Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems

In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question

Bioactive Catalytic Nanocompartments Integrated into Cell Physiology and Their Amplification of a Native Signaling Cascade

Bioactive nanomaterials have the potential to overcome the limitations of classical pharmacological approaches by taking advantage of native pathways to influence cell behavior, interacting with them and eliciting responses. Herein, we propose a cascade system mediated by two catalytic nanocompartments (CNC) with biological activity. Activated by nitric oxide (NO) produced by inducible nitric oxidase synthase (iNOS), soluble guanylyl cyclase (sGC) produces cyclic guanosine monophosphate (cGMP), a second messenger that modulates a broad range of physiological functions. As alterations in cGMP signaling are implicated in a multitude of pathologies, its signaling cascade represents a viable target for therapeutic intervention. Following along this line, we encapsulated iNOS and sGC in two separate polymeric compartments that function in unison to produce NO and cGMP. Their action was tested in vitro by monitoring the derived changes in cytoplasmic calcium concentrations of HeLa and differentiated C2C12 myocytes, where the produced second messenger influenced the cellular homeostasis

Sign patterns for chemical reaction networks

Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector consisting of real-valued functions having a special relationship to $S$. Our main interest will be in the Jacobian matrix, $f'(x)$, of $f(x)$, in particular in whether or not each entry $f'(x)_{ij}$ has the same sign for all $x$ in the orthant, i.e., the Jacobian respects a sign pattern. In other words species $x_j$ always acts on species $x_i$ in an inhibitory way or its action is always excitatory. In Helton, Klep, Gomez we gave necessary and sufficient conditions on the species-reaction graph naturally associated to $S$ which guarantee that the Jacobian of the associated CRN has a sign pattern. In this paper, given $S$ we give a construction which adds certain rows and columns to $S$, thereby producing a stoichiometric matrix $\widehat S$ corresponding to a new CRN with some added species and reactions. The Jacobian for this CRN based on $\hat S$ has a sign pattern. The equilibria for the $S$ and the $\hat S$ based CRN are in exact one to one correspondence with each equilibrium $e$ for the original CRN gotten from an equilibrium $\hat e$ for the new CRN by removing its added species. In our construction of a new CRN we are allowed to choose rate constants for the added reactions and if we choose them large enough the equilibrium $\hat e$ is locally asymptotically stable if and only if the equilibrium $e$ is locally asymptotically stable. Further properties of the construction are shown, such as those pertaining to conserved quantities and to how the deficiencies of the two CRNs compare.Comment: 23 page

Nanoscale Enzymatic Compartments in Tandem Support Cascade Reactions in Vitro

Compartmentalization at the nanoscale is fundamental in nature, where the spatial segregation of biochemical reactions within cells ensures optimal conditions for regulating metabolic pathways. Here, we present a nature-inspired approach to engineer enzymatic cascade reactions taking place between separate vesicular nanocompartments (polymersomes), each containing one enzyme type. We propose, by the selected combination of enzymes, an efficient solution to detoxify the harmful effect of uric acid and prevent the accumulation of the derived H2O2, both being associated with various pathological conditions (e.g., gout and oxidative stress). Fungal uricase and horseradish peroxidase combined to act in tandem, and they were separately encapsulated within nanocompartments that were equipped with channel porins as gates to allow passage of substrates and products from each step of the reaction. We established the molecular factors affecting the efficiency of the overall reaction, and the protective role of the compartments. Interestingly, the cascade reaction between separate nanocompartments was as efficient as for free enzymes in complex media, such as human serum. The nanocompartments were nontoxic toward cells, and more importantly, addition of the tandem catalytic nanocompartments to cells exposed to uric acid provided simultaneous detoxification of uric acid and the H2O2. Such catalytic nanocompartments can be used as a platform for understanding fundamental factors affecting intracellular communication and can introduce non-native metabolic reactions into living systems for therapeutic applications

Investigation of infrared phonon modes in multiferroic single-crystal FeTe2_{2}O5_{5}Br

Reflection and transmission as a function of temperature (5--300 K) have been measured on single crystals of the multiferroic compound FeTe$_{2}$O$_{5}$Br utilizing light spanning the far infrared to the visible portions of the electromagnetic spectrum. The complex dielectric function and optical properties were obtained via Kramers-Kronig analysis and by fits to a Drude-Lortentz model. Analysis of the anisotropic excitation spectra via Drude-Lorentz fitting and lattice dynamical calculations have lead to the observation of all 52 IR-active modes predicted in the $ac$ plane and 43 or the 53 modes predicted along the b axis of the monoclinic cell. Assignments to groups (clusters) of phonons have been made and trends within them are discussed in light of our calculated displacement patterns.Comment: 9 pages, 7 figure

Large and giant vestibular Schwannomas

Background: The main objective in treating large and giant vestibular schwannomas (VS) (large - diameter exceeding 3.5 cm and giant - diameter exceeding 4.5 cm) is their complete removal without significant morbidity. Our experience on 7 cases (4 females, 3 males, mean age 42.5 years) with marked brainstem compression, operated between 2004-2009 focuses on factors influencing recurrence and morbidity, especially related to facial nerve function. These patients were included in a series of 32 consecutive vestibular schwannoma excisions.Methods: This report is a retrospective analysis of the surgical outcome of 7 patients with large and giant VS using the retrosigmoid-transmeatal approach. Several prognostic factors were evaluated: patient age, tumor size and consistency, extent of surgical removal, concurring hydrocephalus, hearing loss, facial nerve function, trigeminal nerve deficits, cranial nerve VI, IX and X palsy, tongue edema, ataxic gait and motor deficits.Results: The mean age was 42.3 years, the mean tumor diameter was 51.8 mm. There were no deaths and the tumors were histologically benign. Extensive microscopic tumor resection was performed in 5 cases related to solid tumor’s consistency. Preoperatively hearing loss and high intracranial pressure were encountered in all patients. 4 patients had cerebellar ataxia. Facial anatomical continuity was preserved in 6 cases with solid tumor consistency; 4 patients had a preoperative facial palsy, a good facial nerve function was achieved in 3 cases – House-Brackmann grade I/II. We have met other distinctive signs: cranial nerve V hypoesthesia, VI, IX and X palsy, tongue edema in 2 cases with slight contralateral motor deficit. All patients were clinical and MRI monitored at 3, 6 and 12 months postoperatively.Conclusion: Total resection associated with a low morbidity rate is possible, avoiding recurrence, reintervention and severe scar tissue. In cases with subtotal resection, radiosurgery is recommended to improve outcome

Personal experience in lumbar spinal stenosis (LSS)

Objective: To investigate the effectiveness of our strategy in lumbar spinal stenosis. This is based on the following: precise clinical radicular description of the level of claudication by electrodiagnosis, fine neuroradiologic studies, microsurgical decompression, assessment of the factors which might influence the outcome.Methods: The study was performed on 145 patients who underwent decompression in the last 8 years: 95 males, 50 females, mean age 65 yrs (50-81). Comorbidities were carefully considered when choosing the surgical procedure, especialy in elderly patients; an initial conservative approach of 3 weeks was used for most patients. Concerning etiology: 105 were degenerative, 16 post trauma, 24 others. Our cases included: 48 cases of single, focal stenosis, 97 diffuse (52 cases in 2 levels and 45 cases in 3 or more levels); 50% were graded as severe and evolved within 6 weeks, 30% were graded severe to moderate and 20% were moderate after a 2 month evolution; 15 were central, 17 lateral, 13 foraminal and 100 mixed. Precise clinical radicular description of the level of claudication by electrodiagnosis was used in all patients, MRI studies – 115 patients, CT studies - 30 patients, plain static x-rays of lumbar spine, dynamic flexion and extension x-rays of lumbar spine – all patients; disability degree evaluation: Oswestry Disability Index, pain (visual analog scale and analgesic consumption), functional improvement (Neurogenic Claudication Outcome Score), walking performance and instability degree (Pre-op and intraoperative) to all patients.We used a 4-5 cm incision for focal stenosis, 5-10 cm incision for 2-3 levels, C-arm for localization, high speed drill, cutting and diamond burrs, microscope, microinstruments, fenestration and medial facet undercutting to ensure an adequate root decompression. We excised the ligamentum flavum in the lateral recess which is often thickened. The lower lateral 6-12 mm of the lamina above and/or the superior lateral 3-9 mm of the lamina below were also resected to expose the root, the disc was excised and the posterior osteophytes were chiseled away with a fine micro chisel or diamond drill. In cases of focal stenosis we performed: foraminotomy, laminotomy, osteophytectomy, ligamentum flavectomy; diffuse/multilevel stenosis was approached as follows: laminotomies, foraminotomies, osteophytectomy, ligamentum flavectomy, medial facetectomy, fusion. In 24 cases we attempted a pedicle screw fixation and in two cases Diam devices. No re-do surgery was required.Results: One week after surgery, pain decreased in 87.9% of patients; nonsteroidal anti- inflammatory drug consumption and analgetics decreased in 81%. Two years after surgery, pain remained decreased in 79.8% of patients, Neurogenic Claudication Outcome Score decreased in 78.7% of patients and walking performance improved in 97.2% of patients. Patients who underwent both multilevel decompression or single - level decompression benefitted. Conclusions: LSS surgery is functional, never preventive; the initial management should be non-surgical except for severe cases. Electrophysiological testing correlated with thorough neurological examination is more accurate than a radiological evaluation alone when choosing the roots to be decompressed. Microsurgical selective decompression accomplishes a good balance between bony and soft tissue decompression, while also maintaining spinal stability

Atypical meningioma: Motto: “Scientific observation is allways a polemic observation” - Gaston Bachelard

Objective: Atypical meningioma are an intermediate group of meningiomas, exhibiting less favourable biological behavior than classic benign tumours, but a relatively more favourable biological behavior than definitive malignant meningiomas. Subject of controversy, atypia in meningioma still generate discordance between accurate criteria defining malignancy and biological behavior, prediction of recurrence.Methods: This retrospective study intend to evaluate diagnosis on clinical and pathological data, treatment trends and early outcomes for 6 cases with atypical meningiomas occuring in 63 patients operated for benign meningioma in the last 5 years in our clinic between 2006-2011. All patients were explored CT, MRI, preoperative selective angiography and in all cases the WHO 2000 classification criteria were used to define atypical meningiomaResults: Between 2006-2011 we operated 6 atypical meningioma of 63 benign meningiomas (9,52%). Tumor sites in the patients were: parasagittal (3 cases), convexity (2 cases), spheno-cavernous (1 case). All patients were operated and dural graft was done to all cases. The extent of surgical resection was Simpson’s grade 1 in 2 cases and Simpson’s grade 2 in four cases, to which radiation was administered after the first surgery with a dose ranging from 52-62 Gy. Regrowth (enlargement of tumour after subtotal resection) was noticed in 2 irradiated cases: one case after 2 years after the first operation, the patient was again operated - pathological diagnosis was malignant meningioma; in another case after 3 years, at operation it was the atypical meningioma. No chemotherapy was used in our cases.Conclusions: Atypical meningiomas are rare tumors, grow more rapidely, the diagnosis age ? 60 years, several histological criteria can define accurate identification to understand the biology of this group of tumors. Heterogenous contrast enhancement with marked peritumoral edema in neuroimaging are important; cerebral edema has prognostic value and should encourage fundamental and farmacologic research using anti VEGF and somatostatine analogs treatments. Surgery (Simpson grade 1) referring both tumor and dural implant area should be done de novo but also for recurrencies. Radiotherapy still are controversial without proven benefit and chemotherapy without statistic argues to improve quality of life