9 research outputs found
Dynamical compensation and structural identifiability: analysis, implications, and reconciliation
The concept of dynamical compensation has been recently introduced to
describe the ability of a biological system to keep its output dynamics
unchanged in the face of varying parameters. Here we show that, according to
its original definition, dynamical compensation is equivalent to lack of
structural identifiability. This is relevant if model parameters need to be
estimated, which is often the case in biological modelling. This realization
prompts us to warn that care should we taken when using an unidentifiable model
to extract biological insight: the estimated values of structurally
unidentifiable parameters are meaningless, and model predictions about
unmeasured state variables can be wrong. Taking this into account, we explore
alternative definitions of dynamical compensation that do not necessarily imply
structural unidentifiability. Accordingly, we show different ways in which a
model can be made identifiable while exhibiting dynamical compensation. Our
analyses enable the use of the new concept of dynamical compensation in the
context of parameter identification, and reconcile it with the desirable
property of structural identifiability
An analysis of -invariance and dynamical compensation properties from a control perspective
Dynamical compensation (DC) provides robustness to parameter fluctuations. As
an example, DC enable control of the functional mass of endocrine or neuronal
tissue essential for controlling blood glucose by insulin through a nonlinear
feedback loop. Researchers have shown that DC is related to structural
unidentifiability and -invariance property, and
-invariance property is a sufficient and necessary condition for
the DC property. In this article, we discuss DC and -invariancy
from an adaptive control perspective. An adaptive controller is a self-tuning
controller used to compensate for changes in a dynamical system. To design an
adaptive controller with the DC property, it is easier to start with a
two-dimensional dynamical model. We introduce a simplified system of ordinary
differential equations (ODEs) with the DC property and extend it to a general
form. The value of the ideal adaptive control lies in developing methods to
synthesize DC to variations in multiple parameters. Then we investigate the
stability of the system with time-varying input and disturbance signals, with a
focus on the system's -invariance properties. This study provides
phase portraits and step-like response graphs to visualize the system's
behavior and stability properties
Observability and Structural Identifiability of Nonlinear Biological Systems
Observability is a modelling property that describes the possibility of
inferring the internal state of a system from observations of its output. A
related property, structural identifiability, refers to the theoretical
possibility of determining the parameter values from the output. In fact,
structural identifiability becomes a particular case of observability if the
parameters are considered as constant state variables. It is possible to
simultaneously analyse the observability and structural identifiability of a
model using the conceptual tools of differential geometry. Many complex
biological processes can be described by systems of nonlinear ordinary
differential equations, and can therefore be analysed with this approach. The
purpose of this review article is threefold: (I) to serve as a tutorial on
observability and structural identifiability of nonlinear systems, using the
differential geometry approach for their analysis; (II) to review recent
advances in the field; and (III) to identify open problems and suggest new
avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods
for Identification and Modelling of Complex Biological Systems" of Complexit
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Mathematical deconvolution of CAR T-cell proliferation and exhaustion from real-time killing assay data.
Chimeric antigen receptor (CAR) T-cell therapy has shown promise in the treatment of haematological cancers and is currently being investigated for solid tumours, including high-grade glioma brain tumours. There is a desperate need to quantitatively study the factors that contribute to the efficacy of CAR T-cell therapy in solid tumours. In this work, we use a mathematical model of predator-prey dynamics to explore the kinetics of CAR T-cell killing in glioma: the Chimeric Antigen Receptor T-cell treatment Response in GliOma (CARRGO) model. The model includes rates of cancer cell proliferation, CAR T-cell killing, proliferation, exhaustion, and persistence. We use patient-derived and engineered cancer cell lines with an in vitro real-time cell analyser to parametrize the CARRGO model. We observe that CAR T-cell dose correlates inversely with the killing rate and correlates directly with the net rate of proliferation and exhaustion. This suggests that at a lower dose of CAR T-cells, individual T-cells kill more cancer cells but become more exhausted when compared with higher doses. Furthermore, the exhaustion rate was observed to increase significantly with tumour growth rate and was dependent on level of antigen expression. The CARRGO model highlights nonlinear dynamics involved in CAR T-cell therapy and provides novel insights into the kinetics of CAR T-cell killing. The model suggests that CAR T-cell treatment may be tailored to individual tumour characteristics including tumour growth rate and antigen level to maximize therapeutic benefit
Computing all identifiable functions of parameters for ODE models
Parameter identifiability is a structural property of an ODE model for
recovering the values of parameters from the data (i.e., from the input and
output variables). This property is a prerequisite for meaningful parameter
identification in practice. In the presence of nonidentifiability, it is
important to find all functions of the parameters that are identifiable. The
existing algorithms check whether a given function of parameters is
identifiable or, under the solvability condition, find all identifiable
functions. However, this solvability condition is not always satisfied, which
presents a challenge. Our first main result is an algorithm that computes all
identifiable functions without any additional assumptions, which is the first
such algorithm as far as we know. Our second main result concerns the
identifiability from multiple experiments (with generically different inputs
and initial conditions among the experiments). For this problem, we prove that
the set of functions identifiable from multiple experiments is what would
actually be computed by input-output equation-based algorithms (whether or not
the solvability condition is fulfilled), which was not known before. We give an
algorithm that not only finds these functions but also provides an upper bound
for the number of experiments to be performed to identify these functions. We
provide an implementation of the presented algorithms
Multiplexing information flow through dynamic signalling systems
We consider how a signalling system can act as an information hub by multiplexing information arising from multiple signals. We formally define multiplexing, mathematically characterise which systems can multiplex and how well they can do it. While the results of this paper are theoretical, to motivate the idea of multiplexing, we provide experimental evidence that tentatively suggests that the NF-κB transcription factor can multiplex information about changes in multiple signals. We believe that our theoretical results may resolve the apparent paradox of how a system like NF-κB that regulates cell fate and inflammatory signalling in response to diverse stimuli can appear to have the low information carrying capacity suggested by recent studies on scalar signals. In carrying out our study, we introduce new methods for the analysis of large, nonlinear stochastic dynamic models, and develop computational algorithms that facilitate the calculation of fundamental constructs of information theory such as Kullback–Leibler divergences and sensitivity matrices, and link these methods to a new theory about multiplexing information. We show that many current models such as those of the NF-κB system cannot multiplex effectively and provide models that overcome this limitation using post-transcriptional modifications
Joining and decomposing reaction networks
In systems and synthetic biology, much research has focused on the behavior
and design of single pathways, while, more recently, experimental efforts have
focused on how cross-talk (coupling two or more pathways) or inhibiting
molecular function (isolating one part of the pathway) affects systems-level
behavior. However, the theory for tackling these larger systems in general has
lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or
decomposing networks (e.g., inhibition or knock-outs) affects three properties
that reaction networks may possess---identifiability (recoverability of
parameter values from data), steady-state invariants (relationships among
species concentrations at steady state, used in model selection), and
multistationarity (capacity for multiple steady states, which correspond to
multiple cell decisions). Specifically, we prove results that clarify, for a
network obtained by joining two smaller networks, how properties of the smaller
networks can be inferred from or can imply similar properties of the original
network. Our proofs use techniques from computational algebraic geometry,
including elimination theory and differential algebra.Comment: 44 pages; extensive revision in response to referee comment
Identifiability of Chemical Reaction Networks with Intrinsic and Extrinsic Noise from Stationary Distributions
Many biological systems can be modeled as a chemical reaction network with
unknown parameters. Data available to identify these parameters are often in
the form of a stationary distribution, such as that obtained from measurements
of a cell population. In this work, we introduce a framework for analyzing the
identifiability of the reaction rate coefficients of chemical reaction networks
from stationary distribution data. Working with the linear noise approximation,
which is a diffusive approximation to the chemical master equation, we give a
computational procedure to certify global identifiability based on Hilbert's
Nullstellensatz. We present a variety of examples that show the applicability
of our method to chemical reaction networks of interest in systems and
synthetic biology, including discrimination between possible molecular
mechanisms for the interaction between biochemical species.Comment: 27 pages, 1 figure, 1 table. The extrinsic noise section is revised,
and minor edits have been made throughou