Showing papers by "University of Sussex published in 1975"

Deterministic and stochastic optimal control

Abstract: I The Simplest Problem in Calculus of Variations.- 1. Introduction.- 2. Minimum Problems on an Abstract Space-Elementary Theory.- 3. The Euler Equation Extremals.- 4. Examples.- 5. The Jacobi Necessary Condition.- 6. The Simplest Problem in n Dimensions.- II The Optimal Control Problem.- 1. Introduction.- 2. Examples.- 3. Statement of the Optimal Control Problem.- 4. Equivalent Problems.- 5. Statement of Pontryagin's Principle.- 6. Extremals for the Moon Landing Problem.- 7. Extremals for the Linear Regulator Problem.- 8. Extremals for the Simplest Problem in Calculus of Variations.- 9. General Features of the Moon Landing Problem.- 10. Summary of Preliminary Results.- 11. The Free Terminal Point Problem.- 12. Preliminary Discussion of the Proof of Pontryagin's Principle.- 13. A Multiplier Rule for an Abstract Nonlinear Programming Problem.- 14. A Cone of Variations for the Problem of Optimal Control.- 15. Verification of Pontryagin's Principle.- III Existence and Continuity Properties of Optimal Controls.- 1. The Existence Problem.- 2. An Existence Theorem (Mayer Problem U Compact).- 3. Proof of Theorem 2.1.- 4. More Existence Theorems.- 5. Proof of Theorem 4.1.- 6. Continuity Properties of Optimal Controls.- IV Dynamic Programming.- 1. Introduction.- 2. The Problem.- 3. The Value Function.- 4. The Partial Differential Equation of Dynamic Programming.- 5. The Linear Regulator Problem.- 6. Equations of Motion with Discontinuous Feedback Controls.- 7. Sufficient Conditions for Optimality.- 8. The Relationship between the Equation of Dynamic Programming and Pontryagin's Principle.- V Stochastic Differential Equations and Markov Diffusion Processes.- 1. Introduction.- 2. Continuous Stochastic Processes Brownian Motion Processes.- 3. Ito's Stochastic Integral.- 4. Stochastic Differential Equations.- 5. Markov Diffusion Processes.- 6. Backward Equations.- 7. Boundary Value Problems.- 8. Forward Equations.- 9. Linear System Equations the Kalman-Bucy Filter.- 10. Absolutely Continuous Substitution of Probability Measures.- 11. An Extension of Theorems 5.1,5.2.- VI Optimal Control of Markov Diffusion Processes.- 1. Introduction.- 2. The Dynamic Programming Equation for Controlled Markov Processes.- 3. Controlled Diffusion Processes.- 4. The Dynamic Programming Equation for Controlled Diffusions a Verification Theorem.- 5. The Linear Regulator Problem (Complete Observations of System States).- 6. Existence Theorems.- 7. Dependence of Optimal Performance on y and ?.- 8. Generalized Solutions of the Dynamic Programming Equation.- 9. Stochastic Approximation to the Deterministic Control Problem.- 10. Problems with Partial Observations.- 11. The Separation Principle.- Appendices.- A. Gronwall-Bellman Inequality.- B. Selecting a Measurable Function.- C. Convex Sets and Convex Functions.- D. Review of Basic Probability.- E. Results about Parabolic Equations.- F. A General Position Lemma.

A theoretical description of the new phases of liquid He-3

Abstract: This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid $^{3}\mathrm{He}$. It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermi-liquid theory of Landau and its application to the normal phase of liquid $^{3}\mathrm{He}$, the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid $^{3}\mathrm{He}$ is considered, with emphasis on the spin-dependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a self-contained discussion of the "weak-coupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "Ginzburg-Landau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spin-dependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weak-coupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weak-coupling theory. An attempt is made to reformulate recent graph-theoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the so-called Anderson-Brinkman-Morel and Balian-Werthamer states, which are commonly identified with $^{3}\mathrm{He}$-A and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finite-wavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the A-normal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of $^{3}\mathrm{He}$-A and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "first-principles" theories of the effective interaction in $^{3}\mathrm{He}$ collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.

Indentation fracture: principles and applications

Abstract: The basic principles and practical applications of indentation fracture are reviewed.

Ataxia telangiectasia: a human mutation with abnormal radiation sensitivity

Abstract: ATAXIA telangiectasia (AT) is an autosomal recessive defect in man showing among the clinical features1 : cerebellar ataxia, telangiectasia, IgA deficiency, an enhanced frequency of malignancy and an enhanced level of spontaneous chromosome instability2 There have also been reports of increased sensitivity to X rays after radiotherapy3–5 and increased chromosome aberrations induced by ionising radiation in leukocyte cultures from AT patients6,7 We report here cell survival experiments which indicate that the clinically observed enhanced sensitivity of AT patients to ionising radiation is manifest at the cellular level

Microfracture beneath point indentations in brittle solids

Abstract: The microfracture patterns observed around point indentations in brittle solids are investigated. A description is first given of the stress field in an elastic half-space loaded normally at a point in its surface. This field is then used as a basis for analysing the crack geometry. A localized zone of irreversible deformation forms about the contact point, thereby removing a singularity in the elasticity solutions and providing nucleation centres for the ensuing microcracks. Generally, two main types of ‘vent’ cracks are observed to propagate from the deformation zone: median vents, formed during indenter loading, spread downward below the point of contact on planes of symmetry, and lateral vents, formed during unloading, spread sideways toward the specimen surface. Of these, the median vent is relatively well-behaved, and is amenable to standard fracture-mechanics analysis. From such an analysis we derive the means for predetermining, in principle, the depth of fracture damage under given point loading conditions. The significance of the results in relation to important practical applications, such as glass cutting and surface fragmentation processes, is discussed.

Visual control of flight behaviour in the hoverflySyritta pipiens L.

Abstract: 1. The visually guided flight behaviour of groups of male and femaleSyritta pipiens was filmed at 50 f.p.s. and analysed frame by frame. Sometimes the flies cruise around ignoring each other. At other times males but not females track other flies closely, during which the body axis points accurately towards the leading fly. 2. The eyes of males but not females have a forward directed region of enlarged facets where the resolution is 2 to 3 times greater than elsewhere. The inter-ommatidial angle in this “fovea” is 0.6°. 3. Targets outside the fovea are fixated by accurately directed, intermittent, open-loop body saccades. Fixation of moving targets within the fovea is maintained by “continuous” tracking in which the angular position of the target on the retina (Θe) is continuously translated into the angular velocity of the tracking fly (\(\dot \Phi _p \)) with a latency of roughly 20 ms (\(\dot \Phi _p = k \Theta _e \), wherek≏30 s−1). 4. The tracking fly maintains a roughly constant distance (in the range 5–15 cm) from the target. If the distance between the two flies is more than some set value the fly moves forwards, if it is less the fly moves backwards. The forward or backward velocity (\(\dot F_p \)) increases with the difference (D-D0) between the actual and desired distance (\(\dot F_p = k^\prime (D - D_0 )\)), wherek′=10 to 20 s−1). It is argued that the fly computes distance by measuring the vertical substense of the target image on the retina. 5. Angular tracking is sometimes, at the tracking fly's choice,supplemented by changes in sideways velocity. The fly predicts a suitable sideways velocity probably on the basis of a running averageΘe, but not its instantaneous value. Alternatively, when the target is almost stationary, angular tracking may bereplaced by sideways tracking. In this case the sideways velocity (\(\dot S\)) is related toΘe about 30 ms earlier (\(\dot S_p = k\prime \prime \Theta _e \), wherek″=2.5 cm · s−1 · deg−1), and the angular tracking system is inoperative. 6. When the leading fly settles the tracking fly often moves rapidly sideways in an arc centred on the leading fly. During thesevoluntary sideways movements the male continues to point his head at the target. He does this not by correctingΘe, which is usually zero, but by predicting the angular velocity needed to maintain fixation. This prediction requires knowledge of both the distance between the flies and the tracking fly's sideways velocity. It is shown that the fly tends to over-estimate distance by about 20%. 7. When two males meet head on during tracking the pursuit may be cut short as a result of vigorous sideways oscillations of both flies. These side-to-side movements are synchronised so that the males move in opposite directions, and the oscillations usually grow in size until the males separate. The angular tracking system is active during “wobbling” and it is shown that to synchronise the two flies the sideways tracking system must also be operative. The combined action of both systems in the two flies leads to instability and so provides a simple way of automatically separating two males. 8. Tracking is probably sexual in function and often culminates in a rapid dart towards the leading fly, after the latter has settled. During these “rapes” the male accelerates continuously at about 500 cm · s−2, turning just before it lands so that it is in the copulatory position. The male rapes flies of either sex indicating that successful copulation involves more trial and error than recognition. 9. During cruising flight the angular velocity of the fly is zero except for brief saccadic turns. There is often a sideways component to flight which means that the body axis is not necessarily in the direction of flight. Changes in flight direction are made either by means of saccades or by adjusting the ratio of sideways to forward velocity (\(\dot S/\dot F\)). Changes in body axis are frequently made without any change in the direction of flight. On these occasions, when the fly makes an angular saccade, it simultaneously adjusts\(\dot S/\dot F\) by an appropriate amount. 10. Flies change course when they approach flowers using the same variety of mechanisms: a series of saccades, adjustments to\(\dot S/\dot F\), or by a mixture of the two. 11. The optomotor response, which tends to prevent rotation except during saccades, is active both during cruising and tracking flight.

The intersection of potential energy surfaces in polyatomic molecules

Abstract: It is proved that if the wave function of a given electronic state changes sign when transported adiabatically round a loop in nuclear configuration space, then the state must become degenerate with another one at some point within the loop. It is further shown that this condition is satisfied by certain unsymmetrical triatomic systems, thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules.

X-ray analysis of glucagon and its relationship to receptor binding

Abstract: X-ray analysis of the pancreatic hormone glucagon shows that in crystals the polypeptide adopts a mainly helical conformation, which is stabilised by hydrophobic interactions between molecules related by threefold symmetry. A model is presented in which the glucagon molecule exists in dilute solutions as an equilibrium population of conformers with little retention of conformers with little retention of structure, and in which the helical conformation is stablised by hydrophobic interactions either as an oligomer or as a complex with the receptor.

Analysis of mathematical programming problems prior to applying the simplex algorithm

Abstract: Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them efficiently. The steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and discussed. An algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.

Colour receptors, and their synaptic connexions, in the retina of a cyprinid fish.

Abstract: Morphologically speaking, there are five kinds of cone cells in the retina of the rudd (Scardinius erythrophthalmus). But two of them, the principal elements of the double cones and the free principal cones, are probably functionally equivalent, while another, sparse, population of small (oblique) cones (which disappear in older fish), is unlikely to make a significant contribution to visual spectral sensitivity. Thus, principal and accessory cones (usually paired with one another), and single cones seem to be the three receptors which underlie the fish's trichromacy. Photographic densitometry of individual cone cells was used to provide evidence that accessory cones contain a green-absorbing photopigment and the single cones a blue one. Other arguments are given in support of those identifications, and they also strongly suggest that principal cones contain the red-absorbing pigment. Golgi-impregnated bipolar cells were examined electron-microscopically to determine the specific patterns of synaptic connexion they make with these different, anatomically identifiable, colour cones and with the retinal rods. Three principal arrangements were distinguished (see figure 69, page 100). (1) Rod bipolar cells comprise two distinct morphological types, both of which connect exclusively to principal (red) cones as well as to the rods within the outlines of their dendritic fields. (2) Selective cone bipolar cells, more delicate neurons with considerably wider dendritic fields, connect (according to type) to one or other of the different colour cone populations. Examples analysed were specific for the accessory (green) or for the single (blue) cones; no bipolar cells were found connected only to red cones. (3) Mixed cone bipolars have the smallest dendritic fields, and connect to combinations of cones (for example, red and green, or green and blue, but not red and blue). They also have synaptic input (usually relatively sparse) from the rods. Cells were encountered connecting to all three cone types, but they were only partially analysed, and are not described at length. The light microscopic morphology of these bipolar cell types consistently reflects the detailed pattern of connexion each makes with the different receptor populations (just as the morphology of the cones reflects the spectral properties of their photopigment). But while their synaptic connectivity is generally highly specific for cone type, they do occasionally make anomalous connexions with the 'wrong' receptors. There is a high degree of divergence (page 85) at the receptor-bipolar synapses, and the different kinds of cones each characteristically connect to different numbers of bipolar cells. Principal (red) cones, which are the most numerous, individually connect to more bipolars than cones of other types, whose characteristic synaptic divergence is likewise related to the frequency with which they occur in the retina. However, rods, which are much more numerous than cones, do not conform with this generalization. The selectivity with which the synaptic terminals of the different cones are connected together by their invaginating basal processes was also examined. These processes link neighbouring synaptic terminals of differently coloured cones: specifically, principal (red) cone basal processes invaginate accessory (green) cone pedicles, and vice versa. Single (blue) cone basal processes connect only to accessory cone pedicles, but that synaptic relation is not reciprocated. These synapses between the cones have important bearing upon interpretation of the bipolar cell connectivity patterns. In their light, the interaction between colour channels which the convergence of different cones onto the mixed cone bipolar dendrites mediates, seems to re-iterate a process already undertaken more peripherally. Likewise, whereas the anatomy of the selective cone bipolars appears designed to convey activity from the individual cone populations, the responses of the receptors they sample must already be influenced by activity in other colour channels.

The reduction of mono-coordinated molecular nitrogen to ammonia in a protic environment

Abstract: WE have reduced ligating molecular nitrogen (dinitrogen) to ammonia in yields of up to 90% at a single metal site This reaction is important for its possible application to our understanding of the chemical mechanism of the reduction of dinitrogen to ammonia by nitrogenase, where the reduction may occur at a single molybdenum ion site1 Our reaction occurs when compounds of the type [M(N2)2(PR3)4](I; M =Mo or W; R = alkyl or aryl) are treated at room temperature with sulphuric acid in methanol solution: This reaction was performed in a vacuum so that the evolved gases could be analysed and measured On mixing the reagents, one molecule of nitrogen gas was rapidly evolved with a trace of dihydrogen The remaining dinitrogen was spontaneously reduced to ammonia together with some hydrazine, presumably also with concomitant oxidation of the metal M

An atomistic model of kinetic crack growth in brittle solids

Abstract: A general theory of kinetic crack growth in ideally brittle solids is developed from first principles. In setting up a basic model, emphasis is placed on the essential need to provide for the existence of an energy barrier to activated, non-linear crack motions at the atomic level. The picture is presented of an ideally brittle fracture crack in which sequential bond rupture occurs via the lateral motion of atomic kinks along the crack front. Approximate solutions to the equations of kink motion are then obtained from the discrete, “lattice trapping” theory of Thomson and co-workers. Assuming a classical distribution of kink sites, an expression for the steady-state crack velocity follows. A feature of the present theory is the formulation in terms of the fundamental energy-balance concept of Griffith, with two major advantages: in the first place, standard fracture-mechanics parameters, such as the mechanical-energy-release rate and the fracture-surface energy, enter into the description in a natural manner; in the second, the effect of extrinsic agents on activated kink motion is readily accountable, through a simple modification of the total energy function for the crack system. To illustrate the model, the case of a slowly growing brittle crack in the presence of an interacting ideal gas environment is treated in some detail.

Diurnal variation in logical reasoning.

Abstract: Subjects performed two tests of logical reasoning at each of six different times of day. In terms of speed, performance on both tests was found to improve markedly from 08.00 to 14.00 and then to fall off fairly rapidly. Accuracy was found to decrease fairly linearly over the day. The results are interpreted as indicating that the different functions relating performance efficiency to time of day found by previous workers are due to differences in task demands rather than to individual differences. It is suggested that the larger the short-term memory component of a task the earlier in the day performance peaks.

A comparison of the 8-azaguanine and ouabain-resistance systems for the selection of induced mutant Chinese hamster cells.

Abstract: The forward mutation selection system based on resistance to 8-azaguanine has been widely used with cells cultured from a diversity of species and with a variety of mutagens. Ouabain resistance is an alternative selective system. Both systems show a substantial influence of expression time on the number of resistant variants observed after addition of the selective agent such that the frequency reaches a maximum which is dose dependent, and then declines rapidly. Metabolic cooperation has been proposed as the mechanism responsible for this decline with the 8-azaguanine system, but it is less likely to account for the loss of ouabain-resistant variants where it is necessary to invoke generalised effects on the viability of variants due to overcrowding on the plates. A comparison of the two selective systems showed that, with the exception of γ-irradiation, which was apparently non-mutagenic in the ouabain system, there was broad agreement between the two systems for each mutagen tested. Ethyl methanesulphonate was the most efficient mutagen by a substantial factor. Ouabain resistance permitted greater discrimination particularly between weak mutagens because of the low frequency of spontaneous variants (4 × 10−7) and also produced data with less intrinsic variability. The absence of γ ray induced mutation in the ouabain system shows that it may fail to detect certain types of mutagens. Thus the two systems should be used to complement each other. Mutation by the fungicide captan was evaluated using both systems and the positive results indicate that it may pose a hazard to man.

Is the evolution of insulin Darwinian or due to selectively neutral mutation

Abstract: A model for the evolution of insulin mainly in terms of adaptive processes is discussed. The model depends critically on the relationship of sequence changes to the three-dimensional structure and the role of various parts of this structure in the conversion of the proinsulin molecule to the active form, the storage of insulin, its transport to the site of action and its interaction with a receptor.

A photographic study of development in the living embryo of Drosophila melanogaster

Abstract: The changes which can be seen occurring during the development of a living embryo of Drosophila melanogaster are described in detail, and represented photographically as a series of developmental stages. This provides an easy, but accurate technique for selecting eggs at precise developmental stages for experiments.

The influence of caffeine on cell survival in excision-proficient and excision-deficient xeroderma pigmentosum and normal human cell strains following ultraviolet-light irradiation.

Abstract: • A uniform response to UV of four normal cell strains was demonstrated. One excision-proficient xeroderma pigmentosum variant strain (XP7TA) had a wild-type UV response but a second (XP30RO) was more sensitive. An excision-deficient xeroderma pigmentosum strain XP4LO was substantially more sensitive than wild-type cell strains. • A continuous post-irradiation treatment with non-toxic levels of caffeine enhanced the lethal effect of UV light in both xeroderma pigmentosum variant cell strains but not in cells from normal individuals. There was no detectable effect on cells from a xeroderma pigmentosum individual from complementation group A. These results correlate well with observations on the influence of caffeine on post-replication repair in the three classes of cells.

Visual spatial memory in a hoverfly

Abstract: 1. We have filmed maleEristalis sp. in their normal environment performing a sequence of behaviour which demonstrates that they have a memory of their position in space relative to visual landmarks in their surroundings. They hover stably in mid-air, periodically leaving their hovering station to chase passing insects. After the chase is over they return to approximately the same position in space. 2. The following findings indicate that they use visual cues to guide their return. The size of the “home” they return to depends on the proximity of landmarks, being more circumscribed the closer the landmarks are to the home (Figs. 3 and 4). The fly on its return decelerates as it approaches home (Figs. 7–10) and generally stops short of its previous hovering position (Fig. 6). The accuracy of the return is unaffected by the length of the previous chase (Fig. 5). 3. The fly seems able to return directly to its home from any direction (Fig. 10), though we have not been able to film the complete return after long chases. During the return the fly normally faces in the direction it is flying, though in the last stages it is not uncommon for it to be oriented at an angle of 40–60° to its line of flight. When hovering or flying slowly the fly changes orientation by rapid saccade-like movements and between saccades the orientation is kept very constant (Figs. 1, 2 and 10). 4. Flies will congregate and hover near to a single mobile marker placed in the middle of an empty lawn and, after a chase, return to a position close to it. If the marker is moved while flies are hovering near-by they follow the movement of the board if it approaches them (Fig. 12), but not if it retreats (Fig. 13). Thus by moving the board away it is possible to change the distance between the fly and the board. In these cases (Fig. 13) the fly remains stationary in its old position until it chases an insect, after which it returns not to this position, but to its original position with respect to the board before this was moved. This shows (1) the board must provide a cue guiding the return, and (2) the homing reflex does not operate constantly when the fly is hovering to correct for small involuntary displacements from a preferred position, but it is only turned on at certain times, for instance after a chase. 5. Blowflies perform a variant of the same behaviour: they bask on sunny walls waiting for passing insects which they chase, afterwards returning to approximately the same position on the wall (Fig. 16). Their resting site tends to shift slightly after each chase (Fig. 17), and an analysis of this drift indicates that they up-date their memory of home on each return. 6. In the Discussion we propose a model of how flies might use their memory of the position and form of landmarks as seen from their home to guide their return.

Theory of dielectric relaxation

Abstract: A theory of dielectric relaxation is presented which relates the frequency-dependent dielectric constant to a truly single-particle correlation function. For a sample of suitable geometry, linear response theory is used to relate the polarization to a many-particle correlation function. This correlation function is shown to have the same form as, and to be related to, a true single-particle correlation function; this relationship, proved in limited form elsewhere but generalized here, is the principal result of this work. This contrasts with the usual method of obtaining ‘ small ’ macroscopic correlation functions by reducing the sample dimension until it contains but a single particle, assuming all along that macroscopic dielectric theory is applicable. We are thus able to devise a relationship between the single-particle relaxation time and the observed many-particle relaxation time which will enable the dielectric relaxation data to be compared with reorientational relaxation times obtained in other ex...

Afterthoughts on analogical representations

Abstract: In 19711 wrote a paper attempting to relate some old philosophical issues about representation and reasoning to problems in Artificial Intelligence A major theme of the paper was the importance of distinguishing "analogical" from "Fregean" representations I still think the distinction is important, though perhaps not as important for current problems in AI as I used to think In this paper I'll try to explain why

The relation of conformation and association of insulin to receptor binding; x-ray and circular-dichroism studies on bovine and hystricomorph insulins.

Abstract: Crystal and solution structure studies on insulins of different sequences and of widely different receptor binding affinities are reported. Bovine insulin, studied as a control, has a circular dichroism spectrum which is dependent both on protein concentration and zinc concentration. The spectrum appears to be related to the level of association of the insulin molecules. This implies that when using circular dichroism to compare solution structures of insulin derivatives or species variants one must make the comparison at equivalent levels of association and not merely at the same concentration. Changes in circular dichroism are related to the known crystal structure of zinc insulin hexamers. The chinchilla insulin spectrum shows a reduced zinc dependence in low-salt conditions which correlates with the inability to form crystals in similar conditions. This is attributed to an amino acid substitution at position B4. Crystals are obtained in high-salt conditions and X-ray diffraction patterns show these to be isomorphous with bovine 4Zn insulin crystals. Guinea pig insulin failed to crystallise under conditions which are normally conducive to the formation of crystals of zinc insulin hexamers and the circular dichroism showed no zinc dependence. This is consistent with a monomeric structure. The significance of the association behaviour of chinchilla and guinea pig insulins may be in the storage of the hormone in vivo. Whereas the monomeric form of chinchilla insulin has a structure closely related to bovine insulin, the circular dichroism indicates a gross structural difference for guinea pig insulin. This may be similar to that in des-A21, des-B30-insulin, as both lack the Arg-B22--Asn-A21 carboxylate ion pair. The similarity of structure of chinchilla and bovine insulins is reflected in their receptor binding whereas the low receptor binding of guinea pig insulin probably results from the changes in its conformation rather than an alteration in residues of a receptor binding region.

Lipid requirement of the membrane sodium-plus-potassium ion-dependent adenosine triphosphatase system.

Abstract: The dependence of the (Na-++K-+)-dependent ATPase (adenosine triphosphatase) (EC 3613) on lipid has been examined in a number of different ways, with the use of various preparations from kidney tissue The main findings were as follows (1) The ATPase activities of the preparations examined were closely correlated with their total phospholipid content (2) Extraction of the ATPase with deoxycholate or Lubrol W, combined with suitable salt-fractionation and washing procedures, removed phospholipid, cholesterol and enzymic activity in parallel; but activity was completely lost before all lipid had been removed (3) The loss of activity could not be attributed to inhibition by residual detergent (4) No selective removal of any particular phospholipid class by detergent could be detected (5) Consistent reactivation of the Lubrol-extracted enzymes was obtained by adding dispersions of exogenous phospholipid, but only some, bearing a net negative charge, such as phosphatidylserine and phosphatidylglycerol, were effective (6) The degree of reactivation was correlated with the amount of residual activity remaining after lipid depletion (7) Partial purification of the ATPase, giving a 50-fold increase in specific activity, was not accompanied by selective enhancement of any particular class of phospholipid We conclude that although the ATPase is dependent on phospholipid, only the reactivation results provide evidence for specificity