Landscape and global stability of nonadiabatic and adiabatic oscillations in a gene network

We quantify the potential landscape to determine the global stability and coherence of biological oscillations. We explore a gene network motif in our experimental synthetic biology studies of two genes that mutually repress and activate each other with self-activation and self-repression. We find that in addition to intrinsic molecular number fluctuations, there is another type of fluctuation crucial for biological function: the fluctuation due to the slow binding/unbinding of protein regulators to gene promoters. We find that coherent limit cycle oscillations emerge in two regimes: an adiabatic regime with fast binding/unbinding and a nonadiabatic regime with slow binding/unbinding relative to protein synthesis/degradation. This leads to two mechanisms of producing the stable oscillations: the effective interactions from averaging the gene states in the adiabatic regime; and the time delays due to slow binding/unbinding to promoters in the nonadiabatic regime, which can be tested by forthcoming experiments. In both regimes, the landscape has a topological shape of the Mexican hat in protein concentrations that quantitatively determines the global stability of limit cycle dynamics. The oscillation coherence is shown to be correlated with the shape of the Mexican hat characterized by the height from the oscillation ring to the central top. The oscillation period can be tuned in a wide range by changing the binding/unbinding rate without changing the amplitude much, which is important for the functionality of a biological clock. A negative feedback loop with time delays due to slow binding/unbinding can also generate oscillations. Although positive feedback is not necessary for generating oscillations, it can make the oscillations more robust.     

Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e., regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.     

Numerical Analysis of Granular Flows in a Silo Bed on Flow Regime Characterization

The flow characteristics of a gravity-driven dense granular flow in a granular bed with a contracted drainage orifice are studied by using discrete element method and quantitative analysis. Three values of discharging rates, ranging from fast to slow dense flows, are investigated. Time variations and derivatives of mean forces and velocities, as well as their respective correlations, are analyzed to quantitatively depict the characteristics of granular flow as well as flow regime categorization. The auto-correlation functions, as well as their Fourier spectrums, are utilized to characterize the differences between the mechanisms of slow and fast granular flows. Finally, it is suggested that the flow regimes of slow and fast flows can be characterized by the kinetic and kinematic flow properties of particles.     

Endotoxin inactivation via steam‐heat treatment in dilute simethicone emulsions used in biopharmaceutical processes

Simethicone emulsion is used to regulate foaming in cell culture operations in biopharmaceutical processes. It is also a potential source of endotoxin contamination. The inactivation of endotoxins in dilute simethicone emulsions was assessed as a function of time at different steam temperatures using a Limulus amebocyte lysate kinetic chromogenic technique. Endotoxin inactivation from steam‐heat treatment was fit to a four‐parameter double exponential decay model, which indicated that endotoxin inactivation was biphasic, consisting of fast and slow regimes. In the fast regime, temperature‐related effects were dominant. Transitioning into the slow regime, the observed temperature dependence diminished, and concentration‐related effects became increasingly significant. The change in the Gibbs free energy moving through the transition state indicated that a large energy barrier must be overcome for endotoxin inactivation to occur. The corresponding Arrhenius pre‐exponential factor was >>10¹² s^?1 suggesting that endotoxins in aqueous solution exist as aggregates. The disorder associated with the endotoxin inactivation reaction pathway was assessed via the change in entropy moving through the transition state. This quantity was positive indicating that endotoxin inactivation may result from hydrolysis of individual endotoxin molecules, which perturbs the conformation of endotoxin aggregates, thereby modulating the biological activity observed. Steam‐heat treatment decreased endotoxin levels by 1–2 logarithm (log) reduction (LRV), which may be practically relevant depending on incoming raw material endotoxin levels. Antifoam efficiency and cell culture performance were negligibly impacted following steam‐heat treatment. The results from this study show that steam‐heat treatment is a viable endotoxin control strategy that can be implemented to support large‐scale biopharmaceutical manufacturing. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1145–1160, 2014     

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

     

Asynchronous Rate Chaos in Spiking Neuronal Circuits

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.     

Temperature-induced lysis of chromaffin granules provides evidence against the two-pool hypothesis of catecholamine storage

The temperature-dependent release of core constituents from isolated chromaffin granules in isotonic sucrose has been a controversial and puzzling phenomenon that has been interpreted either as selective catecholamine efflux from different catecholamine pools or as temperature-dependent lysis. We have analysed the kinetics, temperature dependence and physical basis of this process. Our results demonstrate that, upon increasing the ambient temperature, chromaffin granules show a shift in their osmotic fragility to higher osmolarities, which is linearly dependent on temperature and leads to measurable lysis in 0.26 M buffered sucrose at temperatures above 12 degrees C. It is possible to demonstrate both protein and dopamine beta-hydroxylase release when lysis as a function of temperature is measured in 0.26 M buffered sucrose. Real time measurements of the lysis kinetics were recorded on cassettes and analysed by a computer program for exponential decay kinetics. It is shown that the temperature-dependent lysis proceeds in two separate phases, the fast one of which is associated with temperature-dependent shift in the osmotic fragility curve. It has no characteristics of any exponential decay kinetics. The slow phase, when followed over several hours, leads to complete lysis of the granules in a sigmoidal time course at 30 degrees C. We conclude from the absence of exponentiality that there is no basis on which to assume the existence of different catecholamine pools. The fast phase of temperature-dependent lysis can be best explained as a simple temperature-dependent increase of the granule core solution's osmotic pressure, while the slow phase is probably caused by sucrose permeation into the granules. On the basis of these results, we warn against any efflux experiments measuring the temperature-dependent transmitter release from secretory vesicles with highly concentrated core solutions.     

Anti-CD3 antibody-induced activated killer cells: cytokines as the additional signals for activation of killer cells in effector phase to mediate slow lysis.

This study examines the role of cytokines in activating the effector cells to mediate slow lysis. After activation of splenocytes by alpha CD3, further culturing the cells in the absence of alpha CD3 resulted in the generation of activated killer cells (CD3-AK-) to mediate slow lysis. In contrast to fast lysis which was not affected by a PKC inhibitor H-7, slow lysis was inhibited. These findings suggested that a PKC-dependent activation phase preceded the lytic phase in slow lysis. To explore the mechanism for activating the lytic machinery in slow lysis, we examined the roles of cytokines in these reactions. First, it was found that alpha IL-2 or an alpha IL-2/alpha IL-4 combination inhibited slow lysis but had no effect on fast lysis. Secondly, IL-2, IL-4, or TNF alpha converted a noncytolytic CD3-AK- cells to mediate slow lysis, but they did not augment fast lysis. IL-2 and IL-4 had additive effect, and TNF alpha synergized with IL-2 to further augment the CD3-AK- cytolytic activity. Exogenous IL-6 and INF did not have any appreciable effect on the cytolytic activity of the killer cells. Besides TNF alpha, these cytokines were not directly cytotoxic to the target cells, indicating that they were not cytotoxic factors per se. Treatment with cycloheximide for 24 hr abrogated the cytolytic activities of CD3-AK cells, suggesting that a cytotoxic factor(s) was continuously synthesized to be stored in activated killer cells and was catabolized within 24 hr. Our results indicated that in the effector phase of slow lysis, after activating the CD3-AK- cells by the first signal (appropriate target cells), IL-2 and/or IL-4 appeared to be the second signal to initiate a cascade of events which triggered the release of other cytokines (e.g., TNF). This process resembles the secondary (memory) type of immune response. These events lead to full activation of the killer cells and converted the preformed cytotoxic factors into active form to initiate the lytic reaction and completed the lytic process.     

Aberrations of cortical and subcortical integration during chronic administration of haloperidol to the dog

The character of evoked potentials (EPs) dynamics to signal light stimulus during elaboration of avoidance reaction, allows to assert that during formation of adaptive activity functional balance is established of sensory and integrative-triggering brain parts or functional balance of "motor" and "sensory" integration regimes. Each of the studied subcortical structures is characterized by simultaneous but specific functioning both in the motor and sensory regimes; such conclusion is based on different dynamics of their EPs parameters: the changes of ones correspond to EPs dynamics in the visual cortical area, of the others--in the motor area. During chronic haloperidol administration, the reorganizations of intercentral relations are observed in 10--12 days after the beginning of drug administration. They may be considered as a succession of disturbances of functional balance between "sensory" and "motor" integration regimes: at first the sensory regime domination appears in which subcortical structures are chiefly and uniformly involved (ncd, pall and n. acc.); "motor" regime is weakened; then, as a result, a distortion of the "motor" regime of integration takes place. In this case a bradykinesia is developed.     

Downstream fish assemblage response to river impoundment varies with degree of hydrologic alteration

River impoundments can fundamentally restructure downstream fish assemblages by altering flow regimes. However, the degree of alteration and associated ecological change may depend on pre-existing hydrologic regimes. We used long-term datasets to compare downstream hydrological and fish assemblage responses to impoundment in two catchments classified as having intermittent and perennial-flashy natural hydrologic regimes. We observed significant shifts in fish assemblage structure at both sites after stream impoundment. The historically intermittent stream shifted to a stable perennial flow regime. Changes in fish assemblage structure covaried with changes in five different components of the flow regime; most species that increased in abundance require fluvial habitats and likely benefited from increased flows during historically low flow seasons. Shifts in fish assemblage structure were also observed in the perennial stream, despite minimal flow alteration after impoundment; however, most species shifts were associated with lentic environments, and were more likely related to proximity of reservoirs in the drainage system rather than changes in stream flow. Findings from this study confirm that downstream fish assemblage response to river impoundment can be associated with high levels of hydrologic alteration, but other factors including expansion of lentic species into lotic environments also influence shifts in assemblage structure.     

Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map

 We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and “singular Poincaré maps” that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold. Received: 19 May 1997 / Revised version: 6 April 1998     

Light and temperature, but not UV radiation, affect chlorophylls and carotenoids in Norway spruce needles (Picea abies (L.) Karst.)

Concentrations of chlorophyll a/freshweight (Chl a FW) and photosynthetic pigments/chlorophyll a were studied during one growing season in the current year's (CYN) and last year's needles (LYN) from Norway spruce (Picea abies (L.) Karst.) grown under natural or close‐to‐natural climate. Climate regimes differed in photosynthetic active radiation (PAR), temperature (T) and UV‐B radiation. Pigments were not affected by UV‐B but most of the differences between climate regimes, and also seasonal variations within climate regimes, could be related to PAR and T. Generally, two types of response to climate were observed: firstly, pigments reacted primarily to PAR without marked sensitivity to T and exhibited slow response times (> 30 d), and, secondly, pigments were affected by the combined action of PAR and T and responded faster than 20 d. The Chl a FW and chlorophyll b/chloprophyll a ratio exhibited slow‐type response in CYN and fast‐type response in LYN. Higher amplitudes in CYN than in LYN were observed for the latter two parameters, which are known to be associated with levels of pigment–protein complexes. It is suggested that slow response in CYN ensures that the high investments in proteins in these needles occur only in response to longer‐lasting climate episodes.     

Rapid odorant release in mammalian odour binding proteins facilitates their temporal coupling to odorant signals

We have measured the effect of rat odorant-binding protein 1 on the rates of ligand uptake and liquid-to-air transfer rates with a set of defined odorous compounds. Comparison of observed rate constants (k_obs) with data simulated over a wide range of different kinetic and thermodynamic regimes shows that the data do not agree with the previously held view of a slow off-rate regime (k_off <  0.0004 s^− 1). We propose that a rapid k_off would be a necessary requirement for such a system, since slow odorant-release rates would result in significant decorrelation between the olfactory world and odour perception.     

Modeling the Spontaneous Activity of the Auditory Cortex

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex. D.H is incumbent to the Hass Russell Career Chair Development.     

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.     

Relaxation kinetics and the glassiness of native proteins: coupling of timescales

We provide evidence that the onset of functional dynamics of folded proteins with elevated temperatures is associated with the effective sampling of its energy landscape under physiological conditions. The analysis is based on data describing the relaxation phenomena governing the backbone dynamics of bovine pancreatic trypsin inhibitor derived from molecular dynamics simulations, previously reported by us. By representing the backbone dynamics of the folded protein by three distinct regimes, it is possible to decompose its seemingly complex dynamics, described by a stretch exponential decay of the backbone motions. Of these three regimes, one is associated with the slow timescales due to the activity along the envelope of the energy surface defining the folded protein. Another, with fast timescales, is due to the activity along the pockets decorating the folded-state envelope. The intermediate regime emerges at temperatures where jumps between the pockets become possible. It is at the temperature window where motions corresponding to all three timescales become operative that the protein becomes active.     

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations’ MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.     

Resistance to drought affects persistence of alternative regimes in shallow lakes of the Boreal Plains (Alberta,Canada)

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