Proceedings of the ... IEEE Conference on Decision & Control. IEEE Conference on Decision & Control最新文献

Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations.

The Human Immunodeficiency Virus (HIV) infects helper-T cells, and takes advantage of the naturally occurring quiescent phenotype of T cells to persist even under effective treatment conditions. If an infected cell does not produce virus and enters this quiescent state, it forms a natural reservoir that is not targeted by either the existing antiretroviral drugs or the immune system. These quiescent cells intermittently switch to an activated phenotype and begin to produce virus, and are the primary source of viral rebound following treatment cessation. Recent experimental results have shown that, despite this reservoir having a years-long half-life under treatment, most of the cells in the reservoir were infected in a few weeks prior to the start of treatment. This can only be explained by assuming that this reservoir has a short half-life off treatment and a very long half-life on treatment. In this paper, we introduce a novel model of reservoir formation and turnover explaining this difference as a result of antigen-dependent activation. We introduce a second control input through infusion of HIV antigen, mimicking the non-infection pseudovirus (PV) produced by protease inhibitor therapy. This model is coupled to an existing model of immune response to HIV. We fit the parameters of this model to the existing clinical observations of latency. We show that the use of antigen infusion therapy can result in order-of-magnitude decrease in the size of the quiescent reservoir, and that this may provide a way to rapidly stabilize a post-treatment control state in treated HIV infected individuals.

In this paper we consider the problem of portfolio optimization involving uncertainty in the probability distribution of the assets returns. Starting with an estimate of the mean and covariance matrix of the returns of the assets, we define a class of admissible distributions for the returns and show that optimizing the worst-case risk of loss can be done in a numerically efficient way. More precisely, we show that determining the asset allocation that minimizes the distributionally robust risk can be done using quadratic programming and a one line search. Effectiveness of the proposed approach is shown using academic examples.

Existence of disturbances in unknown environments is a pervasive challenge in robotic locomotion control. Disturbance observers are a class of unknown input observers that have been extensively used for disturbance rejection in numerous robotics applications. In this paper, we extend a class of widely-used nonlinear disturbance observers to underactuated bipedal robots, which are controlled using hybrid zero dynamics-based control schemes. The proposed hybrid nonlinear disturbance observer provides the autonomous biped robot control system with disturbance rejection capabilities, while the underlying hybrid zero-dynamics based control law remains intact.

A central issue in the analysis of multi-stable systems is that of controlling the relative size of the basins of attraction of alternative states through suitable choices of system parameters. We are interested here mainly in the stochastic version of this problem, that of shaping the stationary probability distribution of a Markov chain so that various alternative modes become more likely than others. Although many of our results are more general, we were motivated by an important biological question, that of cell differentiation. In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining the different cell types. Specifically, we study here the "PU.1/GATA-1 circuit" which is involved in the control of the development of mature blood cells from hematopoietic stem cells (HSCs). All mature, specialized blood cells have been shown to be derived from multipotent HSCs. Our first contribution is to introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge. We then find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.

How living cells employ counting mechanisms to regulate their numbers or density is a long-standing problem in developmental biology that ties directly with organism or tissue size. Diverse cells types have been shown to regulate their numbers via secretion of factors in the extracellular space. These factors act as a proxy for the number of cells and function to reduce cellular proliferation rates creating a negative feedback. It is desirable that the production rate of such factors be kept as low as possible to minimize energy costs and detection by predators. Here we formulate a stochastic model of cell proliferation with feedback control via a secreted extracellular factor. Our results show that while low levels of feedback minimizes random fluctuations in cell numbers around a given set point, high levels of feedback amplify Poisson fluctuations in secreted-factor copy numbers. This trade-off results in an optimal feedback strength, and sets a fundamental limit to noise suppression in cell numbers with short-lived factors providing more efficient noise buffering. We further expand the model to consider external disturbances in key physiological parameters, such as, proliferation and factor synthesis rates. Intriguingly, while negative feedback effectively mitigates disturbances in the proliferation rate, it amplifies disturbances in the synthesis rate. In summary, these results provide unique insights into the functioning of feedback-based counting mechanisms, and apply to organisms ranging from unicellular prokaryotes and eukaryotes to human cells.

Multistable dynamical systems are ubiquitous in nature, especially in the context of regulatory networks controlling cell fate decisions, wherein stable steady states correspond to different cell phenotypes. In the past decade, it has become experimentally possible to "reprogram" the fate of a cell by suitable externally imposed input stimulations. In several of these reprogramming instances, the underlying regulatory network has a known structure and often it falls in the class of cooperative monotone dynamical systems. In this paper, we therefore leverage this structure to provide concrete guidance on the choice of inputs that reprogram a cooperative dynamical system to a desired target steady state. Our results are parameter-independent and therefore can serve as a practical guidance to cell-fate reprogramming experiments.

Time series measurements of circular viral episome (2-LTR) concentrations enable indirect quantification of persistent low-level Human Immunodeficiency Virus (HIV) replication in patients on Integrase-Inhibitor intensified Combined Antiretroviral Therapy (cART). In order to determine the magnitude of these low level infection events, blood has to be drawn from a patients at a frequency and volume that is strictly regulated by the Institutional Review Board (IRB). Once the blood is drawn, the 2-LTR concentration is determined by quantifying the amount of HIV DNA present in the sample via a PCR (Polymerase Chain Reaction) assay. Real time quantitative Polymerase Chain Reaction (qPCR) is a widely used method of performing PCR; however, a newer droplet digital Polymerase Chain Reaction (ddPCR) method has been shown to provide more accurate quantification of DNA. Using a validated model of HIV viral replication, this paper demonstrates the importance of considering DNA quantification assay type when optimizing experiment design conditions. Experiments are optimized using a Genetic Algorithm (GA) to locate a family of suboptimal sample schedules which yield the highest fitness. Fitness is defined as the expected information gained in the experiment, measured by the Kullback-Leibler Divergence (KLD) between the prior and posterior distributions of the model parameters. We compare the information content of the optimized schedules to uniform schedules as well as two clinical schedules implemented by researchers at UCSF and the University of Melbourne. This work shows that there is a significantly greater gain information in experiments using a ddPCR assay vs. a qPCR assay and that certain experiment design considerations should be taken when using either assay.

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Numerical computation of the expected information content of a prospective experimental design is computationally expensive, requiring calculating the Kullback-Leibler divergence of the posterior distribution from the prior for simulated data from a large sample of points from the prior distribution. In this work, we investigate whether the Unscented Transform (UT) of the prior distribution can provide an adequate estimate of the expected information content in the context of experiment design for a previously validated HIV-1 2-LTR model. Three different schedules with evenly distributed time points have been used to generate the experimental data along with the incorporation of qPCR noise for the study. The UT shows promise in estimating information content by preserving the optimal ordering of 2-LTR sample collection schedules, when compared to completely stochastic sampling from the underlying multivariate distributions.