Global parameter estimation methods for stochastic biochemical systems

<p>Abstract</p> <p>Background</p> <p>The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.</p> <p>Results</p> <p>Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.</p> <p>Conclusions</p> <p>The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.</p

Nonverbal generics: human infants interpret objects as symbols of object kinds

Human infants are involved in communicative interactions with others well before they start to speak or understand language. It is generally thought that this communication is useful for establishing interpersonal relations and supporting joint activities, but, in the absence of symbolic functions that language provides, these early communicative contexts do not allow infants to learn about the world. However, recent studies suggest that when someone demonstrates something using an object as the medium of instruction, infants can conceive the object as an exemplar of the whole class of objects of the same kind. Thus, an object, just like a word, can play the role of a symbol that stands for something else than itself, and infants can learn general knowledge about a kind of object from nonverbal communication about a single item of that kind. This rudimentary symbolic capacity may be one of the roots of the development of symbolic understanding in children