William T. Baumann

Dynamic modelling of oestrogen signalling and cell fate in breast cancer cells

Cancers of the breast and other tissues arise from aberrant decision-making by cells regarding their survival or death, proliferation or quiescence, damage repair or bypass. These decisions are made by molecular signalling networks that process information from outside and from within the breast cancer cell and initiate responses that determine the cells survival and reproduction. Because the molecular logic of these circuits is difficult to comprehend by intuitive reasoning alone, we present some preliminary mathematical models of the basic decision circuits in breast cancer cells that may aid our understanding of their susceptibility or resistance to endocrine therapy.

Exploring the roles of noise in the eukaryotic cell cycle

The DNA replication–division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (≈1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (<1 min). If these mRNA molecules are longer-lived (perhaps 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise suppression mechanisms at work in cells.

Active suppression of acoustic radiation from impulsively excited structures

The objective is to use active control to suppress the acoustic energy that is radiated to the far field from a structure that has been excited by a short‐duration pulse. The problem is constrained by the assumption that the far‐field pressure cannot be directly measured. Therefore, a method is developed for estimating the total radiated energy from measurements on the structure. Using this estimate as a cost function, a feedback controller is designed using linear quadratic regulator theory to minimize the cost. Computer simulations of a clamped–clamped beam show that there is appreciable difference in the total radiated energy between a system with a controller designed to suppress vibrations of the structure and a system with a controller that takes into account the coupling of these vibrations to the surrounding fluid. The results of this work provide a framework for a general, model‐based method for actively suppressing transient structural acoustic radiation that can also be applied to steady, narro...

Endoplasmic Reticulum Stress, the Unfolded Protein Response, Autophagy, and the Integrated Regulation of Breast Cancer Cell Fate

How breast cancer cells respond to the stress of endocrine therapies determines whether they will acquire a resistant phenotype or execute a cell-death pathway. After a survival signal is successfully executed, a cell must decide whether it should replicate. How these cell-fate decisions are regulated is unclear, but evidence suggests that the signals that determine these outcomes are highly integrated. Central to the final cell-fate decision is signaling from the unfolded protein response, which can be activated following the sensing of stress within the endoplasmic reticulum. The duration of the response to stress is partly mediated by the duration of inositol-requiring enzyme-1 activation following its release from heat shock protein A5. The resulting signals appear to use several B-cell lymphoma-2 family members to both suppress apoptosis and activate autophagy. Changes in metabolism induced by cellular stress are key components of this regulatory system, and further adaptation of the metabolome is affected in response to stress. Here we describe the unfolded protein response, autophagy, and apoptosis, and how the regulation of these processes is integrated. Central topologic features of the signaling network that integrate cell-fate regulation and decision execution are discussed.

A model of yeast cell-cycle regulation based on multisite phosphorylation

In order for the cells genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein‐based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects of molecular fluctuations on cell‐cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln‐ and Clb‐dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell‐cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast‐sized cells (∼50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1‐S transition in budding yeast, which is governed by an underlying sizer+timer control system.

Active structural acoustic control of broadband disturbances

A control design technique is developed to actively suppress the acoustic power radiated from a structure, with negligible fluid loading, that is persistently excited by narrow‐band or broadband disturbances. The problem is constrained by the assumption that the far‐field pressure cannot be measured directly. A method for estimating the total radiated power from measurements on the structure is developed. Using this estimate as a cost function and assuming knowledge of the spectrum of the disturbance, a controller is designed using the linear‐quadratic‐Gaussian (LQG) theory to minimize the cost. Computer simulations of a clamped–clamped beam show that there is a significant difference in the total radiated power between a system with a vibration‐suppression controller and a system with an acoustic controller that accounts for the coupling of these vibrations to the surrounding fluid. In some cases, the acoustic controller increases the system vibration in order to minimize the radiated power.

Stability and operating constraints of adaptive LMS-based feedback control

The filtered-X LMS algorithm has enjoyed widespread usage in both adaptive feedforward and feedback controller architectures. For feedforward controller designs the filtered-X LMS algorithm has been shown to exhibit unstable divergence for plant estimation errors in excess of +/-90^o. Typical implementations of this algorithm in adaptive feedback controllers such as filtered-U and filtered-E have previously been assumed to conform to these same identification constraints. Here we present two instability mechanisms that can arise in filtered-E control that violate the 90^o error assumption: feedback loop instabilities and LMS algorithm divergence. Analysis of the adaptive feedback system indicates that the conventionally interpreted plant estimation error can be arbitrarily small yet induce algorithm divergence; while other cases may have very large estimation errors and feedback loops cause controller instability. These analytical observations are supported by simulations. The implications of the actual plant estimation error, calculated here for the filtered-E controller, are extended to practical constraints placed on applications including filtered-U, on-line system identification, and self-excited system control.

Knockdown of estrogen receptor-α induces autophagy and inhibits antiestrogen-mediated unfolded protein response activation, promoting ROS-induced breast cancer cell death

Approximately 70% of all newly diagnosed breast cancers express estrogen receptor (ER)‐α. Although inhibiting ER action using targeted therapies such as fulvestrant (ICI) is often effective, later emergence of antiestrogen resistance limits clinical use. We used antiestrogen‐sensitive and ‐resistant cells to determine the effect of antiestrogens/ERα on regulating autophagy and unfolded protein response (UPR) signaling. Knockdown of ERα significantly increased the sensitivity of LCC1 cells (sensitive) and also resensitized LCC9 cells (resistant) to antiestrogen drugs. Interestingly, ERα knockdown, but not ICI, reduced nuclear factor (erythroid‐derived 2)‐like (NRF)‐2 (UPR‐induced antioxidant protein) and increased cytosolic kelch‐like ECH‐associated protein (KEAP)‐1 (NRF2 inhibitor), consistent with the observed increase in ROS production. Furthermore, autophagy induction by antiestrogens was prosurvival but did not prevent ERα knockdown‐mediated death. We built a novel mathematical model to elucidate the interactions among UPR, autophagy, ER signaling, and ROS regulation of breast cancer cell survival. The experimentally validated mathematical model explains the counterintuitive result that knocking down the main target of ICI (ERα) increased the effectiveness of ICI. Specifically, the model indicated that ERα is no longer present in excess and that the effect on proliferation from further reductions in its level by ICI cannot be compensated for by increased autophagy. The stimulation of signaling that can confer resistance suggests that combining autophagy or UPR inhibitors with antiestrogens would reduce the development of resistance in some breast cancers.—Cook, K. L., Clarke, P. A. G., Parmar, J., Hu, R., Schwartz‐Roberts, J. L., Abu‐Asab, M., Wärri, A., Baumann, W. T., Clarke, R. Knockdown of estrogen receptor‐α induces autophagy and inhibits antiestrogen‐mediated unfolded protein response activation, promoting ROS‐induced breast cancer cell death. FASEB J. 28, 3891‐3905 (2014). www.fasebj.org

REDUCED-ORDER MODELING OF DYNAMIC HEAT RELEASE FOR THERMOACOUSTIC INSTABILITY PREDICTION

The feedback interaction between dynamic heat release and the acoustic characteristics of a combustor can produce an unstable “self-excited” system that ultimately results in a steady pressure oscillation. A simplified model of this feedback loop is needed to predict the limit cycle frequencies and amplitudes. This paper is focused on the development of a physically-based, reduced-order, nonlinear heat release model for a burner-stabilized, laminar premixed flame in a laboratory combustor. Starting from the governing conservation equations, the heat release dynamics are described by partial differential equations that are simulated by a finite-difference method. Using proper orthogonal decomposition (POD) and a generalized Galerkin procedure, the infinite-dimensional PDE model can be reduced to a set of low-order nonlinear ordinary differential equations. The issues of model order versus accuracy and the selection of mode shapes to be used in the reduction are discussed. In addition, this theoretical model points out some major challenges that need to be faced when trying to identify an accurate nonlinear heat release model from experimental data. A two-mode linear acoustic model for the combustor is coupled to the unsteady heat release model and the resulting closed-loop response is compared to experimental data.

Accurate Modeling of Nonlinear Systems using Volterra Series Submodels

We investigate the problem of accurately modeling nonlinear systems (such as aircraft flight in high angle-of-attack/sideslip flight) using simple low-order Volterra submodels. First, we apply this technique to a simplified nonlinear stall/post-stall aircraft model for the case of a longitudinal limit cycle. Our simulation study demonstrates that the responses of the Volterra submodels accurately match the responses of the original nonlinear model, whereas the responses of a piecewise-linear model do not. Next, we apply the technique to a simplified high a nonlinear model of wing rock. Our simulation study demonstrates that the second-order Volterra approximation predicts the wing rock limit cycle, while a linear approximation does not. Third-, fourth- and fifth-order Volterra approximations are observed to give wing rock amplitudes that converge quadratically to the nonlinear value.