21 research outputs found
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
Inferring serum proteolytic activity from LC-MS/MS data
<p>Abstract</p> <p>Background</p> <p>In this paper we deal with modeling serum proteolysis process from tandem mass spectrometry data. The parameters of peptide degradation process inferred from LC-MS/MS data correspond directly to the activity of specific enzymes present in the serum samples of patients and healthy donors. Our approach integrate the existing knowledge about peptidases' activity stored in MEROPS database with the efficient procedure for estimation the model parameters.</p> <p>Results</p> <p>Taking into account the inherent stochasticity of the process, the proteolytic activity is modeled with the use of Chemical Master Equation (CME). Assuming the stationarity of the Markov process we calculate the expected values of digested peptides in the model. The parameters are fitted to minimize the discrepancy between those expected values and the peptide activities observed in the MS data. Constrained optimization problem is solved by Levenberg-Marquadt algorithm.</p> <p>Conclusions</p> <p>Our results demonstrates the feasibility and potential of high-level analysis for LC-MS proteomic data. The estimated enzyme activities give insights into the molecular pathology of colorectal cancer. Moreover the developed framework is general and can be applied to study proteolytic activity in different systems.</p
Bistability versus Bimodal Distributions in Gene Regulatory Processes from Population Balance
In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the “off” state, and the other at the high end representing the “on” state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the “off” state and the other in the “on” state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model
Noise Management by Molecular Networks
Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise
Adding noise to Markov cohort state-transition model in decision modeling and cost-effectiveness analysis.
Following its introduction over 30 years ago, the Markov cohort state-transition model has been used extensively to model population trajectories over time in health decision modeling and cost-effectiveness analysis studies. We recently showed that a cohort model represents the average of a continuous-time stochastic process on a multidimensional integer lattice governed by a master equation, which represents the time-evolution of the probability function of an integer-valued random vector. By leveraging this theoretical connection, this study introduces an alternative modeling method using a stochastic differential equation (SDE) approach, which captures not only the mean behavior but also the variance of the population process. We show the derivation of an SDE model from first principles, describe an algorithm to construct an SDE and solve the SDE via simulation for use in practice, and demonstrate the two applications of an SDE in detail. The first example demonstrates that the population trajectories, and their mean and variance, from the SDE and other commonly used methods in decision modeling match. The second example shows that users can readily apply the SDE method in their existing works without the need for additional inputs beyond those required for constructing a conventional cohort model. In addition, the second example demonstrates that the SDE model is superior to a microsimulation model in terms of computational speed. In summary, an SDE model provides an alternative modeling framework which includes information on variance, can accommodate for time-varying parameters, and is computationally less expensive than a microsimulation for a typical cohort modeling problem
Adding noise to Markov cohort state‐transition model in decision modeling and cost‐effectiveness analysis
Combining femoral and acetabular parameters in femoroacetabular impingement : the omega surface
The concept of femoroacetabular impingement (FAI) proposes the development of hip osteoarthritis through motion-induced damage to the acetabular cartilage and labrum. Thus, dynamic interaction of the proximal femur and acetabulum is the crux of FAI. Several types of FAI can be distinguished, but FAI classification is mostly done with separate parameters for acetabular and femoral morphology on planar images, without direct representation of the femoroacetabular interaction. Five main parameters influence impingement between the proximal femur and the acetabular rim: alpha and center edge angles, acetabular and femoral version, and neck-shaft angle. We attempted to integrate these five parameters in order to reflect their interaction and derive a signal comprehensive parameter, the omega surface, to characterize the severity of FAI. The omega surface is a CT-based delineation of the femoral head surface that represents the area for impingement-free motion. The omega surface is determined with dedicated software (Articulis (TM)) and can be determined for various positions of the hip joint. We determined the omega surface in a pilot study for five different hip morphotypes and found the omega surface was smaller in FAI morphotypes than in a normal hip. Furthermore, the omega surface was smaller in symptomatic versus control subjects with FAI morphotypes. The omega surface may therefore help in improved differentiation between symptomatic and asymptomatic FAI hips