High Cooperativity in Negative Feedback can Amplify Noisy Gene Expression

Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protein. Increasing the strength of the feedback may lead to dramatically different outcomes depending on a key parameter, the noise load, which is defined as the squared coefficient of variation the protein exhibits in the absence of feedback. Combining stochastic simulation with asymptotic analysis, we identify a critical value of noise load: for noise loads smaller than critical, the coefficient of variation remains bounded with increasing feedback strength; contrastingly, if the noise load is larger than critical, the coefficient of variation diverges to infinity in the limit of ever greater feedback strengths. Interestingly, feedbacks with lower cooperativities have higher critical noise loads, suggesting that they can be preferable for controlling noisy proteins.     

Positive Feedback Promotes Oscillations in Negative Feedback Loops

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.     

Noise Propagation in Gene Regulation Networks Involving Interlinked Positive and Negative Feedback Loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.     

Feedback Circuits in Hepatitis B Virus Infection

A simplified model using kinetic logic is proposed to approach the problem after Hepatitis B viral (HBV) infection. It accounts for several stable regimes or attractors corresponding to the essential dynamic behaviour of the replication of the Hepatitis B virus. Infection with the virus can result in viral clearance, fulminant hepatic failure and death, or chronic transmissible infection, that is multistationarity corresponding to the existence of the positive feedback circuit in our modelling. Another implication of this model is the existence of oscillations or homeostatic mechanisms, sometimes observed in the viral cycle, consistent with the existence of the negative feedback circuit. Thus, this report shows how a simple model of kinetic logic may be used to account for the variety of manifestations of HBV infection. This model implies the presence of the Hepatitis B e antigen, whose conservation suggests that it plays an important role in the life cycle of hepadnaviruses. Its function in the viral cycle is still unknown, but our model suggests that this antigen could explain the passage from one state of the viral infection (acute or latent) to another, as well as the oscillatory behavior which may account for the intermittent symptoms of hepatitis observed in some patients. Furthermore, this model shows a virgin state. This state is also reached after recovery. The model proposed demonstrates that starting from a viral acute infection, the host's immune response, depending on the immunological status of the patient, can lead to viral clearance, or to periodic spontaneous reactivation.     

Inhibition of Receptor Dimerization as a Novel Negative Feedback Mechanism of EGFR Signaling

Dimerization of the epidermal growth factor receptor (EGFR) is crucial for initiating signal transduction. We employed raster image correlation spectroscopy to continuously monitor the EGFR monomer-dimer equilibrium in living cells. EGFR dimer formation upon addition of EGF showed oscillatory behavior with a periodicity of about 2.5 min, suggesting the presence of a negative feedback loop to monomerize the receptor. We demonstrated that monomerization of EGFR relies on phospholipase Cγ, protein kinase C, and protein kinase D (PKD), while being independent of Ca²⁺ signaling and endocytosis. Phosphorylation of the juxtamembrane threonine residues of EGFR (T654/T669) by PKD was identified as the factor that shifts the monomer-dimer equilibrium of ligand bound EGFR towards the monomeric state. The dimerization state of the receptor correlated with the activity of an extracellular signal-regulated kinase, downstream of the EGFR. Based on these observations, we propose a novel, negative feedback mechanism that regulates EGFR signaling via receptor monomerization.     

Tunable Stochastic Pulsing in the Escherichia coli Multiple Antibiotic Resistance Network from Interlinked Positive and Negative Feedback Loops

Cells live in uncertain, dynamic environments and have many mechanisms for sensing and responding to changes in their surroundings. However, sudden fluctuations in the environment can be catastrophic to a population if it relies solely on sensory responses, which have a delay associated with them. Cells can reconcile these effects by using a tunable stochastic response, where in the absence of a stressor they create phenotypic diversity within an isogenic population, but use a deterministic response when stressors are sensed. Here, we develop a stochastic model of the multiple antibiotic resistance network of Escherichia coli and show that it can produce tunable stochastic pulses in the activator MarA. In particular, we show that a combination of interlinked positive and negative feedback loops plays an important role in setting the dynamics of the stochastic pulses. Negative feedback produces a pulsatile response that is tunable, while positive feedback serves to amplify the effect. Our simulations show that the uninduced native network is in a parameter regime that is of low cost to the cell (taxing resistance mechanisms are expressed infrequently) and also elevated noise strength (phenotypic variability is high). The stochastic pulsing can be tuned by MarA induction such that variability is decreased once stresses are sensed, avoiding the detrimental effects of noise when an optimal MarA concentration is needed. We further show that variability in the expression of MarA can act as a bet hedging mechanism, allowing for survival in time-varying stress environments, however this effect is tunable to allow for a fully induced, deterministic response in the presence of a stressor.     

Novel Acylguanidine Derivatives Targeting Smoothened Induce Antiproliferative and Pro-Apoptotic Effects in Chronic Myeloid Leukemia Cells

The most relevant therapeutic approaches to treat CML rely on the administration of tyrosine kinase inhibitors (TKIs) like Imatinib, which are able to counteract the activity of Bcr-Abl protein increasing patient’s life expectancy and survival. Unfortunately, there are some issues TKIs are not able to address; first of all TKIs are not so effective in increasing survival of patients in blast crisis, second they are not able to eradicate leukemic stem cells (LSC) which represent the major cause of disease relapse, and third patients often develop resistance to TKIs due to mutations in the drug binding site. For all these reasons it’s of primary interest to find alternative strategies to treat CML. Literature shows that Hedgehog signaling pathway is involved in LSC maintenance, and pharmacological inhibition of Smoothened (SMO), one of the key molecules of the pathway, has been demonstrated to reduce Bcr-Abl positive bone marrow cells and LSC. Consequently, targeting SMO could be a promising way to develop a new treatment strategy for CML overcoming the limitations of current therapies. In our work we have tested some compounds able to inhibit SMO, and among them MRT92 appears to be a very potent SMO antagonist. We found that almost all our compounds were able to reduce Gli1 protein levels in K-562 and in KU-812 CML cell lines. Furthermore, they were also able to increase Gli1 and SMO RNA levels, and to reduce cell proliferation and induce apoptosis/autophagy in both the tested cell lines. Finally, we demonstrated that our compounds were able to modulate the expression of some miRNAs related to Hedgehog pathway such as miR-324-5p and miR-326. Being Hedgehog pathway deeply implicated in the mechanisms of CML we may conclude that it could be a good therapeutic target for CML and our compounds seem to be promising antagonists of such pathway.     

Mixed Signal Learning by Spike Correlation Propagation in Feedback Inhibitory Circuits

The brain can learn and detect mixed input signals masked by various types of noise, and spike-timing-dependent plasticity (STDP) is the candidate synaptic level mechanism. Because sensory inputs typically have spike correlation, and local circuits have dense feedback connections, input spikes cause the propagation of spike correlation in lateral circuits; however, it is largely unknown how this secondary correlation generated by lateral circuits influences learning processes through STDP, or whether it is beneficial to achieve efficient spike-based learning from uncertain stimuli. To explore the answers to these questions, we construct models of feedforward networks with lateral inhibitory circuits and study how propagated correlation influences STDP learning, and what kind of learning algorithm such circuits achieve. We derive analytical conditions at which neurons detect minor signals with STDP, and show that depending on the origin of the noise, different correlation timescales are useful for learning. In particular, we show that non-precise spike correlation is beneficial for learning in the presence of cross-talk noise. We also show that by considering excitatory and inhibitory STDP at lateral connections, the circuit can acquire a lateral structure optimal for signal detection. In addition, we demonstrate that the model performs blind source separation in a manner similar to the sequential sampling approximation of the Bayesian independent component analysis algorithm. Our results provide a basic understanding of STDP learning in feedback circuits by integrating analyses from both dynamical systems and information theory.     

Constraint and Contingency in Multifunctional Gene Regulatory Circuits

Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuit''s number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype.