Systems and synthetic biology approaches in understanding biological oscillators

From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator

Oscillations are a recurrent phenomenon in biological systems across scales, but deciphering their fundamental principles is very challenging. Here, we tackle this challenge by redesigning the wellcharacterised synthetic oscillator known as "repressilator" in Escherichia coli and controlling it using optogenetics, creating the "optoscillator". Bacterial colonies manifest oscillations as spatial ring patterns. When we apply periodic light pulses, the optoscillator behaves as a forced oscillator and we systematically investigate the properties of the rings under various light conditions. Combining experiments with mathematical modeling, we demonstrate that this simple oscillatory circuit can generate complex dynamics that are transformed into distinct spatial patterns. We report the observation of synchronisation, resonance, subharmonic resonance and period doubling. Furthermore, we present evidence of a chaotic regime. This work highlights the intricate spatiotemporal patterns accessible by synthetic oscillators and underscores the potential of our approach in revealing fundamental principles of biological oscillations.

An oscillating reaction network with an exact closed form solution in the time domain

BACKGROUND

Oscillatory behavior is critical to many life sustaining processes such as cell cycles, circadian rhythms, and notch signaling. Important biological functions depend on the characteristics of these oscillations (hereafter, oscillation characteristics or OCs): frequency (e.g., event timings), amplitude (e.g., signal strength), and phase (e.g., event sequencing). Numerous oscillating reaction networks have been documented or proposed. Some investigators claim that oscillations in reaction networks require nonlinear dynamics in that at least one rate law is a nonlinear function of species concentrations. No one has shown that oscillations can be produced for a reaction network with linear dynamics. Further, no one has obtained closed form solutions for the frequency, amplitude and phase of any oscillating reaction network. Finally, no one has published an algorithm for constructing oscillating reaction networks with desired OCs.

RESULTS

This is a theoretical study that analyzes reaction networks in terms of their representation as systems of ordinary differential equations. Our contributions are: (a) construction of an oscillating, two species reaction network [two species harmonic oscillator (2SHO)] that has no nonlinearity; (b) obtaining closed form formulas that calculate frequency, amplitude, and phase in terms of the parameters of the 2SHO reaction network, something that has not been done for any published oscillating reaction network; and (c) development of an algorithm that parameterizes the 2SHO to achieve desired oscillation, a capability that has not been produced for any published oscillating reaction network.

CONCLUSIONS

Our 2SHO demonstrates the feasibility of creating an oscillating reaction network whose dynamics are described by a system of linear differential equations. Because it is a linear system, we can derive closed form expressions for the frequency, amplitude, and phase of oscillations, something that has not been done for other published reaction networks. With these formulas, we can design 2SHO reaction networks to have desired oscillation characteristics. Finally, our sensitivity analysis suggests an approach to constructing a 2SHO for a biochemical system.

Efficient, Formal, Material, and Final Causes in Biology and Technology

This paper considers how a classification of causal effects as comprising efficient, formal, material, and final causation can provide a useful understanding of how emergence takes place in biology and technology, with formal, material, and final causation all including cases of downward causation; they each occur in both synchronic and diachronic forms. Taken together, they underlie why all emergent levels in the hierarchy of emergence have causal powers (which is Noble's principle of biological relativity) and so why causal closure only occurs when the upwards and downwards interactions between all emergent levels are taken into account, contra to claims that some underlying physics level is by itself causality complete. A key feature is that stochasticity at the molecular level plays an important role in enabling agency to emerge, underlying the possibility of final causation occurring in these contexts.

What Makes a Functional Gene Regulatory Network? A Circuit Motif Analysis

One of the key questions in systems biology is to understand the roles of gene regulatory circuits in determining cellular states and their functions. In previous studies, some researchers have inferred large gene networks from genome wide genomics/transcriptomics data using the top-down approach, while others have modeled core gene circuits of small sizes using the bottom-up approach. Despite many existing systems biology studies, there is still no general rule on what sizes of gene networks and what types of circuit motifs a system would need to achieve robust biological functions. Here, we adopt a gene circuit motif analysis to discover four-node circuits responsible for multiplicity (rich in dynamical behavior), flexibility (versatile to alter gene expression), or both. We identify the most reoccurring two-node circuit motifs and the co-occurring motif pairs. Furthermore, we investigate the contributing factors of multiplicity and flexibility for large gene networks of different types and sizes. We find that gene networks of intermediate sizes tend to have combined high levels of multiplicity and flexibility. Our study will contribute to a better understanding of the dynamical mechanisms of gene regulatory circuits and provide insights into rational designs of robust gene circuits in synthetic and systems biology.

Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations

Transcriptional repression can occur via various mechanisms, such as blocking, sequestration and displacement. For instance, the repressors can hold the activators to prevent binding with DNA or can bind to the DNA-bound activators to block their transcriptional activity. Although the transcription can be completely suppressed with a single mechanism, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems, such as circadian clocks and NF-κB oscillators. This raises the question of what advantages arise if seemingly redundant repression mechanisms are combined. Here, by deriving equations describing the multiple repression mechanisms, we find that their combination can synergistically generate a sharply ultrasensitive transcription response and thus strong oscillations. This rationalizes why the multiple repression mechanisms are used together in various biological oscillators. The critical role of such combined transcriptional repression for strong oscillations is further supported by our analysis of formerly identified mutations disrupting the transcriptional repression of the mammalian circadian clock. The hitherto unrecognized source of the ultrasensitivity, the combined transcriptional repressions, can lead to robust synthetic oscillators with a previously unachievable simple design.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

Oscillating the local milieu of polymersome interiors via single input-regulated bilayer crosslinking and permeability tuning

The unique permselectivity of cellular membranes is of crucial importance to maintain intracellular homeostasis while adapting to microenvironmental changes. Although liposomes and polymersomes have been widely engineered to mimic microstructures and functions of cells, it still remains a considerable challenge to synergize the stability and permeability of artificial cells and to imitate local milieu fluctuations. Herein, we report concurrent crosslinking and permeabilizing of pH-responsive polymersomes containing Schiff base moieties within bilayer membranes via enzyme-catalyzed acid production. Notably, this synergistic crosslinking and permeabilizing strategy allows tuning of the mesh sizes of the crosslinked bilayers with subnanometer precision, showing discriminative permeability toward maltooligosaccharides with molecular sizes of ~1.4-2.6 nm. The permselectivity of bilayer membranes enables intravesicular pH oscillation, fueled by a single input of glucose. This intravesicular pH oscillation can further drive the dissipative self-assembly of pH-sensitive dipeptides. Moreover, the permeabilization of polymersomes can be regulated by intracellular pH gradient as well, enabling the controlled release of encapsulated payloads.

Synthetic Protein Circuits and Devices Based on Reversible Protein-Protein Interactions: An Overview

Protein-protein interactions (PPIs) contribute to regulate many aspects of cell physiology and metabolism. Protein domains involved in PPIs are important building blocks for engineering genetic circuits through synthetic biology. These domains can be obtained from known proteins and rationally engineered to produce orthogonal scaffolds, or computationally designed de novo thanks to recent advances in structural biology and molecular dynamics prediction. Such circuits based on PPIs (or protein circuits) appear of particular interest, as they can directly affect transcriptional outputs, as well as induce behavioral/adaptational changes in cell metabolism, without the need for further protein synthesis. This last example was highlighted in recent works to enable the production of fast-responding circuits which can be exploited for biosensing and diagnostics. Notably, PPIs can also be engineered to develop new drugs able to bind specific intra- and extra-cellular targets. In this review, we summarize recent findings in the field of protein circuit design, with particular focus on the use of peptides as scaffolds to engineer these circuits.

pH-Sensitive Oscillatory Motion of a Urease Motor on the Urea Aqueous Phase

A self-propelled object coupled with an enzyme reaction between urease and urea was investigated at the air/aqueous interface. A plastic object that was fixed to a urease-immobilized filter paper was used as a self-propelled object, termed a urease motor, placed on an aqueous urea solution. The driving force of the urease motor is the difference in the surface tension around the object. Oscillatory motion or no motion was triggered depending on the initial pH of the urea solution. Both the frequency and maximum speed of the oscillatory motion varied depending on the initial pH of the water phase. The mechanisms underlying the oscillatory motion and no motion were discussed in relation to the bell-shaped enzyme activity of urease in the enzyme reaction and the surface tension around the urease motor.

Circadian rhythms and the HPA axis: A systems view

The circadian timing system comprises a network of time-keeping clocks distributed across a living host whose responsibility is to allocate resources and distribute functions temporally to optimize fitness. The molecular structures generating these rhythms have evolved to accommodate the rotation of the earth in an attempt to primarily match the light/dark periods during the 24-hr day. To maintain synchrony of timing across and within tissues, information from the central clock, located in the suprachiasmatic nucleus, is conveyed using systemic signals. Leading among those signals are endocrine hormones, and while the hypothalamic-pituitary-adrenal axis through the release of glucocorticoids is a major pacesetter. Interestingly, the fundamental units at the molecular and physiological scales that generate local and systemic signals share critical structural properties. These properties enable time-keeping systems to generate rhythmic signals and allow them to adopt specific properties as they interact with each other and the external environment. The purpose of this review is to provide a broad overview of these structures, discuss their functional characteristics, and describe some of their fundamental properties as these related to health and disease. This article is categorized under: Immune System Diseases > Computational Models Immune System Diseases > Biomedical Engineering.

Mathematical Model of Fractional Duffing Oscillator with Variable Memory

The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.

Mathematical Modeling of Linear Fractional Oscillators

In this work, based on Newton’s second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov–Caputo fractional derivatives is carried out. For the resulting model equation, local initial conditions are set (the Cauchy problem). Numerical methods for solving the Cauchy problem using an explicit non-local finite-difference scheme (ENFDS) and the Adams–Bashforth–Moulton (ABM) method are considered. An analysis of the errors of the methods is carried out on specific test examples. It is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method. Forced oscillations of linear fractional oscillators (LFO) are investigated. Using the ABM method, the amplitude–frequency characteristics (AFC) were constructed, which were compared with the AFC obtained by the analytical formula. The Q-factor of the LFO is investigated. It is shown that the orders of fractional derivatives are responsible for the intensity of energy dissipation in fractional vibrational systems. Specific mathematical models of LFOs are considered: a fractional analogue of the harmonic oscillator, fractional oscillators of Mathieu and Airy. Oscillograms and phase trajectories were constructed using the ABM method for various values of the parameters included in the model equation. The interpretation of the simulation results is carried out.

The social nature of mitochondria: Implications for human health

Sociality has profound evolutionary roots and is observed from unicellular organisms to multicellular animals. In line with the view that social principles apply across levels of biological complexity, a growing body of data highlights the remarkable social nature of mitochondria - life-sustaining endosymbiotic organelles with their own genome that populate the cell cytoplasm. Here, we draw from organizing principles of behavior in social organisms to reveal that similar to individuals among social networks, mitochondria communicate with each other and with the cell nucleus, exhibit group formation and interdependence, synchronize their behaviors, and functionally specialize to accomplish specific functions within the organism. Mitochondria are social organelles. The extension of social principles across levels of biological complexity is a theoretical shift that emphasizes the role of communication and interdependence in cell biology, physiology, and neuroscience. With the help of emerging computational methods capable of capturing complex dynamic behavioral patterns, the implementation of social concepts in mitochondrial biology may facilitate cross-talk across disciplines towards increasingly holistic and accurate models of human health.

0D–2D heterostructures as nanocatalysts for self-oscillating reactions: an investigation into chemical kinetics

Ceria-decorated graphene nanocomposites as an efficient catalyst for the oscillatory Belousov–Zhabotinsky reaction.