How to Mix Molecules with Mathematics

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general

Changes in Muscles and Tendons Due to Neural Motor Disorders: Implications for Therapeutic Intervention

Patients with an upper motor neurone syndrome (CP) suffer from many disabling primary symptoms: spasms, weakness, and loss of dexterity. These primary ‘neurogenic’ symptoms often lead to secondary disabilities, muscle contractures, and tertiary effects, bone deformations. A common symptom of CP is hypertonia, with. the consequence that the involved muscles remain in an excessively shortened length for most of the time. As a normal reaction of the muscle tissue, the number of sarcomeres is reduced and the muscle fibers shorten permanently: a contracture develops. A possible second type of contracture is that normal muscle lengthening along with bone growth is affected. Current treatments for the secondary effects include (1) reduction of muscle force, (2)lengthening of the muscle fibers by serial plaster casts, and (3)surgical lengthening of tendons or aponeurosis. The choice of treatment depends on the cause of the functional deficit. Bone tissue also adapts itself to abnormal forces, especially in the growth period. The hypertonias or contractures of CP so may give rise to bone malformations that interfere with function (e.g. femur endorotation) or may reduce the action of muscles by changing the lever arm (e.g. ankle varus). Although prevention should always be preferred, a timely surgical intervention cannot always be avoided. The differences in treatment for the various groups require and justify an extensive laboratory investigation, including EMG recordings in gait, measurement of passive elastic properties, and long-term observation of the hypertonia

Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design

Rapid and MR-Independent IK1 activation by aldosterone during ischemia-reperfusion

In ST elevation myocardial infarction (STEMI) context, clinical studies have shown the deleterious effect of high aldosterone levels on ventricular arrhythmia occurrence and cardiac mortality. Previous in vitro reports showed that during ischemia-reperfusion, aldosterone modulates K+ currents involved in the holding of the resting membrane potential (RMP). The aim of this study was to assess the electrophysiological impact of aldosterone on IK1 current during myocardial ischemia-reperfusion. We used an in vitro model of “border zone” using right rabbit ventricle and standard microelectrode technique followed by cell-attached recordings from freshly isolated rabbit ventricular cardiomyocytes. In microelectrode experiments, aldosterone (10 and 100 nmol/L, n=7 respectively) increased the action potential duration (APD) dispersion at 90% between ischemic and normoxic zones (from 95±4ms to 116±6 ms and 127±5 ms respectively, P<0.05) and reperfusion-induced sustained premature ventricular contractions occurrence (from 2/12 to 5/7 preparations, P<0.05). Conversely, potassium canrenoate 100 nmol/L and RU 28318 1 μmol/l alone did not affect AP parameters and premature ventricular contractions occurrence (except Vmax which was decreased by potassium canrenoate during simulated-ischemia). Furthermore, aldosterone induced a RMP hyperpolarization, evoking an implication of a K+ current involved in the holding of the RMP. Cell-attached recordings showed that aldosterone 10 nmol/L quickly activated (within 6.2±0.4 min) a 30 pS K+-selective current, inward rectifier, with pharmacological and biophysical properties consistent with the IK1 current (NPo =1.9±0.4 in control vs NPo=3.0±0.4, n=10, P<0.05). These deleterious effects persisted in presence of RU 28318, a specific MR antagonist, and were successfully prevented by potassium canrenoate, a non specific MR antagonist, in both microelectrode and patch-clamp recordings, thus indicating a MR-independent IK1 activation. In this ischemia-reperfusion context, aldosterone induced rapid and MR-independent deleterious effects including an arrhythmia substrate (increased APD90 dispersion) and triggered activities (increased premature ventricular contractions occurrence on reperfusion) possibly related to direct IK1 activation

Towards domestication of Dimorphotheca pluvialis : studies on the genetic improvement of a potential oilseed crop for industrial applications

World-wide, but particularly in Western Europe and the USA, the interest in arable crops for non-food use has increased substantially over the past few decades. Surpluses of the major food crops and the industrial interest for renewable resources have led to research and development programmes aiming at the introduction of crops with industrial applications. Particularly vegetable oils with fatty acids containing functional groups are very attractive as substitutes for mineral oils used in the production of e.g. lubricants, surfactants, coatings and polymers. Therefore, in recent years much effort has been made to domesticate wild species containing such oils.Although the domestication and development of each new oilseed crop requires a specific approach dependent on the characteristics of the plant species, the history of the crop and its potential uses, some generalisations can be made about the steps involved. Both for crop development (agricultural side) and product development (industrial side), four stages can be distinguished: exploration, examination, expansion and exploitation. A more detailed description of this concept, known as the '4-ex model', can be found in Chapter 1 of this thesis.In 1986, the first of a series of projects on potential industrial crops in the Netherlands was launched. Around 40 oilseed species were evaluated for various agronomic characteristics as well as oil content and quality. After considering the industrial interest and agricultural potential, one of the species selected for further breeding research was Dimorphotheca pluvialis (L.) Moench. Seeds of this species contain ca 21% oil with approximately 60-65% dimorphecolic acid (Δ9-hydroxy,10t,12t-octadecadienoid acid). The highly reactive hydroxydiene structure provides this fatty acid with a unique functionality and properties, making it potentially suitable for application in e.g. pharmaceuticals, surfactants, coatings, plastic foams, polymers, fragrances and flavours.Although species of the genus Dimorphotheca have been known in the Netherlands as garden ornamentals for several centuries, the use of D. pluvialis for the production of seed oil is completely new. With regard to its use as an arable crop no breeding activities have been reported earlier, and as such the species should be considered as undomesticated. In the exploration of its potential as an arable oilseed crop, several constraints were identified, e.g. a long and unsynchronised period of flowering and seed ripening, poor seed retention and rather low oil content of the seeds. Hence, reported seed and oil yields were erratic. Seed retention seemed difficult to quantify, and preliminary observations revealed little variation for this character. Given the relatively short duration of the projects on which this thesis is based, attention was therefore focused on other important yield limiting factors: flowering synchronisation and oil content. Emphasis was laid on genetic improvement of these traits by means of selection. The efficiency of selection was examined by determination of the response to selection and estimations of the heritability.For successful seed production, knowledge on the mode of reproduction of the crop is imperative. In the literature, D. pluvialis is described as a highly allogamous species, but little is known about the mode of pollen transfer. The influence of insects on several yield components was studied by comparing plant populations in the presence and absence of insects (Chapter 2). Exclusion of insects had a dramatic effect on the production of flowers and the duration of the flowering period. The total number of flowers at peak bloom was higher, and flowering continued longer in the absence of insects. Seed weight was somewhat higher, but seed set, seed yield and oil content were severely reduced under these circumstances, thousand seed weight was somewhat higher. The total seed and oil yield of insect-visited plots were, respectively, 4.5 and 5.5 times higher than those of insect-free plots. These results confirm the assumptions on the allogamous nature of the species and underline the importance of insect pollination for adequate seed yield in D. pluvialis .Next to seed yield, oil content is a second important oil yield determining factor. High and stable oil yields of good quality are essential to provide industry with a constant supply. Three different populations of D. pluvialis were therefore subjected to mass selection for higher oil content (Chapter 3). After three cycles of selection at an intensity of 10%, for all three populations a significant increase in oil content was observed. Per selection cycle, an average gain in oil content ranging from 0.5% to 1.2% was achieved, depending on the population used. Realised heritabilities for this feature after three selection cycles in these populations ranged from 0.15 to 0.58. In Chapter 4, heritabilities for oil content were estimated from parent-offspring regression and half-sib family variance components. For this, forty plants were selected and progenies were tested twice, in two consecutive years. Heritability estimates from this experiment were moderately low: 0.34 from parent-offspring regression and 0.27 from variance components. If from this experiment 10% of the parental plants had been selected, an increase in oil content of 0.8% in one selection cycle would have been achieved. These values are in accordance with the values mentioned in Chapter 3. Although heritability estimates are specific for populations and environmental circumstances, it is likely that (mass) selection for increased oil content in general will be effective, particularly in the early generations. Considering the observed additive genetic variation in the populations, an average oil content of at least 30% seems feasible.Particularly in combination with poor seed retention, the long, unsynchronised period of flowering and seed ripening is undesired. When a crop is harvested too early, yield losses occur due to incomplete setting and maturation of the seeds. When harvested too late, however, seed shattering will account for a severe reduction of seed yield. With regard to synchronisation of flowering, two main components can be distinguished; i.e. the synchronisation between plants and the synchronisation within plants. Synchronisation between plants is attained when plants of a population start flowering at the same time. Synchronisation within a plant is achieved when its flowers are produced in a short period of time. Both components are considered important for improvement of flowering synchronisation of the crop. Therefore, the flowering of individual plants was studied by counting the open flowers at regular time intervals (Chapter 5). It appeared that the flowering process of individual plants can be described mathematically by a logistic curve, obtained by the regression of the cumulative number of open flowers plotted against time. The curve is characterised by three parameters, corresponding with the total number of flowers produced by the plant, the rate of flowering development and the day at which peak bloom was reached. From these parameters, subsequently two other characteristics could be derived, namely onset of flowering and duration of flowering within the plant. Similar to the method described for oil content, heritabilities of the flowering traits were estimated by using parent-offspring regression and half-sib family variance components analyses. Onset of flowering and peak bloom showed high (> 0.69) heritabilities for both methods and both years, and total number of flowers showed moderate to high (0.30 - 0.90) heritability values. For these traits considerable progress may be expected from mass selection, particularly in the early selection generations. Duration of flowering showed low to moderate values (0.25 - 0.45), and thus for improvement of this trait methods other than mass selection should be considered.Duration of flowering, total number of flowers and onset of flowering do not seem to be correlated (Chapter 5). Oil content and onset of flowering also seem to be uncorrelated (Chapter 4). Selection for either of these traits will most likely not influence the others.Modern agriculture requires uniform plant populations. The currently available populations of D. pluvialis , however, most often originate from botanical gardens or gene banks and show considerable variation for morphological and agronomic traits. To improve morphological uniformity and to determine a preliminary ideotype for plant architecture, divergent mass selection for this character was carried out (Chapter 6). In order to minimise undesired side-effects due to assortative mating caused by variation in onset of flowering, selection for plant architecture was combined with selection for onset of flowering (earliness). Hence, six selection groups were distinguished: all possible combinations of two plant architecture types (erect and procumbent), with three earliness classes (early, middle and late). Three cycles of combined selection resulted in a significant response for both traits in both directions, even at a low selection pressure. In this experiment, selection for early flowering or procumbent architecture showed a better response and a higher heritability than selection for late flowering or erect plant architecture. The different plant architecture selections showed similar flowering development and seed yield. Therefore, from these results no conclusions on ideal architecture type with regard to breeding for increased yield could be drawn. However, for cultivation generally erect plant types are preferred. Earliness did have a significant effect on seed yield: early flowering types showed the highest yields. As the yield experiment was carried out only in one year, and genotype by environment interactions could not be assessed, no firm conclusions on ideotype with regard to earliness could be drawn. Nevertheless, (very) late flowering selections in general are undesired in the Netherlands because of an increased risk of experiencing unfavourable weather conditions during flowering and seed set.D. pluvialis seems well adapted to the climatic conditions of north-west Europe, and fits well in a crop rotation system with annuals (Chapter 7). Its susceptibility to soil-borne diseases should be taken into consideration, but so far this has not caused major crop damage. Other pests and diseases seem to be easily controlled by agrochemicals. Improvement of resistance to several diseases can most likely be achieved by breeding, and deserves further attention. Genotypes with quick soil cover and improved harvest index may contribute to a higher potential seed production. Apart from further selection for increased oil content and flowering synchronisation, special attention should be directed towards improvement of seed retention. Even under optimal harvest conditions, seed losses of 20% were reported, entirely due to shattering. For good oil quality, relatively expensive methods for oil recovery have to be used. At present, oil of D. pluvialis seems particularly suitable for use in products with a high added value. However, many potential applications have not been explored yet. The unique structure and functionalities of dimorphecolic acid call for further research!</p

Open source software for semi-automated histomorphometry of bone resorption and formation parameters

Micro-CT analysis has become the standard method for assessing bone volume and architecture in small animals. However, micro-CT does not allow the assessment of bone turnover parameters such as bone formation rate and osteoclast (OC) number and surface. For these crucial variables histomorphometric analysis is still an essential technique. Histomorphometry however, is time consuming and, especially in mouse bones, OCs can be difficult to detect. The main purpose of this study was to develop and validate a relatively easy and rapid method to measure static and dynamic bone histomorphometry parameters. Here we present the adaptation of established staining protocols and three novel open source image analysis packages: TrapHisto, OsteoidHisto and CalceinHisto that allow rapid, semi-automated analysis of histomorphometric bone resorption, osteoid, and calcein double labelling parameters respectively. These three programs are based on ImageJ, but use a relatively simple user interface that hides the underlying complexity of the image analysis

Tilings, tiling spaces and topology

To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk properties of the individual tilings (such as the diffraction pattern). The topology of the space of tilings, particularly the Cech cohomology, gives information on how the original tiling can be deformed. Tiling spaces can be constructed as inverse limits of branched manifolds.Comment: 8 pages, including 2 figures, talk given at ICQ

Diffractive point sets with entropy

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition

Random fields on model sets with localized dependency and their diffraction

For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field omega defined on the model set Lambda that satisfies a natural geometric condition, we develop a method to calculate the diffraction measure of the random field. The method partitions the random field into a finite number of random fields, each being independent and admitting the law of large numbers. The diffraction measure of omega consists almost surely of a pure-point component and an absolutely continuous component. The former is the diffraction measure of the expectation E[omega], while the inverse Fourier transform of the absolutely continuous component of omega turns out to be a weighted Dirac comb which satisfies a simple formula. Moreover, the pure-point component will be understood quantitatively in a simple exact formula if the weights are continuous over the internal space of Lambda Then we provide a sufficient condition that the diffraction measure of a random field on a model set is still pure-point.Comment: 21 page