A dual-clock-driven model of lymphatic muscle cell pacemaking to emulate knock-out of Ano1 or IP3R

Lymphatic system defects are involved in a wide range of diseases, including obesity, cardiovascular disease, and neurological disorders, such as Alzheimer's disease. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, which are in turn driven by electrochemical oscillations that cause rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is an incomplete understanding of the mechanisms involved in these repeated events, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a model where autonomous oscillations in the membrane potential (M-clock) drove passive oscillations in the calcium concentration (C-clock). In this paper, to model more accurately what is known about the underlying physiology, we extend this model to the case where the M-clock and the C-clock oscillators are both active but coupled together, thus both driving the action potentials. This extension results from modifications to the model's description of the IP3 receptor, a key C-clock mechanism. The synchronised dual-driving clock behaviour enables the model to match IP3 receptor knock-out data, thus resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms of coupling of the dual clocks. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of some causes of lymphoedema.

IP3R1 underlies diastolic ANO1 activation and pressure-dependent chronotropy in lymphatic collecting vessels

Pressure-dependent chronotropy of murine lymphatic collecting vessels relies on the activation of the Ca2+-activated chloride channel encoded by Anoctamin 1 (Ano1) in lymphatic muscle cells. Genetic ablation or pharmacological inhibition of ANO1 results in a significant reduction in basal contraction frequency and essentially complete loss of pressure-dependent frequency modulation by decreasing the rate of the diastolic depolarization phase of the ionic pacemaker in lymphatic muscle cells (LMCs). Oscillating Ca2+ release from sarcoendoplasmic reticulum Ca2+ channels has been hypothesized to drive ANO1 activity during diastole, but the source of Ca2+ for ANO1 activation in smooth muscle remains unclear. Here, we investigated the role of the inositol triphosphate receptor 1 (Itpr1; Ip3r1) in this process using pressure myography, Ca2+ imaging, and membrane potential recordings in LMCs of ex vivo pressurized inguinal-axillary lymphatic vessels from control or Myh11CreERT2;Ip3r1fl/fl (Ip3r1ismKO) mice. Ip3r1ismKO vessels had significant reductions in contraction frequency and tone but an increased contraction amplitude. Membrane potential recordings from LMCs of Ip3r1ismKO vessels revealed a depressed diastolic depolarization rate and an elongation of the plateau phase of the action potential (AP). Ca2+ imaging of LMCs using the genetically encoded Ca2+ sensor GCaMP6f demonstrated an elongation of the Ca2+ flash associated with an AP-driven contraction. Critically, diastolic subcellular Ca2+ transients were absent in LMCs of Ip3r1ismKO mice, demonstrating the necessity of IP3R1 activity in controlling ANO1-mediated diastolic depolarization. These findings indicate a critical role for IP3R1 in lymphatic vessel pressure-dependent chronotropy and contractile regulation.

Modelling the coupling of the M-clock and C-clock in lymphatic muscle cells

Chronic dysfunction of the lymphatic vascular system results in fluid accumulation between cells: lymphoedema. The condition is commonly acquired secondary to diseases such as cancer or the associated therapies. The primary driving force for fluid return through the lymphatic vasculature is provided by contractions of the muscularized lymphatic collecting vessels, driven by electrochemical oscillations. However, there is an incomplete understanding of the molecular and bioelectric mechanisms involved in lymphatic muscle cell excitation, hampering the development and use of pharmacological therapies. Modelling in silico has contributed greatly to understanding the contributions of specific ion channels to the cardiac action potential, but modelling of these processes in lymphatic muscle remains limited. Here, we propose a model of oscillations in the membrane voltage (M-clock) and intracellular calcium concentrations (C-clock) of lymphatic muscle cells. We modify a model by Imtiaz and colleagues to enable the M-clock to drive the C-clock oscillations. This approach differs from typical models of calcium oscillators in lymphatic and related cell types, but is required to fit recent experimental data. We include an additional voltage dependence in the gating variable control for the L-type calcium channel, enabling the M-clock to oscillate independently of the C-clock. We use phase-plane analysis to show that these M-clock oscillations are qualitatively similar to those of a generalised FitzHugh-Nagumo model. We also provide phase plane analysis to understand the interaction of the M-clock and C-clock oscillations. The model and methods have the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.

Stabilization of antithetic control via molecular buffering

A key goal in synthetic biology is the construction of molecular circuits that robustly adapt to perturbations. Although many natural systems display perfect adaptation, whereby stationary molecular concentrations are insensitive to perturbations, its de novo engineering has proven elusive. The discovery of the antithetic control motif was a significant step towards a universal mechanism for engineering perfect adaptation. Antithetic control provides perfect adaptation in a wide range of systems, but it can lead to oscillatory dynamics due to loss of stability; moreover, it can lose perfect adaptation in fast growing cultures. Here, we introduce an extended antithetic control motif that resolves these limitations. We show that molecular buffering, a widely conserved mechanism for homeostatic control in Nature, stabilizes oscillations and allows for near-perfect adaptation during rapid growth. We study multiple buffering topologies and compare their performance in terms of their stability and adaptation properties. We illustrate the benefits of our proposed strategy in exemplar models for biofuel production and growth rate control in bacterial cultures. Our results provide an improved circuit for robust control of biomolecular systems.

Metabolic buffer analysis reveals the simultaneous, independent control of ATP and adenylate energy ratios

Determining the underlying principles behind biological regulation is important for understanding the principles of life, treating complex diseases and creating de novo synthetic biology. Buffering-the use of reservoirs of molecules to maintain molecular concentrations-is a widespread and important mechanism for biological regulation. However, a lack of theory has limited our understanding of its roles and quantified effects. Here, we study buffering in energy metabolism using control theory and novel buffer analysis. We find that buffering can enable the simultaneous, independent control of multiple coupled outputs. In metabolism, adenylate kinase and AMP deaminase enable simultaneous control of ATP and adenylate energy ratios, while feedback on metabolic pathways is fundamentally limited to controlling one of these outputs. We also quantify the regulatory effects of the phosphagen system-the above buffers and creatine kinase-revealing which mechanisms regulate which outputs. The results are supported by human muscle and mouse adipocyte data. Together, these results illustrate the synergy of feedback and buffering in molecular biology to simultaneously control multiple outputs.

Control theory helps to resolve the measles paradox

Measles virus (MV) is a highly contagious respiratory morbillivirus that results in many disabilities and deaths. A crucial challenge in studying MV infection is to understand the so-called 'measles paradox'-the progression of the infection to severe immunosuppression before clearance of acute viremia, which is also observed in canine distemper virus (CDV) infection. However, a lack of models that match in vivo data has restricted our understanding of this complex and counter-intuitive phenomenon. Recently, progress was made in the development of a model that fits data from acute measles infection in rhesus macaques. This progress motivates our investigations to gain additional insights from this model into the control mechanisms underlying the paradox. In this paper, we investigated analytical conditions determining the control and robustness of viral clearance for MV and CDV, to untangle complex feedback mechanisms underlying the dynamics of acute infections in their natural hosts. We applied control theory to this model to help resolve the measles paradox. We showed that immunosuppression is important to control and clear the virus. We also showed under which conditions T-cell killing becomes the primary mechanism for immunosuppression and viral clearance. Furthermore, we characterized robustness properties of T-cell immunity to explain similarities and differences in the control of MV and CDV. Together, our results are consistent with experimental data, advance understanding of control mechanisms of viral clearance across morbilliviruses, and will help inform the development of effective treatments. Further the analysis methods and results have the potential to advance understanding of immune system responses to a range of viral infections such as COVID-19.

Synthetic negative feedback circuits using engineered small RNAs

Negative feedback is known to enable biological and man-made systems to perform reliably in the face of uncertainties and disturbances. To date, synthetic biological feedback circuits have primarily relied upon protein-based, transcriptional regulation to control circuit output. Small RNAs (sRNAs) are non-coding RNA molecules that can inhibit translation of target messenger RNAs (mRNAs). In this work, we modelled, built and validated two synthetic negative feedback circuits that use rationally-designed sRNAs for the first time. The first circuit builds upon the well characterised tet-based autorepressor, incorporating an externally-inducible sRNA to tune the effective feedback strength. This allows more precise fine-tuning of the circuit output in contrast to the sigmoidal, steep input–output response of the autorepressor alone. In the second circuit, the output is a transcription factor that induces expression of an sRNA, which inhibits translation of the mRNA encoding the output, creating direct, closed-loop, negative feedback. Analysis of the noise profiles of both circuits showed that the use of sRNAs did not result in large increases in noise. Stochastic and deterministic modelling of both circuits agreed well with experimental data. Finally, simulations using fitted parameters allowed dynamic attributes of each circuit such as response time and disturbance rejection to be investigated.

Model reduction for Kuramoto models with complex topologies

Synchronization of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics to social networks and technology. A fundamental and long-time goal in the study of synchronization has been to find low-order descriptions of complex oscillator networks and their collective dynamics. However, for the Kuramoto model, the most widely used model of coupled oscillators, this goal has remained surprisingly challenging, in particular for finite-size networks. Here, we propose a model reduction framework that effectively captures synchronization behavior in complex network topologies. This framework generalizes a collective coordinates approach for all-to-all networks [G. A. Gottwald, Chaos 25, 053111 (2015)CHAOEH1054-150010.1063/1.4921295] by incorporating the graph Laplacian matrix in the collective coordinates. We first derive low dimensional evolution equations for both clustered and nonclustered oscillator networks. We then demonstrate in numerical simulations for Erdős-Rényi networks that the collective coordinates capture the synchronization behavior in both finite-size networks as well as in the thermodynamic limit, even in the presence of interacting clusters.

The Interplay between Feedback and Buffering in Cellular Homeostasis

Buffering, the use of reservoirs of molecules to maintain concentrations of key molecular species, and negative feedback are the primary known mechanisms for robust homeostatic regulation. To our knowledge, however, the fundamental principles behind their combined effect have not been elucidated. Here, we study the interplay between buffering and negative feedback in the context of cellular homeostasis. We show that negative feedback counteracts slow-changing disturbances, whereas buffering counteracts fast-changing disturbances. Furthermore, feedback and buffering have limitations that create trade-offs for regulation: instability in the case of feedback and molecular noise in the case of buffering. However, because buffering stabilizes feedback and feedback attenuates noise from slower-acting buffering, their combined effect on homeostasis can be synergistic. These effects can be explained within a traditional control theory framework and are consistent with experimental observations of both ATP homeostasis and pH regulation in vivo. These principles are critical for studying robustness and homeostasis in biology and biotechnology.

Simplified mechanistic models of gene regulation for analysis and design

Simplified mechanistic models of gene regulation are fundamental to systems biology and essential for synthetic biology. However, conventional simplified models typically have outputs that are not directly measurable and are based on assumptions that do not often hold under experimental conditions. To resolve these issues, we propose a ‘model reduction’ methodology and simplified kinetic models of total mRNA and total protein concentration, which link measurements, models and biochemical mechanisms. The proposed approach is based on assumptions that hold generally and include typical cases in systems and synthetic biology where conventional models do not hold. We use novel assumptions regarding the ‘speed of reactions’, which are required for the methodology to be consistent with experimental data. We also apply the methodology to propose simplified models of gene regulation in the presence of multiple protein binding sites, providing both biological insights and an illustration of the generality of the methodology. Lastly, we show that modelling total protein concentration allows us to address key questions on gene regulation, such as efficiency, burden, competition and modularity.

Tuning the dials of Synthetic Biology

Synthetic Biology is the ‘Engineering of Biology’ – it aims to use a forward-engineering design cycle based on specifications, modelling, analysis, experimental implementation, testing and validation to modify natural or design new, synthetic biology systems so that they behave in a predictable fashion. Motivated by the need for truly plug-and-play synthetic biological components, we present a comprehensive review of ways in which the various parts of a biological system can be modified systematically. In particular, we review the list of ‘dials’ that are available to the designer and discuss how they can be modelled, tuned and implemented. The dials are categorized according to whether they operate at the global, transcriptional, translational or post-translational level and the resolution that they operate at. We end this review with a discussion on the relative advantages and disadvantages of some dials over others.

Kinetics of isotype-specific humoral immunity in rubella vaccine-associated arthropathy

The present study documents the relationship between the development of rubella vaccine-associated arthropathy and isotype-specific rubella antibody responses in a prospectively studied population of 44 adult rubella hemagglutination inhibition (HAI) seronegative females undergoing rubella immunization. Rubella-specific IgM, IgG, and IgA antibody responses were evaluated prior to and at 1, 2, 3, 4, 5, 6, 12, and 24 weeks postvaccine. Detectable preimmunization rubella antibody of the IgG or IgA class was present using ELISA techniques in 6 of 6 individuals developing acute arthritis, 13 of 17 developing acute arthralgia, and in 15 of 21 with no joint manifestations postvaccine. Significantly elevated HAI IgM responses were noted 3 and 4 weeks postvaccine in the acute arthritis group but no significant differences were found in IgG and IgA rubella antibody levels postvaccine in relation to the presence or absence of joint manifestations at any time period postvaccine. The data support rubella reinfection as an important feature of rubella vaccine-associated arthropathy but do not support a role for quantitative differences in rubella IgG and IgA antibody in the pathogenesis of this syndrome.

Tuberculous rheumatism (Poncet's disease) in a child

A 2-year-old boy who had increasing difficulty walking and had large, warm, sterile knee and ankle effusions was found to have active vertebral tuberculosis and a large prevertebral abscess. Lymphocyte proliferation assays demonstrated increased purified protein derivative-induced reactivity of synovial fluid lymphocytes compared with peripheral blood lymphocytes. The arthritis responded rapidly to antituberculous and antiinflammatory drugs. This patient's disease represented an example of tuberculous rheumatism (Poncet's disease).

The effects of cyclophosphamide on in vitro cytotoxic responses to a syngeneic tumour

We have studied the effects of treating DBA/2 mice with high doses of cyclophosphamide upon their subsequent ability to generate cytotoxic cells in vitro against syngeneic tumour antigens or alloantigens. High doses of cyclophosphamide (100-200 mg/kg body weight) eliminated the response to both antigens. The addition of normal DBA/2 thymocytes into these cultures restored the response to allogeneic cells but not to tumour cells. The anti-tumour response could be restored by the addition of interleukin 2 to the cultures. Treatment with high doses of cyclophosphamide decreased the number of anti-tumour cytotoxic cell precursors in the spleen, but did not affect the capacity of bulk cultures of spleen cells to produce interleukin 2 when stimulated with the mitogen concanavalin A.

Helper cells active in the generation of cytotoxicity to a syngeneic tumor

We have examined a population of thymic lymphocytes that augment the generation in vitro of specific cytotoxic T cells against P815.X2, a syngeneic tumor in DBA/2 mice. These helper cells are evident in the thymus of DBA/2 mice 5 to 7 days after subcutaneous injection of live P815 cells. They are Thy-1 positive, resistant to gamma radiation, antigen specific, and appear to exert their influence most effectively when added at the beginning of the culture.

Helper cells active in the generation of cytotoxicity to a syngeneic tumor

We have examined a population of thymic lymphocytes that augment the generation in vitro of specific cytotoxic T cells against P815.X2, a syngeneic tumor in DBA/2 mice. These helper cells are evident in the thymus of DBA/2 mice 5 to 7 days after subcutaneous injection of live P815 cells. They are Thy-1 positive, resistant to gamma radiation, antigen specific, and appear to exert their influence most effectively when added at the beginning of the culture.