An amplified derepression controller with multisite inhibition and positive feedback

How organisms are able to maintain robust homeostasis has in recent years received increased attention by the use of combined control engineering and kinetic concepts, which led to the discovery of robust controller motifs. While these motifs employ kinetic conditions showing integral feedback and homeostasis for step-wise perturbations, the motifs’ performance differ significantly when exposing them to time dependent perturbations. One type of controller motifs which are able to handle exponentially and even hyperbolically growing perturbations are based on derepression. In these controllers the compensatory reaction, which neutralizes the perturbation, is derepressed, i.e. its reaction rate is increased by the decrease of an inhibitor acting on the compensatory flux. While controllers in this category can deal well with different time-dependent perturbations they have the disadvantage that they break down once the concentration of the regulatory inhibitor becomes too low and the compensatory flux has gained its maximum value. We wondered whether it would be possible to bypass this restriction, while still keeping the advantages of derepression kinetics. In this paper we show how the inclusion of multisite inhibition and the presence of positive feedback loops lead to an amplified controller which is still based on derepression kinetics but without showing the breakdown due to low inhibitor concentrations. By searching for the amplified feedback motif in natural systems, we found it as a part of the plant circadian clock where it is highly interlocked with other feedback loops.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

The threshold of an excitable system serves as a control mechanism for noise filtering during chemotaxis

Chemotaxis, the migration of cells in the direction of a chemical gradient, is of utmost importance in various biological processes. In recent years, research has demonstrated that the underlying mechanism that controls cell migration is an excitable network. One of the properties that characterizes excitability is the presence of a threshold for activation. Here, we show that excitable systems possess noise filtering capabilities that enable faster and more efficient directed migration compared to other systems that also include a threshold, such as ultrasensitive switches. We demonstrate that this filtering ability is a consequence of the varying responses of excitable systems to step and pulse stimuli. Whereas the response to step inputs is determined solely by the magnitude of the stimulus, for pulse stimuli, the response depends on both the magnitude and duration of the stimulus. We then show that these two forms of threshold behavior can be decoupled from one another, allowing finer control in chemotaxis. Finally, we use a simple model of chemotaxis to demonstrate that cells that rely on an excitable system display faster and more effective directed migration that a hypothetical cell guided by an ultra-sensitive switch.

Bridging the gap between modules in isolation and as part of networks: A systems framework for elucidating interaction and regulation of signalling modules

While signalling and biochemical modules have been the focus of numerous studies, they are typically studied in isolation, with no examination of the effects of the ambient network. In this paper we formulate and develop a systems framework, rooted in dynamical systems, to understand such effects, by studying the interaction of signalling modules. The modules we consider are (i) basic covalent modification, (ii) monostable switches, (iii) bistable switches, (iv) adaptive modules, and (v) oscillatory modules. We systematically examine the interaction of these modules by analyzing (a) sequential interaction without shared components, (b) sequential interaction with shared components, and (c) oblique interactions. Our studies reveal that the behaviour of a module in isolation may be substantially different from that in a network, and explicitly demonstrate how the behaviour of a given module, the characteristics of the ambient network, and the possibility of shared components can result in new effects. Our global approach illuminates different aspects of the structure and functioning of modules, revealing the importance of dynamical characteristics as well as biochemical features; this provides a methodological platform for investigating the complexity of natural modules shaped by evolution, elucidating the effects of ambient networks on a module in multiple cellular contexts, and highlighting the capabilities and constraints for engineering robust synthetic modules. Overall, such a systems framework provides a platform for bridging the gap between non-linear information processing modules, in isolation and as parts of networks, and a basis for understanding new aspects of natural and engineered cellular networks.

Comparison of adaptation motifs: temporal, stochastic and spatial responses

The cells' ability to adapt to changes in the external environment is crucial for the survival of many organisms. There are two broad classes of signalling networks that achieve perfect adaptation. Both rely on complementary regulation of the response by an external signal and an inhibitory process. In one class of systems, inhibition comes about from the response itself, closing a negative feedback (NFB) loop. In the other, the inhibition comes directly from the external signal in what is referred to as an incoherent feedforward (IFF) loop. Although both systems show adaptive behaviour to constant changes in the level of the stimulus, their response to other forms of stimuli can differ. Here the authors consider the respective response to various such disturbances, including ramp increases, removal of the stimulus and pulses. The authors also consider the effect of stochastic fluctuations in signalling that come about from the interaction of the signalling elements. Finally, the authors consider the possible effect of spatially varying signals. The authors show that both the NFB and the IFF motifs can be used to sense static spatial gradients, under a local excitation, global inhibition assumption. The results may help experimentalists develop protocols that can discriminate between the two adaptation motifs.

Intrinsic and induced drug resistance mechanisms: in silico investigations at the cellular and tissue scales

Basic in silico models used to study intrinsic and acquired variants of two types of cellular resistance mechanisms demonstrate important tissue-level differences and consequences.

Towards an integrated systems-based modelling framework for drug transport and its effect on tumour cells

Background

A systematic understanding of chemotherapeutic influence on solid tumours is highly challenging and complex as it encompasses the interplay of phenomena occurring at multiple scales. It is desirable to have a multiscale systems framework capable of disentangling the individual roles of multiple contributing factors, such as transport and extracellular factors, and purely intracellular factors, as well as the interactions among these factors. Based on a recently developed systems-based modelling framework, we have developed a coupled system in order to further elucidate the role of drug transport, and its interplay with cellular signalling by incorporating intra- and extra-vascular drug transport in tumour, dynamic descriptions of intracellular signalling and tumour cell density dynamics.

Results

Different aspects of the interaction between transport and cell signalling and the effects of transport parameters have been investigated in silico. Limited drug penetration is found to be a major constraint in inducing drug effect; many aspects of the interaction of transport with cell signalling are independent of the details of cell signalling. A sensitivity analysis indicates that the effect of drug diffusivity depends on the balance between interstitial drug transport and the specific requirement for triggering apoptosis (governed by highly nonlinear signalling networks), suggesting that the effect of drug diffusivity in such cases must be considered in conjunction with descriptions of cellular dynamics.

Conclusions

The modelling framework developed in this study provides qualitative and mechanistic insights into the effect of drug on tumour cells. It provides an in silico experimental platform to investigate the interplay between extracellular factors (e.g. transport) and intracellular factors. Such a platform is essential to understanding the individual and combined effects of transport and cellular factors in solid tumour.

Investigating the effects of ABC transporter-based acquired drug resistance mechanisms at the cellular and tissue scale

In this paper we systematically investigate the effects of acquired drug resistance at the cellular and tissue scale, with a specific focus on ATP-binding cassette (ABC) transporter-based mechanisms and contrast this with other representative intracellular resistance mechanisms. This is done by developing in silico models wherein the drug resistance mechanism is overlaid on a coarse-grained description of apoptosis; these cellular models are coupled with interstitial drug transport, allowing for a transparent examination of the effect of acquired drug resistances at the tissue level. While ABC transporter-mediated resistance mechanisms counteract drug effect at the cellular level, its tissue-level effect is more complicated, revealing unexpected trends in tissue response as drug stimuli are systematically varied. Qualitatively different behaviour is observed in other drug resistance mechanisms. Overall the paper (i) provides insight into the tissue level functioning of a particular resistance mechanism, (ii) shows that this is very different from other resistance mechanisms of an apparently similar type, and (iii) demonstrates a concrete instance of how the functioning of a negative feedback based cellular adaptive mechanism can have unexpected higher scale effects.

A systems-based mathematical modelling framework for investigating the effect of drugs on solid tumours

Background

Elucidating the effects of drugs on solid tumours is a highly challenging multi-level problem, since this involves many complexities associated with transport and cellular response, which in turn is characterized by highly non-linear chemical signal transduction. Appropriate systems frameworks are needed to seriously address the sources of these complexities, especially from the cellular side.

Results

We develop a skeletal modelling framework incorporating interstitial drug transport, intracellular signal processing and cell population descriptions. The descriptions aim to appropriately capture the nature of information flow. The model is deliberately formulated to start with simple intracellular descriptions so that additional features can be incorporated in a modular fashion. Two kinds of intracellular signalling modules which describe the drug effect were considered, one a monostable switch and the other a bistable switch. Analysis of our model revealed how different drug stimuli can lead to cell killing in the tumour. Interestingly both modules considered exhibited similar trends. The effects of important parameters were also studied.

Conclusions

We have created a predictive systems platform integrating drug transport and cellular response which can be systematically augmented to include additional layers of cellular complexity. Our results indicate that intracellular signalling models which are qualitatively different can give rise to similar behaviour to simple (and typical) stimuli, and that validating intracellular descriptions must be performed with care by considering a variety of drug stimuli.

The coupling of pathways and processes through shared components

Background

The coupling of pathways and processes through shared components is being increasingly recognised as a common theme which occurs in many cell signalling contexts, in which it plays highly non-trivial roles.

Results

In this paper we develop a basic modelling and systems framework in a general setting for understanding the coupling of processes and pathways through shared components. Our modelling framework starts with the interaction of two components with a common third component and includes production and degradation of all these components. We analyze the signal processing in our model to elucidate different aspects of the coupling. We show how different kinds of responses, including "ultrasensitive" and adaptive responses, may occur in this setting. We then build on the basic model structure and examine the effects of additional control regulation, switch-like signal processing, and spatial signalling. In the process, we identify a way in which allosteric regulation may contribute to signalling specificity, and how competitive effects may allow an enzyme to robustly coordinate and time the activation of parallel pathways.

Conclusions

We have developed and analyzed a common systems platform for examining the effects of coupling of processes through shared components. This can be the basis for subsequent expansion and understanding the many biologically observed variations on this common theme.