A neural model for conditioned avoidance learning

A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared.     

Note on the fusion frequency for stimuli of alternating duration

The case of alternating stimulus patterns of moderately high intensity is considered in terms of the model previously discussed (Landahl, 1957,Bull. Math. Biophysics,19, 157–62). If both of the alternating patterns have the same light-dark ratio, then the relation between the period of the longer and the period of the shorter pattern at the critical flicker frequency is independent of the light-dark ratio and is given by a dimensionless expression which is roughly in agreement with data in which the light-dark ratio is one (C. R. Brown and D. M. Forsyth, 1959,Science,129, 390–91). This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

On the application of the information concept to learning theory

A learning curve derived by H. D. Landahl (Bull. Math. Biophysics,3, 71–77, 1941) from postulated neurological structures is shown to be derivable from simplified assumptions by introducing the information measure of the uncertainty of response. The possible significance of this approach to learning theory is discussed.     

Analysis of tracer experiments: IV. The kinetics of generalN compartment systems

The methods of C. W. Sheppard and A. S. Householder (Jour. App. Physcis,22, 510–20, 1951), H. D. Landahl (Bull. Math. Biophysics,16, 151–54, 1954) and H. E. Hart (Bull. Math. Biophysics,17, 87–94, 1955;ibid.,19, 61–72, 1957;ibid.,20, 281–87, 1958) are employed in studying the kinetics of generalN compartment systems. It is shown that the nature of the transfer processes occurring in fluid flow systems and the chemical processes occurring in quadratic systems and in catalyzed quadratic systems can in principle be completely determined for all polynomial dependencies. Systems involving three-body and higher-order interactions can be completely solved, however, only if supplementary information is available. Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551.     

A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients

A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with those obtained by numerical methods.     

Particle removal by the respiratory system note on the removal of airborne particulates by the human respiratory tract with particular reference to the role of diffusion

Calculations of the contribution of diffusion to lung retention given previously (W. Findeisen,Pflüg. Arch. f. d. ges. Physiol.,236, 367–379, 1935; H. D. Landahl,Bull. Math. Biophysics,12, 43–56, 1950) contained an error appreciably underestimating the role of diffusion for particles less than a few microns in diameter. In the calculations (Landahl, 1950), a schematic representation of the lungs was modified to conform to the actual resting lung volume by increasing the number of alveolar sacs. A recalculation of total deposition with this chematic model gives too large a retention for very small particles. Hence it seemed appropriate to recalculate the retention for various paricle sizes in various regions of the respiratory tract for several respiratory paterns, using the original schematic model but assuming that the estimates reflect conditions in a deflated lung. For a given tidal air the sizes of the alveolar ducts and sacs were assumed to expand so that the total volume of the model was equal to 2.5 liters plus one half of the tidal air, i.e., the mean lung volume. The results of these calculations are appreciably different from those given previously, but the differences are serious only for particles of about 0.1 micron or less. Also given is an approximation method for calculating the probability of impaction of droplets against nasal hairs.     

Mathematical biology of learning to drive an automobile

In learning to drive, an individual must learn to rapidly make small corrective turns to the right or to the left as the car comes too close correspondingly to the left or to the right edges of the lane. The magnitude of the corrective turn depends on the angle at which the edge is approached. Thus, the individual must learn to produce a quantitatively correct response (corrective turn) to any one of an infinite number of possible stimuli (angles of approach). By making a number of highly oversimplifying assumptions, the problem can be reduced to a learning situation, studied previously by H. D. Landahl (Bull. Math. Biophysic,3, 13–26, 71–77, 1941). This is used not so much to obtain any relation that might be considered practically applicable immediately as toillustrate what kind of relation can be obtained from such considerations. It is shown how the safe speed of a driver depends on his total driving experience (total distance driven) as well as on his psychophysical parameters.     

Further studies of some aspects of a neurobiophysical model of schizophrenia

The neurobiophysical model of schizophrenia discussed previously (Bull. Math. Biophysics,26, 167–185, 1964;27, 21–26, 1965) is generalized further, to include catatonic and stuporous states. It is concluded that the development of schizophrenia will proceed through different stages of catatonic and non-catatonic states, depending on parameters which characterize on one hand the general inhibition of the individual, on the other hand what may be called his “stability.” Suggestions for possible clinical verifications of the conclusions are made.     

Some remarks on the central nervous system

It is pointed out that the successes obtained in the mathematical biology of the central nervous system are based mostly on a number of more or less complicated neuronic circuit models, each inventedad hoc for the purpose of explaining a given phenomenon. The individual models remain disconnected from each other, however, and the unity of the CNS is not apparent. (Rashevsky,Mathematical Biophysics, 3rd Edition, Vol. II, 1960. New York, Dover Publications, Inc.) Some “field theories” of the CNS, as for example that of Griffith (Bull. Math. Biophysics,25, 111–120, 1963;27, 187–195, 1965), give more expression to this unity but lose in the explanation of specific phenomena. The present paper starts with the picture thatevery neuron in the brain isdirectly or indirectly affected to some extent byevery other neuron. This leads to a system of equations with a very large number of variables. Such a system can be replaced in the limiting case by an integral equation of the first kind. At least two specific results can be obtained with this approach and suggestions for further improvement are made.     

Two remarks on the mathematical biology of automobile driving

In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics 5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated.     

Models for reserpine effects on normal and brain-operated animals on a continuous reinforcement bar pressing schedule

Mathematical models are presented for the relationship between changes in the bar pressing rate of albino rats on a continuous reinforcement schedule and alterations of the brain amines norepinephrine and serotonin induced by electrolytic lesions in the hypothalamus and by the drug, reserpine. The discussion utilizes central concepts from some of the more prominent hypotheses on the relation of the amines to behavior and for the potentiation effects of the drug by the lesion (A. Carlsson, 1964. “Functional Significance of Drug-induced Changes in Brain Monoamine Levels.” InBiogenic Amines, eds. H. E. Himwich and W. A. Himwich, New York: Elsevier, 9–27; B. B. Brodie and E. Costa, 1962. “Some Current Views on Brain Monoamines.”Psychopharm. Service Centre Bull.,2, 1–25.) Laboratory data (F. Grabarits and J. Harvey, 1966. “The Effects of Reserpine on Behavior and on Brain Concentrations of Serotonin and Norepinephrine in Control Rats and Rats with Hypothalamic Lesions.”J. Pharm.,153, 403–411) are interpreted, and suggestions for further experimental and theoretical work are made.     

Male territorial aggression and androgen modulation in high latitude populations of the Sooty, Passerella iliaca sinuosa, and Red Fox Sparrow, Passerella iliaca zaboria

The Fox Sparrows, Passerella iliaca, include multiple groups and subspecies distributed at several latitudes from the Alaskan arctic to the southwestern United States. As such, this species represents a potential model for investigating latitudinal variation in androgen secretion and aggressive territoriality in male passerines. Breeding male Fox Sparrows from two subspecies within two groups, the Sooty Fox Sparrow, P. i. sinuosa, and the Red Fox Sparrow, P. i. zaboria, were assessed for aggressive territoriality and androgen responsiveness at multiple latitudes in arctic and subarctic Alaska. Subarctic Sooty Fox Sparrows had higher circulating androgen levels in the early (8.54 ng/ml) versus mid–late breeding season (2.44 ng/ml). Males in the mid–late breeding season did not up-regulate androgen secretion in response to social challenge, but were aggressive and spent more time within 5 m of a decoy during a simulated territorial intrusion (STI) than early breeding males. Male subarctic Red Fox Sparrows had slightly higher circulating androgen levels (2.29 ng/ml) than arctic males (1.10 ng/ml) in the mid–late breeding season. However, androgen levels were not correlated with blood collection time after a social challenge in either group, suggesting that neither arctic nor subarctic males up-regulate androgen secretion during the mid–late breeding period. Arctic males spent more time within 5 m of a decoy and sang less than subarctic males during an STI in the mid–late breeding season. These findings demonstrate that the Fox Sparrow is a tractable model for investigating the latitudinal regulation of aggressive territoriality and androgen responsiveness in passerines.     

Effect of growth temperature and pH on the aminopeptidase activity of Pseudomonas putida, P. fluorescens and Flavobacterium odoratum; the 4-nitroaniline test is reliable

No significant difference (p > 0.05) was observed in the specific aminopeptidase activity (SAA) developed by Pseudomonas fluorescens, P. putida and Flavobacterium odoratum either growing at pH 5.0–6.5 or at 7 and 12 °C. Nevertheless, a significant difference was found when comparing the SAA of these organisms. The SAA of F. odoratum was lower than those of pseudomonads. The 4-nitroaniline test is reliable to estimate the G⁻ load of fresh food products.     

Purification and characterization of extracellular lipases from <Emphasis Type="Italic">Pseudomonas monteilii</Emphasis> TKU009 by the use of soybeans as the substrate

A lipase-producing bacterium was isolated and identified as Pseudomonas monteilii TKU009. A lipase (F2) and lipase-like materials (F1) were purified from the culture supernatant of P. monteilii TKU009 with soybean powder as the sole carbon/nitrogen source. The molecular mass of F1 and F2 was estimated to be 44 kDa by SDS-PAGE and gel filtration. The optimum pH, optimum temperature, and pH and thermal stabilities of F2 were 7, 40°C, 8–11, and 50°C; and of F1 were 6, 40°C, 6–7, and 50°C, respectively. F2 was completely inhibited by EDTA and slightly by Mg²⁺, Fe²⁺, Mn²⁺, and SDS. F1 was completely inhibited by EDTA and Fe²⁺ and strongly by Zn²⁺, Mn²⁺, Ca²⁺, Mg²⁺, and SDS. The activities of both the enzymes were enhanced by the addition of non-ionic surfactants Triton X–100 and Tween 40, especially for F1. F2 preferably acted on substrates with a long chain (C10–C18) of fatty acids, while F1 showed a broad spectrum on those with chain length of C4–C18. The marked activity of F2 in organic solvents makes it an ideal choice for application in a water-restricted medium including organic synthesis. Li-June Ming is a visiting Professor at the National Cheng Kung University.     

19F NMR study on the biological Baeyer-Villiger oxidation of acetophenones

The biological Baeyer–Villiger oxidation of acetophenones was studied by ¹⁹F nuclear magnetic resonance (NMR). The ¹⁹F NMR method was used to characterise the time-dependent conversion of various fluorinated acetophenones in either whole cells of Pseudomonas fluorescens ACB or in incubations with purified 4′-hydroxyacetophenone monooxygenase (HAPMO). Whole cells of P. fluorescens ACB converted 4′-fluoroacetophenone to 4-fluorophenol and 4′-fluoro-2′-hydroxyacetophenone to 4-fluorocatechol without the accumulation of 4′-fluorophenyl acetates. In contrast to 4-fluorophenol, 4-fluorocatechol was further degraded as evidenced by the formation of stoichiometric amounts of fluoride anion. Purified HAPMO catalysed the strictly NADPH-dependent conversion of fluorinated acetophenones to fluorophenyl acetates. Incubations with HAPMO at pH 6 and 8 showed that the enzymatic Baeyer–Villiger oxidation occurred faster at pH 8 but that the phenyl acetates produced were better stabilised at pH 6. Quantum mechanical characteristics explained why 4′-fluoro-2′-hydroxyphenyl acetate was more sensitive to base-catalysed hydrolysis than 4′-fluorophenyl acetate. All together, ¹⁹F NMR proved to be a valid method to evaluate the biological conversion of ring-substituted acetophenones to the corresponding phenyl acetates, which can serve as valuable synthons for further production of industrially relevant chemicals. Journal of Industrial Microbiology & Biotechnology (2001) 26, 35–42. Received 20 April 2000/ Accepted in revised form 16 September 2000     

Mathematical theory of biological periodicities: Formulation of then-body case

In a series of papers, L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956;19, 9–18, 1957) showed that a non-linear biochemical interaction between the anterior pituary gland and the thyroid gland may result under certain conditions in sustained periodical oscillations of the rates of production and of the blood level of the thyrotropic and of the thyroid hormone. They treated the systems, however, as a homogeneous one. N. Rashevsky (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1965;Bull. Math. Biophysics,29, 395–401, 1967) generalized the above results by taking into account the histological structures of the two glands as well as the diffusion coefficients and permeabilities of cells involved. The present paper is the first step toward the theory of interaction of any numbern of glands or, more generally,n components. The differential equations which govern the behavior of such a system represent a system of2n ²+n non-linear first order ordinary equations and involve a total of 7 n ²+3n parameters of partly histological, partly biochemical nature. The requirements of the existence of sustained oscillations demand 4n ²+2n+2 inequalities between those 7n ²+3n parameters.     

Diastereoselective functionalisation of Baylis–Hillman adducts: a convenient approach to α-methyl-α-amino acids

The N-tosyl carbamates 4a–e, easily prepared starting from the Baylis–Hillman adducts 3a–e, underwent cyclization carried out with I₂/NIS in the presence of NaH, to give the corresponding 2-oxo-1,3-oxazolidines 5a–e in good yield and total stereoselection when the substituent at C-5 is Ar. After the removal of tosyl group, followed by the cleavage of the heterocyclic ring, the α-methyl-α-amino acids 8a,b and 10 were obtained in good yield as hydrochlorides.     

Phytoplankton and nutrient dynamics of shallow coastal stations at Bay of Bengal,Eastern Indian coast

Phytoplankton dynamics of Eastern Indian coast was studied from surface water for a period of 24 months (April 2005–March 2007) in relation to environmental variables like, temperature, pH, dissolved oxygen, biochemical oxygen demand (BOD), salinity and nutrient contents—including nitrate, phosphate and silicate. Total 43 taxa were recorded during the study period. Phytoplankton density ranged from approximately 350–3,000 cells/ml and showed complete dominance of diatom genera namely, Asterionella japonica in winter and Odontella rhombus in summer. Other frequently occurring diatoms were Coscinodiscus perforatus, Actinocyclus normanii f. subsala, Thalassiothrix fraunfeldii, Ditylum brightwelli, Stephanodiscus hantzschoides, Cyclotella meneghiniana, Thalassionema nitzschoides etc. Seasonal changes in abundance and diversity of phytoplankton significantly differed showing maximum diversity in autumn with high diversity index (2.76-Oct, 05) and minimum in winter (0.326-January, 06). The species evenness varied from 0.137 (January 06) to 0.991 (August 06), which signifies minimum variation in percentage contribution of individual species to total phytoplankton population in monsoon and maximum in winter. Correlation studies of total cell count to physicochemical variables indicated significant positive relation with dissolved oxygen, salinity and pH but negative relation with nitrate, silicate and BOD of the water body. Multivariate procedures like ordination by principal component analysis and multi dimensional scaling of phytoplankton population based on their occurrence data and magnitude of abundance indicated that some genera (Biddulphia heteroceros, B. dubia, Odontella aurita, Gyrosigma acuminatum, Coscinodiscus granii, Paralia sulcata, etc.) have specific preference for water temperature and salinity and flourished maximally in particular season(s). While other genera (A. japonica, C. meneghiniana, C. perforatus, D. brightwelli, S. hantzschoides, etc.) appeared in wide range of temperature and salinity gradient.     

Antioxidant activity of the chemical constituents from the flower buds of <Emphasis Type="Italic">Magnolia denudata</Emphasis>

The scavenging activity of the flower buds of Magnolia denudata Desrousseaux on reactive oxygen species (ROS) was evaluated using 2′,7′-dichlorofluorescin diacetate (DCFH-DA) in HT 1080 cells. Methanol (MeOH) and dichloromethane (CH₂Cl₂) extracts inhibited dose-dependently generation of ROS in the cellular system. MeOH and CH₂Cl₂ extracts were combined and fractionated with n-hexane, 85% aqueous MeOH, and n-butanol (n-BuOH). Both n-hexane-soluble and 85% aqueous-soluble fractions showing strong radical-scavenging activity in the cellular system were further separated by diverse chromatographic methods to give five known lignans (1–5). All these compounds exhibited significant radical-scavenging effect on intracellular ROS in a dose-dependent manner. Their scavenging activity on various reactive oxygen species (ROS) was also evaluated using electron spin resonance (ESR) spin-trap techniques.     

Physics,biology and sociology: II. Suggestion for a synthesis

In continuation of previous studies (Bull. Math. Biophysics,28, 283–308; 655–661, 1966;29, 139–152, 1967) it is shown that the difference between the “metric” aspects of physics and the “relational” aspects of biological and social sciences disappear by accepting the broader definition of “relation”, such as that given in mathematics and logic. A conceptual superstructure then becomes possible from which all three branches of knowledge may be derived, though none of them can be derived from the others.