The stochasticity of gene expression is manifested in the fluctuations of mRNA and protein copy numbers within a cell lineage over time. While data of this type can be obtained for many generations, most mathematical models are unsuitable to interpret such data since they assume non-growing cells. Here we develop a theoretical approach that quantitatively links the frequency content of lineage data to subcellular dynamics. We elucidate how the position, height, and width of the peaks in the power spectrum provide a distinctive fingerprint that encodes a wealth of information about mechanisms controlling transcription, translation, replication, degradation, bursting, promoter switching, cell cycle duration, cell division, gene dosage compensation, and cell size homeostasis. Predictions are confirmed by analysis of single-cell Escherichia coli data obtained using fluorescence microscopy. Furthermore, by matching the experimental and theoretical power spectra, we infer the temperature-dependent gene expression parameters, without the need of measurements relating fluorescence intensities to molecule numbers.
Hau-Tieng WuDepartment of Mathematics, Duke University, DurhamTze Leung LaiDepartment of Statistics, Stanford University, StanfordGabriel G. Haddad3Department of Pediatrics and Rady Children’s Hospital, University of CaliforniaAlysson MuotriDepartment of Cellular & Molecular Medicine and Department of Pediatrics
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2105.45001
Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time-frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.
Songting LiShanghai JIao Tong UniversityNan LiuBeijing Normal UniversityLi YaoBeijing Normal UniversityXiaohui ZhangBeijing Normal UniversityDongzhuo ZhouShanghai JIao Tong UniversityDavid CaiNew York University
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2104.42005
The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the
traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the
concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance
measurement and provides a reliable approach to assess synaptic influence on neuronal computation.
Songting LiShanghai Jiao Tong UniversityNan LiuBeijing Normal UniversityXiaohui ZhangBeijing Normal UniversityDavid McLaughlinCourant Institute New York UniversityDouglas ZhouShanghai Jiao Tong UniversityDavid CaiCourant Institute New York University
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2104.42004
Proceedings of the National Academy of Sciences of the United States of America, 116, (30), 15244-15252, 2019.7
Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.