Mathematical biology of automobile driving: III

In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study, increases with the speedv, widths _o and lengthl _o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described.     

Further contributions to the mathematical biophysics of automobile driving

The discussions of a previous paper (Bull. Math. Biophysics,21, 299–308, 1959) are generalized by considering that the angular direction error made by the driver, as well as the driver's reaction time are not constant but are randomly distributed. Instead of a critical speed, at which the car will jump off the road, we now find that for every speed there is a probability of the car to jump off the road but that this probability is vanishingly small for sufficiently low speeds, yet increases rapidly for high speeds. Thus a more realistic picture of the process of driving is obtained. When the standard deviation of the distribution functions for the angle and the reaction time are very small, the expression obtained here reduces to the expression obtained previously.     

A contribution to the mathematical biology of automobile driving: II. Passing as a case of psychophysical discrimination

The decision to pass or not to pass in view of an oncoming car is considered as a case of comparative judgment in which it is to be decided whether the time it will take to pass safely is greater or less than the time it will take to collide with the oncoming car. H. D. Landahl's well-known theory of psychophysical discrimination is used, and it is assumed that the “distracting stimuli” considered previously (Rashevsky, 1959,Bull. Math. Biophysics,21, 375–85) tend to increase the standard deviation of Landahl's fluctuation function. Effects of the “distracting stimuli” on the threshold of the neuroelements in Landahl's circuit are also considered. On this basis an expression is derived which gives the probability of a collision accident in passing as a function of the “distracting stimuli.”     

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.     

Mathematical biology of automobile driving: I. The shape of the tracking curve on an empty straight road

The idea was suggested by the author previously (Bull. Math. Biophysics,22, 257–262, 1962) that the keeping of the car close to the center of the lane is a problem of psychophysical discrimination between two conflicting stimuli, namely a stimulus to turn away from the left, resp. right edge of the lane. This is elaborated in the present paper. The effects of discrimination threshold and of the endogenous fluctuations which result in erroneous judgments are discussed. In order that driving should be possible at all, a relation, derived in this paper, must hold between the threshold of discriminationh, the sensitivity coefficientb of the driver to changes in the distance between the car and the edge of the lane, and the width of the lane. General expressions are derived which characterize the stochastic nature of the tracking curve.     

An evolution of pulse speed in arteries

In this work, treating the artery as a thick-walled cylindrical shell made of an incompressible, isotropic and elastic solid, utilizing the large deformation theory and the stress-strain relation proposed by Demiray (1976b,Trans. ASME Ser. E, J. Appl. Mech.,98, 194–197), an explicit expression for the pulse speed is obtained and the effect of lumen pressure and the axial stretch on wave speed is discussed. Numerical results indicate that the wave speed increases with lumen pressure but decreases with the axial stretch. The results of the present model are compared with our previous work (Demiray, 1988,J. Biomech. 21, 55–58) on the same subject.     

Some further comments on the DNA-protein coding problem

A notion of quasi-ergodicity is defined in free monoids, generalizing a notion introduced in a previous paper (Rosen, 1959,Bull. Math. Biophysics,21, 71–95). It is shown that under certain conditions the algebraic properties of quasi-ergodicity are very similar to those derived for the more specialized concept inloc. cit. If it is assumed that the DNA-protein coding processes in nature are of a quasi-ergodic nature, then a condition is specified under which only a finite number of different DNA-protein codes are possible, and an upper bound for the total number of different quasi-ergodic codes is obtained.     

Some possible quantitative aspects of a neurophysiological model of schizophrenias

In continuation of a previous paper (Bull. Math. Biophysics,26, 167–185, 1964) simple equations are derived for the rate of development of schizophrenia as a function of some psychobiological parameters of the individual and of an index which characterizes the frequency of traumatic experiences of the individual. A clue to the understanding of why schizophrenia is more likely to develop at an early adult age is thus provided. Formerly of the Committee on Mathematical Biology, The University of Chicago.     

Parasitism and symbiosis in an N-person non-constant-sum continuous game

A non-constant-sum continuous game analyzed in a previous paper by one of the authors (A. Rapoport,Bull. Math. Biophysics,18, 15–30, 1956) is extended from two toN players with special emphasis onN=3. It is shown that the concept of stability becomes in this case one of “pairwise stability,” and depends on the so-called distribution matrix of rewards. The distribution matrix and the collusion structure jointly determine the end states of the game. Conditions which lead to the emergence of one, two, or no “parasites” are derived. An apparatus is described which provides a physical analogue of the game, making possible the isolation of behavioral variables under the prescribed conditions of the game.     

Window automata analysis of population dynamics in the immune system

A formalism based on window automata is proposed as a method to analyse complex population dynamics. The method is applied to a model of the immune network (Weisbuch, G.et al., 1990.J. theor. Biol. 146, 483–499), and used to predict which attractor the system reaches after antigenic stimulation, as a function of the parameters. The attractors of the dynamics are interpreted in terms of immune conditions such as vaccination or tolerance. Scaling laws that define the regimes in the parameter space corresponding to the specific attractor reached under antigenic stimulation are derived.     

On the equilibrium distribution of population in space

Spatial equilibrium distributions of population are derived from the spatial distribution of net rates of reproduction, and from a relationship between migratory flow and gradients of population density and of locational “attractiveness.” Conditions are discussed for which population approaches a uniform spatial density. Under certain conditions a particularly simple statement of the equilibrium conditions is possible in terms of the “potential of population,” a concept introduced by demographers (J. Q. Stewart,Geographical Review,37, 46–85, 1947) to measure the proximity of a point to people. This paper was first written at the Center for Advanced Study in the Behavioral Sciences.     

Erythrocyte distribution in arterial blood flow: II. The hypothesis of minimal energy dissipation

In a previous paper (Bull. Math. Biophysics,29, 549–563, 1967) the author derived equations to represent the flow of blood in an artery. It was pointed out that these did not completely characterize the system and that an additional hypothesis was required. The hypothesis of minimal energy dissipation had been thought to imply a central tendency on the part of suspended particles (erythrocytes). It is here shown that if the fluid is non-Newtonian this may not be so.     

A note on imitative behavior

In a preceding paper (Bull. Math. Biophysics,27, 175–185) the distribution function ofφ=ɛ ₁-ɛ ₂,—the difference of excitations in the two mutually inhibiting centers, has been derived in terms of the distribution functionsf ₁(ɛ ₁) andf ₂(ɛ ₂) of the two excitations. In the present note some properties of the distribution functionf(ϕ) in terms of the propertiesf ₁(ɛ ₁) andf ₂(ɛ ₂) are derived.     

The basic flow equations of electrophysiology in the presence of chemical reactions: II. A practical application concerning the pH and voltage effects accompanying the diffusion of O2 through hemoglobin solution

Previous papers by F. M. Snell (Jour. Theor. Biol.,8, 469–479, 1965) and M. A. Fox and H. D. Landahl (Bull. Math. Biophysics,27, Spec. Issue, 183–190, 1965) have found that the formulation by previous authors for the oxygen flow rates through hemoglobin solution as a function of pressure determined by E. Hemmingsen and P. F. Scholander (Science,132, 1379–1381, 1960) did not give a satisfactory quantitative fit of the curve for constant pressure difference. The suggestion of Fox and Landahl that the Bohr effect involving the shift in acidity accompanying the oxidation of Hb should give rise to voltage and pH differences in oxyhemoglobin transport is examined in more detail. In this paper, the previous expressions for the total oxygen flow rate in terms of the end point concentrations are extended to include the effects of the electrical field. Estimates of the potential difference shows it to be negligible. A derivation of a voltage-pH relation shows that the Nernst relation does not apply and a negligible voltage difference does not preclude a pH shift which is the more probable explanation of the discrepancies observed. Several other predictions suitable for experimental testing are made.     

Note on psychophysical discrimination with more than two stimuli

H. D. Landahl's well-known theory of psychophysical discrimination between two stimuli (Psychometrica,3, 107–125, 1938) is generalized to the case ofn mutually inhibiting stimuli, such that all the corresponding reactions are mutually incompatible so that only one response at most can occur at a time. It is shown that while in the two-stimulus case a “no-response” situation does not necessarily need to occur, in the case ofn stimuli andn responses a “no-response” situation always occurs with finite probability. Therefore, there is a probabilityP _i of the occurrence of each responsei as well as a probabilityP _e of no response, with . The probabilitiesP _i andP _e are expressed in terms of the intensities of then stimuliS _i and in terms of then distribution functions of the fluctuations at then corresponding connections. The expressions are in the form of sums ofn-tuple integrals of the products of the distribution functions, the limits of integration being determined by the intensities of then stimuli.     

Facile and Rapid Deprotection Conditions for the Cleavage of Synthetic Oligonucleotides from 1,4-Anhydroerythritol-Based Universal Polymer Support

In our previous report [Kumar, P.; Dhawan, G.; Chandra, R.; Gupta, K.C. Polyamine-assisted rapid and clean cleavage of oligonucleotides from cis-diol bearing universal support. Nucl. Acids Res. 2002, 30, e130 (1-8)], we demonstrated polyamine-mediated deprotection of oligonucleotides from cis-diol group bearing universal polymer support (I). However, vulnerability of the conventional dC^bz to modifications under these conditions compelled us to employ dC^ac during synthesis of oligonucleotide using conventional synthons. Here, a new set of simple and rapid deprotection conditions has been developed for the complete cleavage of oligonucleotides from the 1,4-anhydroerythritol-based universal polymer support employing conventional dC^bz synthon. Using manganese-imidazole complex in aqueous ammonium hydroxide (～30%), fully deprotected oligonucleotide sequences were obtained in 40 min, which were analyzed on reverse phase-HPLC and compared with the standard oligomers in terms of their retention time. Finally, their biological compatibility was established by analyzing PCR amplified products of npsA gene of N. meningitidis.     

The Effect of Motivation on Movement: A Study of Bradykinesia in Parkinson’s Disease

Background

Bradykinesia is a cardinal feature of Parkinson’s disease (PD). Despite its disabling impact, the precise cause of this symptom remains elusive. Recent thinking suggests that bradykinesia may be more than simply a manifestation of motor slowness, and may in part reflect a specific deficit in the operation of motivational vigour in the striatum. In this paper we test the hypothesis that movement time in PD can be modulated by the specific nature of the motivational salience of possible action-outcomes.

Methodology/Principal Findings

We developed a novel movement time paradigm involving winnable rewards and avoidable painful electrical stimuli. The faster the subjects performed an action the more likely they were to win money (in appetitive blocks) or to avoid a painful shock (in aversive blocks). We compared PD patients when OFF dopaminergic medication with controls. Our key finding is that PD patients OFF dopaminergic medication move faster to avoid aversive outcomes (painful electric shocks) than to reap rewarding outcomes (winning money) and, unlike controls, do not speed up in the current trial having failed to win money in the previous one. We also demonstrate that sensitivity to distracting stimuli is valence specific.

Conclusions/Significance

We suggest this pattern of results can be explained in terms of low dopamine levels in the Parkinsonian state leading to an insensitivity to appetitive outcomes, and thus an inability to modulate movement speed in the face of rewards. By comparison, sensitivity to aversive stimuli is relatively spared. Our findings point to a rarely described property of bradykinesia in PD, namely its selective regulation by everyday outcomes.     

Contribution to the mathematical biophysics of automobile driving

Traffic in one direction on a multilane highway is considered, and a general expression for the number of cars which pass a car travelling at a given velocity, as well as the number of cars which the given car passes, is derived for the case when the speeds of different cars are distributed in some arbitrary manner. Closed expressions are derived and discussed for a rectangular distribution. Each passing by another car or of another car is considered as a distracting stimulus which affects the reaction times of the driver. Using previously derived expressions for the safe speed as a function of reaction times, expressions for the safe average speed are derived, in terms of the volume of traffic and of the spread of the distribution of speeds.     

Photosynthetic Properties of Photosystem Ⅱ in Arabidopsis thaliana Ipa1 Mutant

In a previous study, we characterized a high chlorophyll fluorescence Ipal mutant of Arabidopsis thallana, in which approximately 20% photosystem （PS） Ⅱ protein is accumulated. In the present study, analysis of fluorescence decay kinetics and thermoluminescence profiles demonstrated that the electron transfer reaction on either the donor or acceptor side of PSII remained largely unaffected in the Ipa1 mutant. In the mutant, maximal photochemical efficiency （Fv/Fm, where Fm is the maximum fluorescence yield and Fv is variable fluorescence） decreased with increasing light intensity and remained almost unchanged in wildtype plants under different light conditions. The Fv/Fm values also increased when mutant plants were transferred from standard growth light to low light conditions. Analysis of PSll protein accumulation further confirmed that the amount of PSll reaction center protein is correlated with changes in Fv/Fm in Ipal plants. Thus, the assembled PSll in the mutant was functional and also showed increased photosensitivity compared with wild-type plants.     

Furfural formation from d-xylose: the use of different halides in dilute aqueous acidic solutions allows for exceptionally high yields

Starting from the results achieved in a previous work on the effects of Cl⁻ ions on furfural formation in aqueous acid solution [Marcotullio, G. et al., Green Chem.2010, 12, 1739], the general effect of different halides is addressed. Experimental results show the halides to influence at least two distinct steps in the reaction leading from d-xylose to furfural under acidic conditions, via different mechanisms. The nucleophilicity of the halides appears to be critical for the dehydration, but not for the initial enolization reaction. By combining different halides synergic effects become evident resulting in very high selectivities and furfural yields.