Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal-gain cascades (i.e., when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.Comment: 18 pages, 7 figure

Adaptive Control For Autonomous Navigation Of Mobile Robots Considering Time Delay And Uncertainty

Autonomous control of mobile robots has attracted considerable attention of researchers in the areas of robotics and autonomous systems during the past decades. One of the goals in the field of mobile robotics is development of platforms that robustly operate in given, partially unknown, or unpredictable environments and offer desired services to humans. Autonomous mobile robots need to be equipped with effective, robust and/or adaptive, navigation control systems. In spite of enormous reported work on autonomous navigation control systems for mobile robots, achieving the goal above is still an open problem. Robustness and reliability of the controlled system can always be improved. The fundamental issues affecting the stability of the control systems include the undesired nonlinear effects introduced by actuator saturation, time delay in the controlled system, and uncertainty in the model. This research work develops robustly stabilizing control systems by investigating and addressing such nonlinear effects through analytical, simulations, and experiments. The control systems are designed to meet specified transient and steady-state specifications. The systems used for this research are ground (Dr Robot X80SV) and aerial (Parrot AR.Drone 2.0) mobile robots. Firstly, an effective autonomous navigation control system is developed for X80SV using logic control by combining ‘go-to-goal’, ‘avoid-obstacle’, and ‘follow-wall’ controllers. A MATLAB robot simulator is developed to implement this control algorithm and experiments are conducted in a typical office environment. The next stage of the research develops an autonomous position (x, y, and z) and attitude (roll, pitch, and yaw) controllers for a quadrotor, and PD-feedback control is used to achieve stabilization. The quadrotor’s nonlinear dynamics and kinematics are implemented using MATLAB S-function to generate the state output. Secondly, the white-box and black-box approaches are used to obtain a linearized second-order altitude models for the quadrotor, AR.Drone 2.0. Proportional (P), pole placement or proportional plus velocity (PV), linear quadratic regulator (LQR), and model reference adaptive control (MRAC) controllers are designed and validated through simulations using MATLAB/Simulink. Control input saturation and time delay in the controlled systems are also studied. MATLAB graphical user interface (GUI) and Simulink programs are developed to implement the controllers on the drone. Thirdly, the time delay in the drone’s control system is estimated using analytical and experimental methods. In the experimental approach, the transient properties of the experimental altitude responses are compared to those of simulated responses. The analytical approach makes use of the Lambert W function to obtain analytical solutions of scalar first-order delay differential equations (DDEs). A time-delayed P-feedback control system (retarded type) is used in estimating the time delay. Then an improved system performance is obtained by incorporating the estimated time delay in the design of the PV control system (neutral type) and PV-MRAC control system. Furthermore, the stability of a parametric perturbed linear time-invariant (LTI) retarded type system is studied. This is done by analytically calculating the stability radius of the system. Simulation of the control system is conducted to confirm the stability. This robust control design and uncertainty analysis are conducted for first-order and second-order quadrotor models. Lastly, the robustly designed PV and PV-MRAC control systems are used to autonomously track multiple waypoints. Also, the robustness of the PV-MRAC controller is tested against a baseline PV controller using the payload capability of the drone. It is shown that the PV-MRAC offers several benefits over the fixed-gain approach of the PV controller. The adaptive control is found to offer enhanced robustness to the payload fluctuations

Evolutionary comparison between viral lysis rate and latent period

Marine viruses shape the structure of the microbial community. They are, thus, a key determinant of the most important biogeochemical cycles in the planet. Therefore, a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems. The infection cycle, for example, is indistinctly modeled in two very different ways. In one representation, the process is described including explicitly a fixed delay between infection and offspring release. In the other, the offspring are released at exponentially distributed times according to a fixed release rate. By considering obvious quantitative differences pointed out in the past, the latter description is widely used as a simplification of the former. However, it is still unclear how the dichotomy "delay versus rate description" affects long-term predictions of host-virus interaction models. Here, we study the ecological and evolutionary implications of using one or the other approaches, applied to marine microbes. To this end, we use mathematical and eco-evolutionary computational analysis. We show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments. However, rate-based descriptions can fail to describe properly long-term microbe-virus interactions. Moreover, additional information about trade-offs between life-history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics. This result affects deeply most of the marine ecosystem models that include viruses, especially when used to answer evolutionary questions.Comment: to appear in J. Theor. Bio

Quantum optical memory protocols in atomic ensembles

We review a series of quantum memory protocols designed to store the quantum information carried by light into atomic ensembles. In particular, we show how a simple semiclassical formalism allows to gain insight into various memory protocols and to highlight strong analogies between them. These analogies naturally lead to a classification of light storage protocols into two categories, namely photon echo and slow-light memories. We focus on the storage and retrieval dynamics as a key step to map the optical information into the atomic excitation. We finally review various criteria adapted for both continuous variables and photon-counting measurement techniques to certify the quantum nature of these memory protocols

Implementation of Delayed-Feedback Controllers on Continuous Systems and Analysis of their Response under Primary Resonance Excitations

During the last three decades, a considerable amount of research has been directed toward understanding the influence of time delays on the stability and stabilization of dynamical systems. From a control perspective, these delays can either have a compounding and destabilizing effect, or can actually improve controllers\u27 performance. In the latter case, additional time delay is carefully and deliberately introduced into the feedback loop so as to augment inherent system delays and produce larger damping for smaller control efforts. While delayed-feedback algorithms have been successfully implemented on discrete dynamical systems with limited degrees of freedom, a critical issue appears in their implementation on systems consisting of a large number of degrees of freedom or on infinite-dimensional structures. The reason being that the presence of delay in the control loop renders the characteristic polynomial of the transcendental type which produces infinite number of eigenvalues for every discrete controller\u27s gain and time delay. As a result, choosing a gain-delay combination that stabilizes the lower vibration modes can easily destabilize the higher modes. To address this problem, this dissertation introduces the concept of filter-augmented delayed-feedback control algorithms and applies it to mitigate vibrations of various structural systems both theoretically and experimentally. In specific, it explores the prospect of augmenting proper filters in the feedback loop to enhance the robustness of delayed-feedback controllers allowing them to simultaneously mitigate the response of different vibration modes using a single sensor and a single gain-delay actuator combination. The dissertation goes into delineating the influence of filter\u27s dynamics (order and cut-off frequency) on the stability maps and damping contours clearly demonstrating the possibility of effectively reducing multi-modal oscillations of infinite-dimensional structures when proper filters are augmented in the feedback loop. Additionally, this research illustrates that filters may actually enhance the robustness of the controller to parameter\u27s uncertainties at the expense of reducing the controller\u27s effective damping. To assess the performance of the proposed control algorithm, the dissertation presents three experimental case studies; two of which are on structures whose dynamics can be discretized into a system of linearly-uncoupled ordinary differential equations (ODEs); and the third on a structure whose dynamics can only be reduced into a set of linearly-coupled ODEs. The first case study utilizes a filter-augmented delayed-position feedback algorithm for flexural vibration mitigation and external disturbances rejection on a macro-cantilever Euler-Bernoulli beam. The second deals with implementing a filter-augmented delayed-velocity feedback algorithm for vibration mitigation and external disturbances rejection on a micro-cantilever sensor. The third implements a filter-augmented delayed-position feedback algorithm to suppress the coupled flexural-torsional oscillations of a cantilever beam with an asymmetric tip rigid body; a problem commonly seen in the vibrations of large wind turbine blades. This research also fills an important gap in the open literature presented in the lack of studies addressing the response of delay systems to external resonant excitations; a critical issue toward implementing delayed-feedback controllers to reduce oscillations resulting from persistent harmonic excitations. To that end, this dissertation presents a modified multiple scaling approach to investigate primary resonances of a weakly-nonlinear second-order delay system with cubic nonlinearities. In contrast to previous studies where the implementation is confined to the assumption of linear feedback with small control gains; this effort proposes an approach which alleviates that assumption and permits treating a problem with arbitrarily large gains. The modified procedure lumps the delay state into unknown linear damping and stiffness terms that are function of the gain and delay. These unknown functions are determined by enforcing the linear part of the steady-state solution acquired via the Method of Multiple Scales to match that obtained directly by solving the forced linear problem. Through several examples, this research examines the validity of the modified procedure by comparing its results to solutions obtained via a Harmonic Balance approach demonstrating the ability of the proposed methodology to predict the amplitude, softening-hardening characteristics, and stability of the resulting steady-state responses

Pole Placement and Reduced-Order Modelling for Time-Delayed Systems Using Galerkin Approximations

The dynamics of time-delayed systems (TDS) are governed by delay differential equa- tions (DDEs), which are infinite dimensional and pose computational challenges. The Galerkin approximation method is one of several techniques to obtain the spectrum of DDEs for stability and stabilization studies. In the literature, Galerkin approximations for DDEs have primarily dealt with second-order TDS (second-order Galerkin method), and the for- mulations have resulted in spurious roots, i.e., roots that are not among the characteristic roots of the DDE. Although these spurious roots do not affect stability studies, they never- theless add to the complexity and computation time for control and reduced-order modelling studies of DDEs. A refined mathematical model, called the first-order Galerkin method, is proposed to avoid spurious roots, and the subtle differences between the two formulations (second-order and first-order Galerkin methods) are highlighted with examples. For embedding the boundary conditions in the first-order Galerkin method, a new pseudoinverse-based technique is developed. This method not only gives the exact location of the rightmost root but also, on average, has a higher number of converged roots when compared to the existing pseudospectral differencing method. The proposed method is combined with an optimization framework to develop a pole-placement technique for DDEs to design closed-loop feedback gains that stabilize TDS. A rotary inverted pendulum system apparatus with inherent sensing delays as well as deliberately introduced time delays is used to experimentally validate the Galerkin approximation-based optimization framework for the pole placement of DDEs. Optimization-based techniques cannot always place the rightmost root at the desired location; also, one has no control over the placement of the next set of rightmost roots. However, one has the precise location of the rightmost root. To overcome this, a pole- placement technique for second-order TDS is proposed, which combines the strengths of the method of receptances and an optimization-based strategy. When the method of receptances provides an unsatisfactory solution, particle swarm optimization is used to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. The Galerkin approximation method contains both converged and unconverged roots of the DDE. By using only the information about the converged roots and applying the eigenvalue decomposition, one obtains an r-dimensional reduced-order model (ROM) of the DDE. To analyze the dynamics of DDEs, we first choose an appropriate value for r; we then select the minimum value of the order of the Galerkin approximation method system at which at least r roots converge. By judiciously selecting r, solutions of the ROM and the original DDE are found to match closely. Finally, an r-dimensional ROM of a 3D hovercraft apparatus in the presence of delay is validated experimentally

Complex oscillations in the delayed Fitzhugh-Nagumo equation

Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays. Beyond this regime, delays significantly enrich the dynamics, leading to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a delay-induced subcritical Bogdanov-Takens instability arising at the fold points of the S-shaped critical manifold. Underlying the transition from canard-induced to delay-induced dynamics is an abrupt switch in the nature of the Hopf bifurcation

Cyber-Physical Codesign of Wireless Structural Control System

Structural control systems play a critical role in protecting civil infrastructure from natural hazards such as earthquakes and extreme winds. Utilizing wireless sensors for sensing, communication and control, wireless structural control systems provide an attractive alternative for structural vibration mitigation. Although wireless control systems have advantages of flexible installation, rapid deployment and low maintenance cost, there are unique challenges associated with them, such as wireless network induced time delay and potential data loss. These challenges need to be considered jointly from both the network (cyber) and control (physical) perspectives. This research aims to develop a framework facilitating cyber-physical codesign of wireless control system. The challenges of wireless structural control are addressed through: (1) a numerical simulation tool to realistically model the complexities of wireless structural control systems, (2) a codesign approach for designing wireless control system, (3) a sensor platform to experimentally evaluate wireless control performance, (4) an estimation method to compensate for the data loss and sensor failure, and (5) a framework for fault tolerance study of wireless control system withreal-time hybrid simulation. The results of this work not only provide codesign tools to evaluate and validate wireless control design, but also the codesign strategies to implement on real-world structures for wireless structural control

PV panel modeling and identification

In this chapter, the modelling techniques of PV panels from I-V characteristics are discussed. At the beginning, a necessary review on the various methods are presented, where difficulties in mathematics, drawbacks in accuracy, and challenges in implementation are highlighted. Next, a novel approach based on linear system identification is demonstrated in detail. Other than the prevailing methods of using approximation (analytical methods), iterative searching (classical optimization), or soft computing (artificial intelligence), the proposed method regards the PV diode model as the equivalent output of a dynamic system, so the diode model parameters can be linked to the transfer function coefficients of the same dynamic system. In this way, the problem of solving PV model parameters is equivalently converted to system identification in control theory, which can be perfectly solved by a simple integral-based linear least square method. Graphical meanings of the proposed method are illustrated to help readers understand the underlying principles. As compared to other methods, the proposed one has the following benefits: 1) unique solution; 2) no iterative or global searching; 3) easy to implement (linear least square); 4) accuracy; 5) extendable to multi-diode models. The effectiveness of the proposed method has been verified by indoor and outdoor PV module testing results. In addition, possible applications of the proposed method are discussed like online PV monitoring and diagnostics, noncontact measurement of POA irradiance and cell temperature, fast model identification for satellite PV panels, and etc