Global dynamics, thermodynamics and non-equilibrium origin of bifurcations for single neuron dynamics.

The understanding of neural excitability and oscillations in single neuron dynamics remains incomplete in terms of global stabilities and the underlying mechanisms for phase formation and associated phase transitions. In this study, we investigate the mechanism of single neuron excitability and spontaneous oscillations by analyzing the potential landscape and curl flux. The topological features of the landscape play a crucial role in assessing the stability of resting states and the robustness/coherence of oscillations. We analyze the excitation characteristics in Class I and Class II neurons and establish their relation to biological function. Our findings reveal that the average curl flux and associated entropy production exhibit significant changes near bifurcation or phase transition points. Moreover, the curl flux and entropy production offer insights into the dynamical and thermodynamical origins of nonequilibrium phase transitions and exhibit distinct behaviors in Class I and Class II neurons. Additionally, we quantify time irreversibility through the difference in cross-correlation functions in both forward and backward time, providing potential indicators for the emergence of nonequilibrium phase transitions in single neurons.

[Design and application of a new heat-and-moisture exchanger with anti-splash sputum suctioning function].

In the emergency department, open endotracheal suctioning for mechanically ventilated patients with endotracheal intubation will lead to the spread of respiratory droplets and aerosols, polluting the surrounding environment and medical staff. The traditional heat-and-moisture exchanger has the effect of warming and humidifying, and can block pathogenic microorganisms, but it does not have the function of inserting a sputum suction tube. When the heat-and-moisture exchanger is pulled out for sputum suction, it is easy to cause sputum splash, which pollutes the surrounding environment and medical personnel. The addition of closed sputum suction devices will increase the economic burden on patients. Thus, the medical staff of emergency department of the First People's Hospital of Tongxiang City of Zhejiang Province designed a new type of heat-and-moisture exchanger with anti-splash sputum suctioning function and obtained the National Utility Model Patent of China (ZL 2021 2 0017615.0). The new heat-and-moisture exchanger is mainly composed of a receiving cavity, a connecting tube, a sputum suction tube intubation tube, a sealing valve, etc. The disposable sputum suction tube can be used to insert sputum suction, and at the same time, it can prevent the secretion from splashing to ensure sealing. The patent combines the humidification and pathogen blocking functions of the heat-and-moisture exchanger with the anti-splash sputum suctioning function, which is suitable for use in the emergency and critical care medicine departments and has clinically practical value.

Noise-induced quasiperiod and period switching.

We employ a typical genetic circuit model to explore how noise can influence dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure regions. We find that a quasiperiodic component, which is not allowed by deterministic dynamics, will be generated by noise inducing in the first two regions, and this quasiperiod will be more and more stable along with the increase in noise. In particular, in the second region the quasiperiod will compete with a stable limit cycle and perform a new transient rhythm. Furthermore, we ascertain the entropy production rate and the heat dissipation rate, and discover a minimal value with theoretical elucidation. In the end, we unveil the mechanism of the formation of quasiperiods, and show a practical biological example. We expect this work to be helpful in solving some biological or ecological problems, such as the genetic origin of periodical cicadas and population dynamics with fluctuation.

The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system.

Chaos appears widely in various chemical and physical systems and is often accompanied by nonequilibrium due to its dissipative nature. However, it is still not clear how dissipative chaos is influenced by nonequilibrium conditions. Here, we study chaos from the perspective of nonequilibrium dynamics by considering a chemical Lorenz system. We found that its nonequilibrium nature can be quantified from the steady-state probability flux in the state space. The dynamic origin for the onset and offset of dissipative chaos was from the sudden appearance and disappearance of such nonequilibrium fluxes. Meanwhile, the dissipation associated with the flux as quantified by the entropy production rate provides the thermodynamic origin of dissipative chaos. Sharp changes in the degree of nonequilibrium also provide alternative quantitative indicators for the onset and offset of dissipative chaos.

Trade-offs between effectiveness and cost in bifunctional enzyme circuit with concentration robustness.

A fundamental trade-off in biological systems is whether they consume resources to perform biological functions or save resources. Bacteria need to reliably and rapidly respond to input signals by using limited cellular resources. However, excessive resource consumption will become a burden for bacteria growth. To investigate the relationship between functional effectiveness and resource cost, we study the ubiquitous bifunctional enzyme circuit, which is robust to fluctuations in protein concentration and responds quickly to signal changes. We show that trade-off relationships exist between functional effectiveness and protein cost. Expressing more proteins of the circuit increases concentration robustness and response speed but affects bacterial growth. In particular, our study reveals a general relationship between free-energy dissipation rate, response speed, and concentration robustness. The dissipation of free energy plays an important role in the concentration robustness and response speed. High robustness can only be achieved with a large amount of free-energy consumption and protein cost. In addition, the noise of the output increases with increasing protein cost, while the noise of the response time decreases with increasing protein cost. We also calculate the trade-off relationships in the EnvZ-OmpR system and the nitrogen assimilation system, which both have the bifunctional enzyme. Similar results indicate that these relationships are mainly derived from the specific feature of the bifunctional enzyme circuits and are not relevant to the details of the models. According to the trade-off relationships, bacteria take a compromise solution that reliably performs biological functions at a reasonable cost.

Exploration of nucleoprotein α-MoRE and XD interactions of Nipah and Hendra viruses.

Henipavirus, including Hendra virus (HeV) and Nipah virus (NiV), is a newly discovered human pathogen genus. The nucleoprotein of Henipavirus contains an α-helical molecular recognition element (α-MoRE) that folds upon binding to the X domain (XD) of the phosphoprotein (P). In order to explore the conformational dynamics of free α-MoREs and the underlying binding-folding mechanism with XD, atomic force field-based and hybrid structure-based MD simulations were carried out. In our empirical force field-based simulations, characteristic structures and helicities of α-MoREs reveal the co-existence of partially structured and disordered conformations, as in the case of the well characterized cognate measles virus (MeV) α-MoRE. In spite of their overall similarity, the two α-MoREs display subtle helicity differences in their C-terminal region, but much different from that of MeV. For the α-MoRE/XD complexes, the results of our hybrid structure-based simulations provide the coupled binding-folding landscapes, and unveil a wide conformational selection mechanism at early binding stages, followed by a final induce-fit mechanism selection process. However, the HeV and NiV complexes have a lower binding barrier compared to that of MeV. Moreover, the HeV α-MoRE/XD complex shows much less coupling effects between binding and folding compared to that from both NiV and MeV. Our analysis revealed that contrary to NiV and MeV, the N- and C-terminal regions of the HeV α-MoRE maintains a low helicity also in the bound form.

Funneled potential and flux landscapes dictate the stabilities of both the states and the flow: Fission yeast cell cycle.

Using fission yeast cell cycle as an example, we uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. These two landscapes can be quantified through the decomposition of the dynamics into the detailed balance preserving part and detailed balance breaking non-equilibrium part. While the funneled potential landscape is often crucial for the stability of the single attractor networks, we have uncovered that the funneled flux landscape is crucial for the emergence and maintenance of the stable limit cycle oscillation flow. This provides a new interpretation of the origin for the limit cycle oscillations: There are many cycles and loops existed flowing through the state space and forming the flux landscapes, each cycle with a probability flux going through the loop. The limit cycle emerges when a loop stands out and carries significantly more probability flux than other loops. We explore how robustness ratio (RR) as the gap or steepness versus averaged variations or roughness of the landscape, quantifying the degrees of the funneling of the underlying potential and flux landscapes. We state that these two landscapes complement each other with one crucial for stabilities of states on the cycle and the other crucial for the stability of the flow along the cycle. The flux is directly related to the speed of the cell cycle. This allows us to identify the key factors and structure elements of the networks in determining the stability, speed and robustness of the fission yeast cell cycle oscillations. We see that the non-equilibriumness characterized by the degree of detailed balance breaking from the energy pump quantified by the flux is the cause of the energy dissipation for initiating and sustaining the replications essential for the origin and evolution of life. Regulating the cell cycle speed is crucial for designing the prevention and curing strategy of cancer.

Effects of flexibility and electrostatic interactions on the coupled binding-folding mechanisms of Chz.core and H2A.z-H2B.

The intrinsically disordered protein (IDP) Chz.core, which is the interaction core of Chz1, shows binding preference to histone variant H2A.z. Although there are several studies on the binding process of Chz.core, the detailed coupled binding-folding processes are still elusive. In this study, we explored the coupled binding-folding mechanism and the effect of flexibility by continuously monitoring the flexibility degree of Chz.core. We applied an all-atom structure-based model (SBM), which takes advantage of providing both backbone and sidechain information about the conformational changes of Chz.core during binding. We presented a somewhat different "fly-casting" picture that the long IDP can undergo a tertiary stretching and bending with larger capture radii than ordered proteins. Our results suggest that the higher flexibility of Chz.core contributes to the shorter times for capturing events, leading to higher recognition efficiencies. In addition, compared to the ordered proteins, the high flexibility of the intrinsically disordered protein enables Chz.core to have a lower binding barrier and a faster association rate, which are favorable for the binding process to its partner H2A.z-H2B.

Strategy of tuning gene expression ratio in prokaryotic cell from perspective of noise and correlation.

Genes are organized into operons in procaryote, and these genes in one operon generally have related functions. However, genes in the same operon are usually not equally expressed, and the ratio needs to be fine-tuned for specific functions. We examine the difference of gene expression noise and correlation when tuning the expression level at the transcriptional or translational level in a bicistronic operon driven by a constitutive or a two-state promoter. We get analytic results for the noise and correlation of gene expression levels, which is confirmed by our stochastic simulations. Both the noise and the correlation of gene expressions in an operon with a two-state promoter are higher than in an operon with a constitutive promoter. Premature termination of mRNA induced by transcription terminator in the intergenic region or changing translation rates can tune the protein ratio at the transcriptional level or at the translational level. We find that gene expression correlation between promoter-proximal and promoter-distal genes at the protein level decreases as termination increases. In contrast, changing translation rates in the normal range almost does not alter the correlation. This explains why the translation rate is a key factor of modulating gene expressions in an operon. Our results can be useful to understand the relationship between the operon structure and the biological function of a gene network, and also may help in synthetic biology design.

The energy pump and the origin of the non-equilibrium flux of the dynamical systems and the networks.

The global stability of dynamical systems and networks is still challenging to study. We developed a landscape and flux framework to explore the global stability. The potential landscape is directly linked to the steady state probability distribution of the non-equilibrium dynamical systems which can be used to study the global stability. The steady state probability flux together with the landscape gradient determines the dynamics of the system. The non-zero probability flux implies the breaking down of the detailed balance which is a quantitative signature of the systems being in non-equilibrium states. We investigated the dynamics of several systems from monostability to limit cycle and explored the microscopic origin of the probability flux. We discovered that the origin of the probability flux is due to the non-equilibrium conditions on the concentrations resulting energy input acting like non-equilibrium pump or battery to the system. Another interesting behavior we uncovered is that the probabilistic flux is closely related to the steady state deterministic chemical flux. For the monostable model of the kinetic cycle, the analytical expression of the probabilistic flux is directly related to the deterministic flux, and the later is directly generated by the chemical potential difference from the adenosine triphosphate (ATP) hydrolysis. For the limit cycle of the reversible Schnakenberg model, we also show that the probabilistic flux is correlated to the chemical driving force, as well as the deterministic effective flux. Furthermore, we study the phase coherence of the stochastic oscillation against the energy pump, and argue that larger non-equilibrium pump results faster flux and higher coherence. This leads to higher robustness of the biological oscillations. We also uncovered how fluctuations influence the coherence of the oscillations in two steps: (1) The mild fluctuations influence the coherence of the system mainly through the probability flux while maintaining the regular landscape topography. (2) The larger fluctuations lead to flat landscape and the complete loss of the stability of the whole system.

Theoretical analysis of catalytic-sRNA-mediated gene silencing.

Small regulatory RNA (sRNA) that acts by an antisense mechanism is critical for gene regulation at the posttranscriptional level. Recently, an Hfq-dependent sRNA named MicM, which is related to the regulation of outer membrane protein, was verified as a novel antisense sRNA due to its catalytic mode of regulation. Here we propose a simple kinetic model for the enzyme-like regulation mode of sRNA and study in detail the noise properties of the target gene under various recycling rates of the regulator. We predict that the recycling rate of sRNA and other relative parameters have significant influence on the noise strength of target expression. In comparison with the stoichiometric regulatory mode, a lesser fluctuation of target expression was observed near the threshold at which the transcription rates of both sRNA and target mRNA equal each other. We also found that the new mode is better in terms of rapid response to external signals. However, it needs more time to achieve target recovery if the stimulating signal disappears. Additionally, the obtained time evolution results of the MicM-ybfM interaction system based on our model are consistent with previous experimental results, serving as experimental evidence to back up our theoretical analysis.