiography of [3H]4-aminopyridine. The c-fos protein was detected in every layer of the neocortex (primary focus) and in some allocortical areas of the treated hemisphere. Scattered immunostained nuclei were observed in layers II, III, IV and VI of the contralateral neocortex (mirror focus). Several parvalbumin- and calbindin-positive neurons contained the c-fos protein in both foci. The medium-sized non-pyramidal parvalbumin neurons were found in layers II-IV and VI of the neocortex and in stratum multiforme of the prepiriform cortex. The c-fos protein was colocalized with calbindin mainly in layers II and III in small and medium-sized non-pyramidal neurons. The results prove that focal epileptiform activity of the neocortex activates diverse inhibitory neuronal populations. As concluded, the inhibitory control is probably more effective in the contralateral hemisphere (mirror focus) than on the side of 4-APY treatment (primary focus).

Expression and quantitative changes of carbonic anhydrase in developing neurones of rat central nervous system.

Postnatal changes in carbonic anhydrase activity were investigated in the islands of Calleja, which have been previously reported to contain the enzyme. Results obtained with a new modified method of Hansson provided further evidence for the distinction between the medial and lateral islands of Calleja. The enzyme was localized mainly in the nucleus and cytoplasm of granule cells without showing binding to any cytoplasmic organelle. No large neurons of the islands displayed carbonic anhydrase reactivity. The time course and rate of increase of carbonic anhydrase expression were different in the giant island of Calleja and lateral islands and this finding may strengthen the hypothesis regarding the medio-lateral diversity of Calleja's islands. On the other hand, at the end of the maturation process the granule cell complexes showed no significant difference in the proportion of carbonic anhydrase positive neurones. The almost equal rate of appearance of carbonic anhydrase reactive granule cells raises the possibility of a basic common role of both medial and lateral islets.