Heterogeneous organ models

A theoretical study is made of three organ flow models with heterogeneity of capillary transit times. A new parametrization of Rose and Goresky's Model III facilitates in many cases a reduction to Goresky's Model II, accomplished by a special time shift. The shift parameter defined here is critical in this analysis of Model III. A new expression of the series for outflow concentration in Model III is given and proves useful in examining the model as an operator and in relating it to Models I and II. A result on parameter optimization is given: if then Model III cannot fit better than Model II. This is applied to some data from Rose and Goresky [Circulation Res. 39, 541–544 (1976)] and raises a new question about their model. A heart model of Levin and Bassingthwaighte based on regional flow measurement is shown to be a discretized generalization of Model II. This work supported in part by PHS Grant Nos. HL-19153 (SCOR for Pulmonary Vascular Disease) and HL-19370 at Vanderbilt University.     

An evolutionary analytical model of a complementary circular code simulating the protein coding genes, the 5′ and 3′ regions

The self-complementary subset ∪{AAA,TTT} with = {AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC} of 22 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. The subsets ∪{CCC} and ∪{GGG} of 21 trinucleotides have a preferential occurrence in the shifted frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5′-3′ direction). and are complementary to each other. The subset contains the subset which has the rarity property (6 × 10⁻⁸) to be a complementary maximal circular code with two permutated maximal circular codes and in the frames 1 and 2 respectively. is called a C³ code. A quantitative study of these three subsets in the three frames 0, 1, 2 of protein genes, and the 5′ and 3′ regions of eukaryotes, shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of in the frame 0 of protein genes are 49, 28.5 and 22.5% respectively. In contrast, the frequencies of in the 5′ and 3′ regions of eukaryotes, are independent of the frame. Indeed, the frequency of in the three frames of 5′ (respectively 3′) regions is equal to 35.5% (respectively 38%) and is greater than the frequencies and , both equal to 32.25% (respectively 31%) in the three frames. Several frequency asymmetries unexpectedly observed (e.g. the frequency difference between and in the frame 0), are related to a new property of the subset involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 22 codons (trinucleotides in frame 0) of with equiprobability (1/22) followed by t ≈ 4 substitutions per codon according to the proportions p ≈ 0.1; q ≈ 0.1 and r = 1 − p − q ≈ 0.8 in the three codon sites respectively, retrieves the frequencies of observed in the three frames of protein genes and explains these asymmetries. Furthermore, the same model (0.1, 0.1, t) after t ≈ 22 substitutions per codon, retrieves the statistical properties observed in the three frames of the 5′ and 3′ regions. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine.     

Studies on a continuous recycle reactor for a lipase-catalysed processing of ricebran oil

The authors have developed a continuous recycle reactor which efficiently performs emulsion type enzymatic reactions. The reactor column is filled with immobilised lipase and the reactions are effected by pumping the pre-prepared oil-water emulsion through the bottom of the reactor. A part of the product was recycled back and this type of recycling greatly improves the productivity of fatty acid compared to continuous once-through reactor without recycling. The recycle reactor could be continuously run for 35 days without decrease in conversions. The performance of the reactor was interpreted by a model and the theoretical conversion was compared with the experimental data.List of Symbols F _AO mol/min feed rate - K _M g/l Michaelis constant - R recycle ratio - r ₅ mol/(ml · min) reaction rate - S ₀ g/l initial substrate concentration - V _max mol/(ml · min) maximum reaction velocity - V _R l void volume of the reactor - x _s fractional conversion - Standard deviation      

Measuring frequency domain granger causality for multiple blocks of interacting time series

In the past years, several frequency-domain causality measures based on vector autoregressive time series modeling have been suggested to assess directional connectivity in neural systems. The most followed approaches are based on representing the considered set of multiple time series as a realization of two or three vector-valued processes, yielding the so-called Geweke linear feedback measures, or as a realization of multiple scalar-valued processes, yielding popular measures like the directed coherence (DC) and the partial DC (PDC). In the present study, these two approaches are unified and generalized by proposing novel frequency-domain causality measures which extend the existing measures to the analysis of multiple blocks of time series. Specifically, the block DC (bDC) and block PDC (bPDC) extend DC and PDC to vector-valued processes, while their logarithmic counterparts, denoted as multivariate total feedback $f^\mathrm{m}$ and direct feedback $g^\mathrm{m}$ , represent into a full multivariate framework the Geweke’s measures. Theoretical analysis of the proposed measures shows that they: (i) possess desirable properties of causality measures; (ii) are able to reflect either direct causality (bPDC, $g^\mathrm{m})$ or total (direct + indirect) causality (bDC, $f^\mathrm{m})$ between time series blocks; (iii) reduce to the DC and PDC measures for scalar-valued processes, and to the Geweke’s measures for pairs of processes; (iv) are able to capture internal dependencies between the scalar constituents of the analyzed vector processes. Numerical analysis showed that the proposed measures can be efficiently estimated from short time series, allow to represent in an objective, compact way the information derived from the causal analysis of several pairs of time series, and may detect frequency domain causality more accurately than existing measures. The proposed measures find their natural application in the evaluation of directional interactions in neurophysiological settings where several brain activity signals are simultaneously recorded from multiple regions of interest.     

Use of the force-velocity test to determine the optimal braking force for a sprint exercise on a friction-loaded cycle ergometer

A group of 15 untrained male subjects pedalled on a friction-loaded cycle ergometer as fast as possible for 5–7 s to reach the maximal velocity (V{immax}) against different braking forces (F _B). Power was averaged during a complete crank rotation by adding the power dissipated againstF _B to the power necessary to accelerate the flywheel. For each sprint, determinations were made of peak power output ( ) power output attained atV _max ( ) calculated as the product ofV _max andF _B and the work performed to reachV _max expressed in mean power output ( ). The relationships between these parameters andF _B were examined. A biopsy taken from the vastus lateralis muscle and tomodensitometric radiographs of both thighs were taken at rest to identify muscle metabolic and morphometric properties. The value was similar for allF _B. Therefore, the average of values was defined as corrected maximal power ( ). This value was 11 higher than the maximal power output uncorrected for the acceleration. Whereas the determination did not require high loads, the highest value ( ) was produced when loading was heavy, as evidenced by the -F _B parabolic relationship. For each subject, the braking force ( ) giving was defined as optimal. The , equal to 0.844 (SD 0.108) N · kg⁻¹ bodymass, was related to thigh muscle area (r = 0.78,P < 0.05). The maximal velocity ( ) reached against this force seemed to be related more to intrinsic fibre properties (% fast twitch b fibre area and adenylate kinase activity). Thus, from the determination, it is suggested that it should be possible to predict the conditions for optimal exercise on a cycle ergometer.     

Dynamics of cardiorespiratory function in Standardbred horses during different intensities of constant-load exercise

Summary Six Standardbred horses were used to evaluate the time course of pulmonary gas exchange, ventilation, heart rate (HR) and acid base balance during different intensities of constant-load treadmill exercise. Horses were exercised at approximately 50%, 75% and 100% maximum oxygen uptake ( max) for 5 min and measurements taken every 30 s throughout exercise. At all work rates, the minute ventilation, respiratory frequency and tidal volume reached steady state values by 60 s of exercise. At 100% max, the oxygen consumption ( ) increased to mean values of approximately 130 ml/kg·min, which represents a 40-fold increase above resting . At the low and moderate work rates, showed no significant change from 30 s to 300 s of exercise. At the high work rate, the mean at 30 s was 80% of the value at 300 s. The HR showed no significant change over time at the moderate work rate but differing responses at the low and high work rates. At the low work rate, the mean HR decreased from 188 beats/min at 30 s to 172 beats/min at 300 s exercise, whereas at the high work rate the mean HR increased from 204 beats/min at 30 s to 221 beats/min at 300 s exercise. No changes in acid base status occurred during exercise at the low work rate. At the moderate work rate, a mild metabolic acidosis occurred which was nonprogressive with time, whereas the high work rate resulted in a progressive metabolic acidosis with a base deficit of 16 mmol/l by 300 s exercise. It is concluded that the kinetics of gas exchange during exercise are more rapid in the horse than in man, despite the relatively greater change in in the horse when going from rest to high intensity exercise.Symbols and abbreviations E minute ventilation - V _T tidal volume - oxygen uptake - carbon dioxide output - oxygen pulse - ventilatory equivalent for oxygen - ventilatory equivalent for carbon dioxide - R respiratory exchange ratio - HR heart rate - SBC standard bicarbonate - STPD standard temperature and pressure dry - BTPS body temperature and pressure saturated - arterial oxygen content - arteriovenous oxygen content difference - Rf respiratory frequency     

Analysis of spatial association between two species based on the interspecies mean crowding

Summary and Conclusion The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ andC _μ, are derived as geometric and weighted arithmetic means of the same component ratios related to inter- and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita’s (1959)C _δ index. Indices to measure the degree of spatial correlation between species, ω andR _μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra- and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested. This study was supported by Science Research Fund (No. 148041) from the Ministry of Education.     

Complexation of oxoanions and cationic metals by the biscatecholate siderophore azotochelin

Azotochelin is a biscatecholate siderophore produced by the nitrogen-fixing soil bacterium Azotobacter vinelandii. The complexation properties of azotochelin with a series of oxoanions [Mo(VI), W(VI) and V(V)] and divalent cations [Cu(II), Zn(II), Co(II) and Mn(II)] were investigated by potentiometry, UV–vis and X-ray spectroscopy. Azotochelin forms a strong 1:1 complex with molybdate (log K = 7.6 ± 0.4) and with tungstate and vanadate; the stability of the complexes increases in the order Mo < V < W (log K _app^Mo = 7.3 ± 0.4; log K _app^V = 8.8 ± 0.4 and log K _app^W = 9.0 ± 0.4 at pH 6.6). The Mo atom in the 1:1 Mo–azotochelin complex is bound to two oxo groups in a cis position and to the two catecholate groups of azotochelin, resulting in a slightly distorted octahedral configuration. Below pH 5, azotochelin appears to form polynuclear complexes with Mo in addition to the 1:1 complex. Azotochelin also forms strong complexes with divalent metals. Of the metals studied, Cu(II) binds most strongly to azotochelin , followed by Zn(II) , Mn(II) and Co(II) . Since very few organic ligands are known to bind strongly to oxoanions (and particularly molybdate) at circumneutral pH, the unusual properties of azotochelin may be used for the separation and concentration of oxoanions in the laboratory and in the field. In addition, azotochelin may prove useful for the investigation of the biogeochemistry of Mo, W and V in aquatic and terrestrial systems. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Dependency as a measure to estimate the order and the values of Markov processes

To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure dependency:D _m = (H ₀ –H _m )/H ₀ , whereH ₀ andH _m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that is a better point estimator ofD _m, giving a total value of them-th order Markov process. Here and are the estimate ofD _m and the arithmetic mean of when them-th order shuffling is made many times for a given observed series, respectively. The value represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by, where |S _m | is the determinant of serial correlation coefficients. It is shown that is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that analysis is basically equivalent to the least mean-square analysis of autoregressive models.     

An improved Four-Russians method and sparsified Four-Russians algorithm for RNA folding

Background

The basic RNA secondary structure prediction problem or single sequence folding problem (SSF) was solved 35 years ago by a now well-known \(O(n^3)\)-time dynamic programming method. Recently three methodologies—Valiant, Four-Russians, and Sparsification—have been applied to speedup RNA secondary structure prediction. The sparsification method exploits two properties of the input: the number of subsequence Z with the endpoints belonging to the optimal folding set and the maximum number base-pairs L. These sparsity properties satisfy \(0 \le L \le n / 2\) and \(n \le Z \le n^2 / 2\), and the method reduces the algorithmic running time to O(LZ). While the Four-Russians method utilizes tabling partial results.

Results

In this paper, we explore three different algorithmic speedups. We first expand the reformulate the single sequence folding Four-Russians \(\Theta \left(\frac{n^3}{\log ^2 n}\right)\)-time algorithm, to utilize an on-demand lookup table. Second, we create a framework that combines the fastest Sparsification and new fastest on-demand Four-Russians methods. This combined method has worst-case running time of \(O(\tilde{L}\tilde{Z})\), where \(\frac{{L}}{\log n} \le \tilde{L}\le min\left({L},\frac{n}{\log n}\right)\) and \(\frac{{Z}}{\log n}\le \tilde{Z} \le min\left({Z},\frac{n^2}{\log n}\right)\). Third we update the Four-Russians formulation to achieve an on-demand \(O( n^2/ \log ^2n )\)-time parallel algorithm. This then leads to an asymptotic speedup of \(O(\tilde{L}\tilde{Z_j})\) where \(\frac{{Z_j}}{\log n}\le \tilde{Z_j} \le min\left({Z_j},\frac{n}{\log n}\right)\) and \(Z_j\) the number of subsequence with the endpoint j belonging to the optimal folding set.

Conclusions

The on-demand formulation not only removes all extraneous computation and allows us to incorporate more realistic scoring schemes, but leads us to take advantage of the sparsity properties. Through asymptotic analysis and empirical testing on the base-pair maximization variant and a more biologically informative scoring scheme, we show that this Sparse Four-Russians framework is able to achieve a speedup on every problem instance, that is asymptotically never worse, and empirically better than achieved by the minimum of the two methods alone.