On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Transition temperature and enthalpy change dependence on stabilizing and destabilizing ions in the helix–coil transition in native tendon collagen

The transition temperatures t_t and enthalpy changes ΔH in the helix–coil transition of solid tendon collagen soaked in a solution containing one of the following stabilizing or destabilizing agents, HCHO, NaF, NaCl, NaI, NaBr, NaOH, NH₂CONH₂, CaCl₂, MgCl₂, were measured as a function of molar concentration by a calorimetric method. The temperature and the enthalpy changes accompanying the transition behaved in a similar manner: when the t_t was depressed by the presence of ions, similar behaviour was observed in ΔH. Both parameters (t_t and ΔH) increased for HCHO, and decreased for NaF and NaCl at concentrations lower than 0.2 M. Above 0.2 M they increased for NaF and NaCl, and decreased in the presence of the other reagents listed above. The average t_t and the ΔH observed in collagen soaked in water were 63.5°C and 12.3 cal/g, respectively. In addition to the parameters mentioned above, the molar effectiveness of the various reagents was obtained for the cases where there was a linear relationship between the t_t and molar concentration of the reagent in the solution. Since both the t_t and the ΔH were observed to vary, the entropy change (ΔS) accompanying the transition was calculated using thermodynamic relations. In order to explain the ΔS observed as a function of ionic concentration, the thermodynamic relationships have been obtained from a partition function under suitable assumptions. Since the partition function is dependent on the number of hydrogen bonds responsible for collagen stability, the result obtained has been compared with the values predicted by the two most quoted models for collagen. The present study is in accordance with the Ramachandran model for collagen structure, which predicts more than one hydrogen bond per three residues.     

Activity coefficients of KCl in highly concentrated protein solutions

As a contribution to the understanding of the thermodynamic state of single salts in living systems, the activity coefficients of KCl were determined in concentrated bovine serum albumin (BSA) solutions. The concentration range studied was 0.01 to 0.5 M KCl and zero to 18% wt BSA, thus amply covering physiological conditions. The activity coefficients of the salt were measured using the EMF method with ion exchange membrane electrodes. Keeping the salt concentration constant, the activity coefficients of the salt decrease linearly with protein concentration, the effect being more pronounced for low salt content. The maximal deviations of the activity coefficients with respect to those in pure salt solution amount to ca. 40% for 0.01 M KCl and 18% wt BSA. The results were interpreted on the assumption of the superposition of three effects i.e. water bound to BSA molecules as non-solvent water, specific Cl^– ion binding and the electrostatic interactions of the polyions with the salt ions. In view of the results it can be concluded that only a small portion of simple intracellular ions are bound, based on the assumption that the cytoplasm of living cells may be regarded as a concentrated protein-salt solution.     

Malthusian parameters,reproductive values and change under selection in self fertilizing age-structured populations

A population, reproducing wholly by selfing, is assumed to be observed at times . Individuals between x–1 and x units of age at time t are said to be in age class x at that time. The rate of increase in the long run of individuals of type A_iAj is denoted by m_ij+1=m_ji+1. For each genotype there is also a set of reproductive values, corresponding to all age classes and genotypes of individuals having descendants of that genotype. Then, if the number of individuals of each sort of ancestor is multiplied by its reproductive value and the products are summed, the result is the total value, which is V_ij(t) for genotype A_iAj. Then V_ij(t+1)–V_ij(t) is equal to m_ijV_ij(t), where m_ij is the Malthusian parameter for A_iAj. Furthermore, if the mean and variance at time t of the m_ijs, weighted by their corresponding reproductive values, are respectively (t) and _m²(t), then m¯(t+1)–m¯(t)=_m²(t)/(1+m¯(t)).     

A new pathway in the photoreaction cycle of trans-bacteriorhodopsin and the absorption spectra of its intermediates

The intermediates of trans-bacteriorhodopsin (trans-bR) in the photoreaction cycle were investigated under two different conditions. In a low salt and neutral pH medium (10 mM phosphate buffer, pH 6.6), trans-bR was irradiated with 500 nm light at –190 C, resulting in formation of batho-trans-bR (batho-bR^t). On warming in the dark, batho-bR^t converted to lumi-trans-bR (lumi-bR^t), meta-trans-bR (meta-bR^t) and finally to trans-bR. The intermediates N and O, which had been detected by others by flash photolysis, were not observed. The thermal decay of lumi-bR^t in a high salt and high pH medium (10 mM borate buffer with l M NaCl, pH 10.0) proceeded simultaneously through two pathways; one to meta-bR^t and another to trans-bR. About 72% of lumi-bR^t converted to trans-bR directly and the residue converted to meta-bR^t. By use of this value, the absorption spectra of batho-bR^t (_max: 626 nm), lumi-bR^t (_max: 543 nm) and meta-bR^t (_max: 418 nm) were calculated. A photoreaction cycle of bacteriorhodopsin was proposed on the basis of the above findings.     

Slow conductance changes due to potassium depletion in the transverse tubules of frog muscle fibers during hyperpolarizing pulses

Summary When hyperpolarizing currents are applied between the inside and outside of a muscle fiber it is known that there is a slow transient decrease (300- to 600-msec time constant) in the measured fiber conductance sometimes referred to as creep which is maximal in K₂SO₄ Ringer's solutions and which disappears on disruption of the transverse tubular system. An approximate mathematical analysis of the situation indicates that these large, slow conductance changes are to be expected from changes in the K⁺ concentration in the tubular system and are due to differences in transport numbers between the walls and lumen of the tubules. Experiments using small constant-voltage and constant-current pulses (membrane p. d. changes 20 to 30 mV) on the same fibers followed by an approximate mathematical and more exact computed numerical analysis using the measured fiber parameters and published values of tubular system geometry factors showed close agreement between the conductance creep predicted and that observed, thus dispensing with the need for postulated changes in individual membrane conductances at least during small voltage pulses. It is further suggested that an examination of creep with constant-voltage and constant-current pulses may provide a useful tool for monitoring changes in tubular system parameters, such as those occurring during its disruption by presoaking the fibers in glycerol.Table of main symbols used R, T, F Gas constant, Temperature in °K and the Faraday - a Fiber radius - r Radial distance from the center of the fiber (cf. Fig. 2A) - t Time in sec - V ₁,V ₂ Voltages measured by electrodes 1 and 2 (cf. p. 248) - Longitudinal fiber space constant ( ²=R _m a/2R _i ) - R _m ,R _m (t) Total membrane resistance per unit surface area of fiber ( cm²) - R _m (0),R _m () As above att=0 (excluding capacity transient) and att= during a current or voltage pulse - G _m ,G _m (t) Total membrane conductance (mho·cm^–2) per unit area of fiber surface - G _m (0),G _m () As above att=0 (excluding the capacity transient) and att= during a current or voltage pulse - R _sm ,G _sm Surface membrane resistance ( cm²) and conductance (mho·cm^–2), respectively, excluding the TTS - R _T ,G _T Input resistance ( cm²) and conductance (mho·cm^–2) of the TTS referred to unit area of fiber surface - f _T Fraction of the K⁺ conductance in the TTS to the total K⁺ conductance of the fiber [cf. Eq. (7)] - R _i Internal resistivity of the fiber ( cm) - r _s Electrical access resistance of the TTS [ cm²;cf. Fig. 3 and Eq. (24)] - h Diffusional access resistance of the TTS [cf. Eq. (27)] - I ₀ Total current entering fiber (amp) - I _m ,i _m Total current per unit area of fiber surface (amp·cm^–2; considered positive in the hyperpolarizing direction) - i _sm Current going through the surface membrane alone (amp·cm^–2;cf. Fig. 3) - i ₀,i ₀(t) Total current entering the TTS referred to unit area of surface membrane (amp·cm^–2;cf. Fig. 3) - I _K,I _K(r) K⁺ current density crossing the equivalent TTS disc at radial distancer [cf. Fig. 2A and Eq. (23)] - i, i(r, t) Radial current in the lumen of the TTS at radial distancer and timet (cf. Fig. 2B) - C, C(r, t) K⁺ concentration within the TTS at radial distancer and timet (mEquiv·liter^–1) - C _o ,C _K Both refer to external solution and initial TTS K⁺ concentration (mEquiv·liter^–1) - V, V(r, t) The potential at radial distancer in the lumen of the TTS with respect to the external solution at timet (cf. Figs. 2 and 3) - V(a), V(a, t) The p.d. across the access resistance (cf. Figs. 3B and 3C) - V ₀,V ₀(t) The potential of the sarcoplasm with respect to the external solution (cf. Figs. 2 and 3) - E _K The K⁺ equilibrium potential between the sarcoplasm and the externa solution or across the tubular wall - t _K ^m ,t _K ^s The transport number for K⁺ in the TTS membranes and in the solution of the tubular lumen, respectively - The fraction of fiber volume occupied by tubules, and not implicitly including branches - As above but always including branches - A dimensionless network factor for the TTS - G _W Conductance per unit area of tubular wall (mho·cm^–2) - G _L Conductance of tubular lumen (mho·cm^–1) - Volume-to-surface ratio of the TTS - Effective wall conductance of TTS membranes per unit volume of fiber [mho·cm^–3;cf. Eq. (14)] - Effective radial conductance of the lumen of the TTS per unit volume of fiber [cf. Eq. (20)] - d The thickness of the equivalent disc representing the TTS [cf. Eq. (15)] - _T Space constant of the TTS [cf. Eq. (37).cp. Eq. (11)] - D _K The diffusion coefficient of K⁺ ions in the lumen of the TTS (cm² sec^–1) - The effective radial K⁺ diffusion coefficient in the TTS [cf. Eq. (28)] - J ₀,J ₁ Bessel functions of order 0 and 1, respectively - I ₀,I ₁ Modified Bessel functions of order 0 and 1, respectively - Time constants of slow conductance changes - _vc Time constant of slow conductance changes during a constant-voltage pulse - _cc Time constant of slow conductance changes during a constant-current pulse - , _m Roots of various Bessel function equations - g ₁,g ₂,g ₃,g ₄ Constants used to fit cubic equation for conductance-voltage curves [cf. Eq. (71)]     

A simulation program based on a structured population model for biotechnological yeast processes

Summary A segregated population model for budding yeasts and a simulation program based on it are presented. They enable the study of bioprocesses utilizing yeasts in steady and perturbed conditions and in particular the comparison between the model predictions and the experimental results obtained by flow cytometry, which allows the measurement of segregated parameters of cell populations.Nomenclature a genealogical age - A parameter of the budding law - CV coefficient of variation - F _in(t) volumetric input flow - F _out(t) volumetric output flow - h parameter of the division law - K _s parameter of the Monod's law - m cell mass - M _i discretized cell mass - m _b (a,s) critical mass level for budding - m _p cell mass at the time of budding - n(t) cell number per unit volume - n _p number of sub-populations - n _c number of channels - p (a, i, j, k) discrete density function - Q parameter of the budding law - s(t) substrate concentration - S _in(t) substrate concentration in the input flow - t time - T _m minimal length of the budded phase - V(t) culture volume - x(t) biomass concentration - Y yield coefficient - channel width - (s) specific growth rate - _max parameter of the Monod's law     

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

Effects of salt stress on the growth,ion content,stomatal behaviour and photosynthetic capacity of a salt-sensitive species,Phaseolus vulgaris L.

Phaseolus vulgaris (cv. Hawkesbury Wonder) was grown over a range of NaCl concentrations (0–150 mM), and the effects on growth, ion relations and photosynthetic performance were examined. Dry and fresh weight decreased with increasing external NaCl concentration while the root/shoot ratio increased. The Cl^- concentration of leaf tissue increased linearly with increasing external NaCl concentration, as did K⁺ concentration, although to a lesser degree. Increases in leaf Na⁺ concentration occurred only at the higher external NaCl concentrations (100 mM). Increases in leaf Cl^- were primarily balanced by increases in K⁺ and Na⁺. X-ray microanalysis of leaf cells from salinized plants showed that Cl^- concentration was high in both the cell vacuole and chloroplast-cytoplasm (250–300 mM in both compartments for the most stressed plants), indicating a lack of effective intracellular ion compartmentation in this species. Salinity had little effect on the total nitrogen and ribulose-1,5-bisphosphate (RuBP) carboxylase (EC 4.1.1.39) content per unit leaf area. Chlorophyll per unit leaf area was reduced considerably by salt stress, however. Stomatal conductance declined substantially with salt stress such that the intercellular CO₂ concentration (C _i) was reduced by up to 30%. Salinization of plants was found to alter the ¹³C value of leaves of Phaseolus by up to 5 and this change agreed quantitatively with that predicted by the theory relating carbon-isotope fractionation to the corresponding measured intercellular CO₂ concentration. Salt stress also brought about a reduction in photosynthetic CO₂ fixation independent of altered diffusional limitations. The initial slope of the photosynthesis versus C _i response declined with salinity stress, indicating that the apparent in-vivo activity of RuBP carboxylase was decreased by up to 40% at high leaf Cl^- concentrations. The quantum yield for net CO₂ uptake was also reduced by salt stress.Abbreviations and symbols A net CO₂ assimilation rate - C _a ambient CO₂ concentration - C _i intercellular CO₂ concentration - RuBP ribulose-1,5-bisphosphate - ¹³C ratio of ¹³C to ¹²C relative to standard limestone     

Current–voltage–time records of ion translocating enzymes

Membrane currents, as non-linear functions of membrane voltage, V, and time, t, can be recorded quickly by triangular V protocols. From the differences, dI(V,t), of these relationships upon addition of a putative substrate of a charge-translocating membrane protein, the I(V,t) relationships of the transporter itself can be determined. These relationships likely comprise a steady-state component, I_a(V), of the active transporter, and a dynamic component, p_a(V,t), of its V- and time-dependent activity, p_a. Here, the steady-state component is modeled by a central reaction cycle, which senses a fraction _tr of the total V, whereas 1–_tr can be assigned to an inner and outer pore section with _i and _o, respectively (_i+_tr+_o = 1). For the enzymatic cycle, fast binding/debinding is assumed, plus V-sensitive and -insensitive reaction steps which may become rate limiting for charge translocation. At given substrate concentrations, I_a(V) is defined by eight independent system parameters, including a coefficient for the barrier shape of charge translocation. In ordinary cases, the behavior of p_a(V,t) can be described by two rate constants (for activation and inactivation) and their respective V-sensitivity coefficients. Here, the effects of the individual system parameters on I(V,t) from triangular V-clamp experiments are investigated systematically. The results are illustrated by panels of typical curve shapes for non-gated and gated transporters to enable a first classification of mechanisms. We demonstrate that all system parameters can be determined fairly well by fitting the model to experimental data of known origin. Applicability of the model to channels, pumps and cotransporters is discussed.     

Energetics of Contraction in Phasic and Tonic Skeletal Muscles of the Chicken

Comparative energetics of chicken latissimus dorsi muscles, tonic anterior (ALD) and phasic posterior (PLD), were investigated by measuring initial heat production. Heat components were analyzed in terms of the equation: E = A + W + α_F(L) + f(P, t) As the muscles were stretched by increments, heat produced in isometric twitches and tetani decreased in a linear fashion. Two processes are involved: one tension independent, the activation heat, or A; and the other tension dependent, W_i + α_F(L) + f(P, t). In twitches, A, per unit tension, is equivalent in the PLD and ALD. Tension-dependent heat, per unit tension, is greater in the PLD due to W_i; but tension-time-related heat, f(P, t), per unit tension, is similar in both muscles. In tetanic contractions, differences in A and f(P, t), per unit tension, are attributed to the greater V_max in the PLD. The differences in the energetics of isometric contractions in the PLD and ALD, therefore, can be explained by inherent differences in tension development, compliance, and myosin and reticular ATPase activities. Data from isotonic twitches were quantified by means of the equivalent tension technique. Both muscles exhibited an extra heat associated with shortening, α_F(L). In the PLD, the ratio α_F/P_ot is greater; it is load independent and ½ the value of a/P_o in both muscles. Enthalpy efficiency, W_e + W_i/E, is comparable in both muscles. A Fenn effect is observed only when isotonic energy liberation is compared to a decreasing isometric energy expenditure base line.     

Redistribution of cell membrane probes following contraction-induced injury of mouse soleus muscle

Our aim was to study how mouse skeletal muscle membranes are altered by eccentric and isometric contractions. A fluorescent dialkyl carbocyanine dye (DiOC₁₈(3)) was used to label muscle membranes, and the membranes accessible to the dye were observed by confocal laser scanning microscopy. Experiments were done on normal mouse soleus muscles and soleus muscles injured by 20 eccentric or 20 isometric contractions. Longitudinal optical sections of control muscle fibers revealed DiOC₁₈(3) staining of the plasmalemma and regularly spaced transverse bands corresponding in location to the T-tubular system. Transverse optical sections showed an extensive reticular network with the DiOC₁₈(3) staining. Injured muscle fibers showed distinctively different staining patterns in both longitudinal and transverse optical sections. Longitudinal optical sections of the injured fibers revealed staining in a longitudinally-oriented pattern. No correlations were found between the abnormal DiOC₁₈(3) staining and the reductions in maximal isometric tetanic force or release of lactate dehydrogenase (P0.32). Additionally, no difference in the extent of abnormal staining was found between muscles performing eccentric contractions and those performing the less damaging isometric contractions. However, many fibers in muscles injured by eccentric contractions showed swollen regions with marked loss of membrane integrity and an elevated free cytosolic calcium concentration as observed in Fluo-3 images. In conclusion, a loss of cell membrane integrity results from contractile activity, enabling DiOC₁₈(3) staining of internal membranes. The resulting staining pattern is striking and fibers with damaged cell membranes are easily distinguished from uninjured ones.     

Chondrogenesis and hypertrophy in response to aggregate behaviors of human mesenchymal stem cells on a dendrimer-immobilized surface

Objectives

To investigate the behaviors of aggregates of human mesenchymal stem cells (hMSCs) on chondrogenesis and chondrocyte hypertrophy using spatiotemporal expression patterns of chondrogenic (type II collagen) and hypertrophic (type X collagen) markers during chondrogenesis.

Results

hMSCs were cultured on either a polystyrene surface or polyamidoamine dendrimer surface with a fifth generation (G5) dendron structure in chondrogenic medium and growth medium. At day 7, cell aggregates without stress fibers formed on the G5 surface and triggered differentiation of hMSCs toward the chondrogenic fate, as indicated by type II collagen being observed while type X collagen was undetectable. In contrast, immunostaining of hMSCs cultured on polystyrene, which exhibited abundant stress fibers and did not form aggregates, revealed no evidence of either type II and or type X collagen. At day 21, the morphological changes of the cell aggregates formed on the G5 surface were suppressed as a result of stress fiber formation. Type II collagen was observed throughout the aggregates whereas type X collagen was detected only at the basal side of the aggregates. Change of cell aggregate behaviors derived from G5 surface alone regulated chondrogenesis and hypotrophy, and this was enhanced by chondrogenic medium.

Conclusions

Incubation of hMSCs affects the expression of type II and X collagens via effects on cell aggregate behavior and stress fiber formation.

     

Evolution under the multilocus Levene model without epistasis

Evolution under the multilocus Levene model is investigated. The linkage map is arbitrary, but epistasis is absent. The geometric-mean fitness, , depends only on the vector of gene frequencies, ρ; it is nondecreasing, and the single-generation change is zero only on the set, Λ, of gametic frequencies at gene-frequency equilibrium. The internal gene-frequency equilibria are the stationary points of . If the equilibrium points of ρ(t) (where t denotes time in generations) are isolated, as is generic, then ρ(t) converges as t→∞ to some . Generically, ρ(t) converges to a local maximum of . Write the vector of gametic frequencies, p, as , where d represents the vector of linkage disequilibria. If is a local maximum of , then the equilibrium point is asymptotically stable. If either there are only two loci or there is no dominance, then d(t)→0 globally as t→∞. In the second case, has a unique maximum and is globally asymptotically stable. If underdominance and overdominance are excluded, and if at each locus, the degree of dominance is deme independent for every pair of alleles, then the following results also hold. There exists exactly one stable gene-frequency equilibrium (point or manifold), and it is globally attracting. If an internal gene-frequency equilibrium exists, it is globally asymptotically stable. On Λ, (i) the number of demes, Γ, is a generic upper bound on the number of alleles present per locus; and (ii) if every locus is diallelic, generically at most Γ−1 loci can segregate. Finally, if migration and selection are completely arbitrary except that the latter is uniform (i.e., deme independent), then every uniform selection equilibrium is a migration-selection equilibrium and generically has the same stability as under pure selection.     

Kidney concentrating ability of a subterranean xeric rodent,the naked mole-rat (Heterocephalus glaber)

The naked mole-rat (Heterocephalus glaber) is a strictly subterranean mammal inhabiting the arid zones of north-east Africa. These animals have no access to free water and water balance thus might be facilitated by regulating renal water loss. The urinary concentrating ability of the naked mole-rat was determined using five dietary manipulations in which both water and salt content were altered. Control animals (n=7) received a high quality protein cereal mixed to a thin paste with water (1 g cereal: 85 g water). Water stress was induced by reducing the water content of the diet by either 50% (n=7) or 65% (n=7). Salt loading was facilitated by replacing the water with the same volume of either 0.9% salt (n=7) or 3.0% salt (n=4) solutions. Changes in body mass, food consumption and urine volume were measured daily. The effect of diet on osmolality and electrolyte concentrations of urine and plasma were determined on termination of the diet trials. Although energy intake was not reduced, naked mole-rats lost body weight with both water stress treatments. Urine volume voided per day decreased significantly with both water stress treatments (P<0.05), such that the most extreme water stress led to an 80% reduction in urine volume. Mildly salt-loaded animals gained weight, yet underwent a sodium diuresis, as indicated by a 1.3-fold increase in the daily volume of urine voided (P<0.05). Maximum urine concentration (1521±250 mmol·kg^-1) was achieved with mild water stress and was 4.6±0.9 times that of plasma. Neither further water stress nor salt loading further increased urine osmolality (P>0.05). The naked mole-rat exhibits a moderate kidney concentrating ability and cannot maintain plasma osmolality or body mass with either extreme water stress or salt loading. Although this species succesfully inhabits arid zones, survival in these areas is not facilitated by renal water conservation, but rather by their underground existence in a microhabitat where humidities are high and radiant heat loads low. In this milieu a moderate kidney concentrating ability is adequate.Abbreviations Bm body mass - ESL extreme salt load - EWS extreme water stress - MSL mild salt load - MWS mild water stress     

A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

It is proposed that distinct anatomical regions of cerebral cortex and of thalamic nuclei are functionally two-dimensional. On this view, the third (radial) dimension of cortical and thalamic structures is associated with a redundancy of circuits and functions so that reliable signal processing obtains in the presence of noisy or ambiguous stimuli.A mathematical model of simple cortical and thalamic nervous tissue is consequently developed, comprising two types of neurons (excitatory and inhibitory), homogeneously distributed in planar sheets, and interacting by way of recurrent lateral connexions. Following a discussion of certain anatomical and physiological restrictions on such interactions, numerical solutions of the relevant non-linear integro-differential equations are obtained. The results fall conveniently into three categories, each of which is postulated to correspond to a distinct type of tissue: sensory neo-cortex, archior prefrontal cortex, and thalamus.The different categories of solution are referred to as dynamical modes. The mode appropriate to thalamus involves a variety of non-linear oscillatory phenomena. That appropriate to archior prefrontal cortex is defined by the existence of spatially inhomogeneous stable steady states which retain contour information about prior stimuli. Finally, the mode appropriate to sensory neo-cortex involves active transient responses. It is shown that this particular mode reproduces some of the phenomenology of visual psychophysics, including spatial modulation transfer function determinations, certain metacontrast effects, and the spatial hysteresis phenomenon found in stereopsis.List of Symbols (t) Post-synaptic membrane potential (psp) - Maximum amplitude of psp - t Time - The neuronal membrane time constant - Threshold value of membrane potential - r Absolute refractory period - Synaptic operating delay - v Velocity of propagation of action potentil - x Cartesian coordinate - _jj (x) The probability that cells of class j are connected with cells of class j a distance x away - b _jj The mean synaptic weight of synapses of the jj-th class at x - _jj The space constant for connectivity - _e Surface density of excitatory neurons in a one-dimensional homogeneous and isotropic tissue - _i Surface density of inhibitory neurons in a one-dimensional homogeneous and isotropic tissue - E(x, t) Excitatory Activity, proportion of excitatory cells becoming active per unit time at the instant t, at the point x - I(x, t) Inhibitory Activity, proportion of inhibitory cells becoming active per unit time at the instant t, at the point x - x A small segment of tissue - t A small interval of time - P(x, t) Afferent excitation or inhibition to excitatory neurons - Q(x, t) Afferent excitation or inhibition to inhibitory neurons - N _e (x, t) Mean integrated excitation generated within excitatory neurons at x - N _i (x, t) Mean integrated excitation generated within inhibitory neurons at x - _e [N _e ] Expected proportion of excitatory neurons receiving at least threshold excitation per unit time, as a function of N _e - _i [N _i ] Expected proportion of inhibitory neurons receiving at least threshold excitation per unit time, as a function of N _i - G( _e ) Distribution function of excitatory neuronal thresholds - G( ₁ ) Distribution function of inhibitory neuronal thresholds - ₁ A fixed value of neuronal threshold - h(N _e ; ₁) Proportion per unit time of excitatory neurons at x reaching ₁ with a mean excitation N _e - 1[ ] Heaviside's step-function - R _e (x, t) Number of excitatory neurons which are sensitive at the instant t - R _i (x, t) Number of inhibitory neurons which are sensitive at the instant t - R _e Refractory period of excitatory neurons - r _i Refractory period of inhibitory neurons - E(x, t) Time coarse-grained excitatory activity - I(x, t) Time coarse-grained inhibitory activity - Spatial convolution - Threshold of a neuronal aggregate - v Sensitivity coefficient of response of a neuronal aggregate - E(t) Time coarse-grained spatially localised excitatory activity - I(t)> Time coarse-grained spatially localised inhibitory activity - L ₁,L ₂,L,Q See § 2.2.1, § 2.2.7, § 3.1 - Velocity with which retinal images are moved apart - Stimulus width - E _o, I _o Spatially homogeneous steady states of neuronal activity - k _e ,k _ij S _e S _ij See § 5.1     

Optimal control of continuous fermentation processes

Three layer control structure is proposed for optimal control of continuous fermentation processes. The start-up optimization problems are solved as a first step for optimization layer building. A steady state optimization problem is solved by a decomposition method using prediction principle. A discrete minimum time optimal control problem with state delay is formulated and a decomposition method, based on an augmented Lagrange's function is proposed to solve it. The problem is decomposed in time domain by a new coordinating vector. The obtained algorithms are used for minimum time optimal control calculation of Baker's Yeast fermentation process.List of Symbols x(t) g/l biomass concentration - s(t) g/l limiting substrate concentration - x ⁰ g/l inlet biomass concentration - s ⁰(t) g/l inlet substrate concentration - D(t) h^–1 dilution rate - (t) h^–1 specific growth rate - Y g/g yield coefficient - (t) h^–1 specific limiting substrate consumption rate - k _D h^–1 disappearing constant - w ₁, w ₂ known constant or piece-wise disturbances - _m h^–1 maximum specific growth rate - k _s g/l Michaelis-Menten's parameter - h time delay - x ₀, s ₀ g/l initial concentrations - ¯x, ¯s, ¯D optimal steady state value - V _min , V _max , v=x,s,d,t bounds of variables - t h sampling period - K number of steps in the optimization horison - Js, J _d performance indexes - L _s Lagrange's function - L _d Lagrange's functional - ₀ weighting coefficient for the amount of the limiting substrate throwing out of the fermentor - ₁, ₂ dual variables of Lagrange's function - steps in steady state coordination procedure - errors values for steady state coordination process - _v , v=x, s conjugate variables of Lagrange's functional - _v , v=x,s penalty coefficients of augmented Lagrange's functional - _v , v=x, s interconnections of the time - e _v , v=x,s, D, _x , _s gradients of Lagrange's functional - j, l indexes of calculation procedures - values of errors in calculations The researches was supported by National Scientific Research Foundation under grants No NITN428/94 and No NITN440/94