Dmitry Gokhman

Mitochondrion-Specific Antioxidants as Drug Treatments for Alzheimer Disease

Age-related dementias such as Alzheimer disease (AD) have been linked to vascular disorders like hypertension, diabetes and atherosclerosis. These risk factors cause ischemia, inflammation, oxidative damage and consequently reperfusion, which is largely due to reactive oxygen species (ROS) that are believed to induce mitochondrial damage. At higher concentrations, ROS can cause cell injury and death which occurs during the aging process, where oxidative stress is incremented due to an accelerated generation of ROS and a gradual decline in cellular antioxidant defense mechanisms. Neuronal mitochondria are especially vulnerable to oxidative stress due to their role in energy supply and use, causing a cascade of debilitating factors such as the production of giant and/or vulnerable young mitochondrion whos DNA has been compromised. Therefore, mitochondria specific antioxidants such as acetyl-L-carnitine and R-alphalipoic acid seem to be potential treatments for AD. They target the factors that damage mitochondria and reverse its effect, thus eliminating the imbalance seen in energy production and amyloid beta oxidation and making these antioxidants very powerful alternate strategies for the treatment of AD.

Oxidative Stress Induced Mitochondrial Failure and Vascular Hypoperfusion as a Key Initiator for the Development of Alzheimer Disease.

Mitochondrial dysfunction may be a principal underlying event in aging, including age-associated brain degeneration. Mitochondria provide energy for basic metabolic processes. Their decay with age impairs cellular metabolism and leads to a decline of cellular function. Alzheimer disease (AD) and cerebrovascular accidents (CVAs) are two leading causes of age-related dementia. Increasing evidence strongly supports the theory that oxidative stress, largely due to reactive oxygen species (ROS), induces mitochondrial damage, which arises from chronic hypoperfusion and is primarily responsible for the pathogenesis that underlies both disease processes. Mitochondrial membrane potential, respiratory control ratios and cellular oxygen consumption decline with age and correlate with increased oxidant production. The sustained hypoperfusion and oxidative stress in brain tissues can stimulate the expression of nitric oxide synthases (NOSs) and brain endothelium probably increase the accumulation of oxidative stress products, which therefore contributes to blood brain barrier (BBB) breakdown and brain parenchymal cell damage. Determining the mechanisms behind these imbalances may provide crucial information in the development of new, more effective therapies for stroke and AD patients in the near future.

Resonance in the menstrual cycle: a new model of the LH surge

In vertebrates, ovulation is triggered by a surge of LH from the pituitary. The precise mechanism by which rising oestradiol concentrations initiate the LH surge in the human menstrual cycle remains a fundamental open question of reproductive biology. It is well known that sampling of serum LH on a time scale of minutes reveals pulsatile release from the pituitary in response to pulses of gonadotrophin releasing hormone from the hypothalamus. The LH pulse frequency and amplitude vary considerably over the cycle, with the highest frequency and amplitude at the midcycle surge. Here a new mathematical model is presented of the pituitary as a damped oscillator (pulse generator) driven by the hypothalamus. The model LH surge is consistent with LH data on the time scales of both minutes and days. The model is used to explain the surprising pulse frequency characteristics required to treat human infertility disorders such as Kallmanns syndrome, and new experimental predictions are made.

Differentially transcendental formal power series

We prove that a formal power series in 1/x, whose coefficients are in a field extension of Q and are algebraically independent over Q, is differentially transcendental (i.e. not differentially algebraic) over this field extension. This is stated without proof in [2]. This result provides a source of functions analytic at ∞ that are not differentially algebraic over R. Such functions are of particular interest, because their germs belong to Hardy fields, but not to the class E of [1]-the intersection of all maximal Hardy fields.

An asymptotic existence theorem in C for the Riccati equation

We prove a generalization to C of a well known theorem [3] that in R, the Riccati equation W 1 + W 2=F 2 with F real and positive on the positive real axis, such that lim x→+∞ F=+∞, has a family of solution asymptotic to F and a unique solution asymptotic to -F. The Riccati equation W 1 + W 2=F 2 in the complex domain, where F is a holomorphic function in a partial neighborhood of infinity D and F(z)→∞ as z→∞ in D, has uniformly approximate solutions F and -F, Furthermore we show that there exist solutions W which arc uniformly asymptotic to ± F. We establish criteria for the shape of partial neighborhoods of infinity where this occurs. There is a family of solutions uniformly asymptotic to F and a unique solution uniformly asymptotic to -F or vice versa. The situation is reversed in adjacent neighborhoods. We establish a criterion for determining the particular case. Specific examples are provided for the following cases: 1. F is of polynomial or iterated logarithmic growth and the region is a sector (th...

Functional discrimination of sea anemone neurotoxins using 3D-plotting

One of the most important goals in structural biology is the identification of functional relationships among the structure of proteins and peptides. The purpose of this study was to (1) generate a model based on theoretical and computational considerations among amino acid sequences within select neurotoxin peptides, and (2) compare the relationship these values have to the various toxins tested. We employed isolated neurotoxins from sea anemones with established specific potential to act on voltage-dependent sodium and potassium channel activity as our model. Values were assigned to each amino acid in the peptide sequence of the neurotoxins tested using the Number of Lareo and Acevedo algorithm (NULA). Once the NULA number was obtained, it was then plotted using three dimensional space coordinates. The results of this study allow us to report, for the first time, that there is a different numerical and functional relationship between the sequences of amino acids from sea anemone neurotoxins, and the resulting numerical relationship for each peptide, or NULA number, has a unique location in three-dimensional space.

Functions in a hardy field not ultimately C

I construct a class of functions, whose germs belong to Hardy elds and all of whose derivatives a fortiori ultimately exist, but the functions are not ultimately C 1 .T he existence of such functions, while counterintuitive at rst glance, is explained by the fact that the higher order derivatives exist in progressively smaller neighborhoods of +1. A function not a Hardy eld satisfying the required smoothness properties was given in [1]. I provide a proof of the required smoothness properties of this function (omitted in [1]), and then use this function in the present construction. A Hardy eld is a dierential eld of germs of continuous real valued functions at +1. The reader is referred to [5] for an introduction to Hardy elds. Any function whose germ is in a Hardy eld must have derivatives of any order. However, it is not necessarily true that there is a single (one-sided) neighborhood of +1, where all these derivatives exist. We prove this result by explicitly constructing a function (actually many functions), whose germ belongs to a Hardy eld containing R, but which is not C 1 in any neighborhood of +1.

Regular growth of solutions of the riccati equation W′ + W 2=e 2z in the complex plane

Solutions of the Riccati equation W′ + W 2=e 2z are known to be asymptotic to e z or e -z . We show that those solutions which are asymptotic to e z have regular growth over C(e z ) as z→∞ in funnel-like regions D between curves of the form . Here the notion of regular growth over a differential field H of holomorphic germs on D is inspired by real Hardy field theory and is a generalization of the classical notion of non-oscillation. It means that for any differential polynomial P(X,X′,…) with coefficients in H, the function P(W,W′,…) is ultimately zero free in D or identically zero.

Limits in differential fields of holomorphic germs

Differential fields of germs of continuous real valued functions of one real variable (Hardy fields) have the property that all elements have limits in the extended real numbers and thus have a canonical valuation. For differential fields of holomorphic germs this is not generally the case. We provide a criterion for differential fields of holomorphic germs for its elements to have uniform limits in a partial neighborhood of infinity as an extended complex number. We apply the criterion to the specific case of a differential field of germs generated by the solutions of the Riccati equations W ′ + W 2 = 2z and extend the asympotic validity of the usual series for the solutions from the positive real axis to a region in the complex plane.

Boundary Element Method for Internal Axisymmetric Flow

We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.