Niche theory for within-host parasite dynamics: Analogies to food web modules via feedback loops

Why do parasites exhibit a wide dynamical range within their hosts? For instance, why does infecting dose either lead to infection or immune clearance? Why do some parasites exhibit boom-bust, oscillatory dynamics? What maintains parasite diversity, that is coinfection v single infection due to exclusion or priority effects? For insights on parasite dose, dynamics and diversity governing within-host infection, we turn to niche models. An omnivory food web model (IGP) blueprints one parasite competing with immune cells for host energy (PIE). Similarly, a competition model (keystone predation, KP) mirrors a new coinfection model (2PIE). We then drew analogies between models using feedback loops. The following three points arise: first, like in IGP, parasites oscillate when longer loops through parasites, immune cells and resource regulate parasite growth. Shorter, self-limitation loops (involving resources and enemies) stabilise those oscillations. Second, IGP can produce priority effects that resemble immune clearance. But, despite comparable loop structure, PIE cannot due to constraints imposed by production of immune cells. Third, despite somewhat different loop structure, KP and 2PIE share apparent and resource competition mechanisms that produce coexistence (coinfection) or priority effects of prey or parasites. Together, this mechanistic niche framework for within-host dynamics offers new perspective to improve individual health.     

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.     

A Critical Quantity for Noise Attenuation in Feedback Systems

Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as “signed activation time”. We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.     

Feedback regulation of EGFR signalling: decision making by early and delayed loops

Human-made information relay systems invariably incorporate central regulatory components, which are mirrored in biological systems by dense feedback and feedforward loops. This type of system control is exemplified by positive and negative feedback loops (for example, receptor endocytosis and dephosphorylation) that enable growth factors and receptor Tyr kinases of the epidermal growth factor receptor (EGFR)/ERBB family to regulate cellular function. Recent studies show that the collection of feedback regulatory loops can perform computational tasks - such as decoding ligand specificity, transforming graded input signals into a digital output and regulating response kinetics. Aberrant signal processing and feedback regulation can lead to defects associated with pathologies such as cancer.     

On the dynamics of controlled metabolic network and cellular behavior

The existence of elaborate control mechanisms for the various biochemical processes inside and within living cells is responsible for the coherent behaviour observed in its spatio-temporal organisation. Stability and sensitivity are both necessary properties of living systems and these are achieved through negetive and positive feedback loops as in other control systems. We have studied a three-step reaction scheme involving a negative and a positive feedback loop in the form of end-product inhibition and allosteric activation. The variety of behaviour exhibited by this system, under different conditions, includes steady state, simple limit cycle oscillations, complex oscillations and period bifurcations leading to random oscillations or chaos. The system also shows the existence of two distinct chaotic regimes under the variation of a single parameter. These results, in comparison with single biochemical control loops, show that new behaviours can be exhibited in a more complex network which are not seen in the single control loops. The results are discussed in the light of a diverse variety of cellular functions in normal and altered cells indicating the role of controlled metabolic network as the underlying basis for cellular behaviour.     

Feedback signaling controls leading-edge formation during chemotaxis

Chemotactic cells translate shallow chemoattractant gradients into a highly polarized intracellular response that includes the localized production of PI(3,4,5)P(3) on the side of the cell facing the highest chemoattractant concentration. Research over the past decade began to uncover the molecular mechanisms involved in this localized signal amplification controlling the leading edge of chemotaxing cells. These mechanisms have been shown to involve multiple positive feedback loops, in which the PI(3,4,5)P(3) signal amplifies itself independently of the original stimulus, as well as inhibitory signals that restrict PI(3,4,5)P(3) to the leading edge, thereby creating a steep intracellular PI(3,4,5)P(3) gradient. Molecules involved in positive feedback signaling at the leading edge include the small G-proteins Rac and Ras, phosphatidylinositol-3 kinase and F-actin, as part of interlinked feedback loops that lead to a robust production of PI(3,4,5)P(3).     

Cellular Sensory Mechanisms for Detecting Specific Fold-Changes in Extracellular Cues

Cellular sensory systems often respond not to the absolute levels of inputs but to the fold-changes in inputs. Such a property is called fold-change detection (FCD) and is important for accurately sensing dynamic changes in environmental signals in the presence of fluctuations in their absolute levels. Previous studies defined FCD as input-scale invariance and proposed several biochemical models that achieve such a condition. Here, we prove that the previous FCD models can be approximated by a log-differentiator. Although the log-differentiator satisfies the input-scale invariance requirement, its response amplitude and response duration strongly depend on the input timescale. This creates limitations in the specificity and repeatability of detecting fold-changes in inputs. Nevertheless, FCD with specificity and repeatability by cells has been reported in the context of Drosophila wing development. Motivated by this fact and by extending previous FCD models, we here propose two possible mechanisms to achieve FCD with specificity and repeatability. One is the integrate-and-fire type: a system integrates the rate of temporal change in input and makes a response when the integrated value reaches a constant threshold, and this is followed by the reset of the integrated value. The other is the dynamic threshold type: a system response occurs when the input level reaches a threshold, whose value is multiplied by a certain constant after each response. These two mechanisms can be implemented biochemically by appropriately combining feed-forward and feedback loops. The main difference between the two models is their memory of input history; we discuss possible ways to distinguish between the two models experimentally.     

Cellular Sensory Mechanisms for Detecting Specific Fold-Changes in Extracellular Cues

Cellular sensory systems often respond not to the absolute levels of inputs but to the fold-changes in inputs. Such a property is called fold-change detection (FCD) and is important for accurately sensing dynamic changes in environmental signals in the presence of fluctuations in their absolute levels. Previous studies defined FCD as input-scale invariance and proposed several biochemical models that achieve such a condition. Here, we prove that the previous FCD models can be approximated by a log-differentiator. Although the log-differentiator satisfies the input-scale invariance requirement, its response amplitude and response duration strongly depend on the input timescale. This creates limitations in the specificity and repeatability of detecting fold-changes in inputs. Nevertheless, FCD with specificity and repeatability by cells has been reported in the context of Drosophila wing development. Motivated by this fact and by extending previous FCD models, we here propose two possible mechanisms to achieve FCD with specificity and repeatability. One is the integrate-and-fire type: a system integrates the rate of temporal change in input and makes a response when the integrated value reaches a constant threshold, and this is followed by the reset of the integrated value. The other is the dynamic threshold type: a system response occurs when the input level reaches a threshold, whose value is multiplied by a certain constant after each response. These two mechanisms can be implemented biochemically by appropriately combining feed-forward and feedback loops. The main difference between the two models is their memory of input history; we discuss possible ways to distinguish between the two models experimentally.     

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.     

Optimizing interneuron circuits for compartment-specific feedback inhibition

Cortical circuits process information by rich recurrent interactions between excitatory neurons and inhibitory interneurons. One of the prime functions of interneurons is to stabilize the circuit by feedback inhibition, but the level of specificity on which inhibitory feedback operates is not fully resolved. We hypothesized that inhibitory circuits could enable separate feedback control loops for different synaptic input streams, by means of specific feedback inhibition to different neuronal compartments. To investigate this hypothesis, we adopted an optimization approach. Leveraging recent advances in training spiking network models, we optimized the connectivity and short-term plasticity of interneuron circuits for compartment-specific feedback inhibition onto pyramidal neurons. Over the course of the optimization, the interneurons diversified into two classes that resembled parvalbumin (PV) and somatostatin (SST) expressing interneurons. Using simulations and mathematical analyses, we show that the resulting circuit can be understood as a neural decoder that inverts the nonlinear biophysical computations performed within the pyramidal cells. Our model provides a proof of concept for studying structure-function relations in cortical circuits by a combination of gradient-based optimization and biologically plausible phenomenological models.     

Stochastic Modeling of Autoregulatory Genetic Feedback Loops: A Review and Comparative Study

Autoregulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic parameters of the main biochemical steps. These models differ according to 1) which subcellular processes are explicitly modeled, 2) the modeling methodology employed (discrete, continuous, or hybrid), and 3) whether they can be analytically solved for the steady-state distribution of protein numbers. We discuss the assumptions and properties of the main models in the literature, summarize our current understanding of the relationship between them, and highlight some of the insights gained through modeling.     

T cell receptor binding transition states and recognition of peptide/MHC

T cell receptor recognition of peptide/MHC has been described as proceeding through a "two-step" process in which the TCR first contacts the MHC molecule prior to formation of the binding transition state using the germline-encoded CDR1 and CDR2 loops. The receptor then contacts the peptide using the hypervariable CDR3 loops as the transition state decays to the bound state. The model subdivides TCR binding into peptide-independent and peptide-dependent steps, demarcated at the binding transition state. Investigating the two-step model, here we show that two TCRs that recognize the same peptide/MHC bury very similar amounts of solvent-accessible surface area in their transition states. However, 1300-1500 A2 of surface area is buried in each, a significant amount suggestive of participation of peptide and associated CDR3 surface. Consistent with this interpretation, analysis of peptide and TCR variants indicates that stabilizing contacts to the peptide are formed within both transition states. These data are incompatible with the original two-step model, as are transition state models built using the principle of minimal frustration commonly employed in the investigation of protein folding and binding transition states. These findings will be useful in further explorations of the nature of TCR binding transition states, as well as ongoing efforts to understand the mechanisms by which T cell receptors recognize the composite peptide/MHC surface.     

How is functional specificity achieved through disordered regions of proteins?

N‐type inactivation of potassium channels is controlled by cytosolic loops that are intrinsically disordered. Recent experiments have shown that the mechanism of N‐type inactivation through disordered regions can be stereospecific and vary depending on the channel type. Variations in mechanism occur despite shared coarse grain features such as the length and amino acid compositions of the cytosolic disordered regions. We have adapted a phenomenological model designed to explain how specificity in molecular recognition is achieved through disordered regions. We propose that the channel‐specific observations for N‐type inactivation represent distinct mechanistic choices for achieving function through conformational selection versus induced fit. It follows that the dominant mechanism for binding and specificity can be modulated through subtle changes in the amino acid sequences of disordered regions, which is interesting given that specificity in function is realized in the absence of autonomous folding.     

Pushed to the edge: Spatial sorting can slow down invasions

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.     

Prediction of folding mechanism for circular-permuted proteins

Recent theoretical and experimental studies have suggested that real proteins have sequences with sufficiently small energetic frustration that topological effects are central in determining the folding mechanism. A particularly interesting and challenging framework for exploring and testing the viability of these energetically unfrustrated models is the study of circular-permuted proteins. Here we present the results of the application of a topology-based model to the study of circular permuted SH3 and CI2, in comparison with the available experimental results. The folding mechanism of the permuted proteins emerging from our simulations is in very good agreement with the experimental observations. The differences between the folding mechanisms of the permuted and wild-type proteins seem then to be strongly related to the change in the native state topology.