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Applied BioDynamics Research

Contents

  1. Human posture control
  2. Controlling cell cycle dynamics
  3. Frequency control of an oscillatory reaction
  4. Gene dynamics


1. Human posture control

During quiet standing, the human body sways in a stochastic manner. Recently, Michael Lauk, Carson Chow, Ann Pavlik and Jim Collins applied the fluctuation-dissipation theorem (FDT) to the human postural control system and showed that the dynamic response of the postural control system to a weak mechanical perturbation can be predicted from the fluctuations exhibited by the system under quasi-static conditions. They also showed that the estimated correlation and response functions can be described by a simple stochastic model consisting of a pinned polymer. These results demonstrate that the FDT exists for human balance control and that postural sway can be modeled by an equilibrium stochastic process. These findings also suggest that the postural control system utilizes the same control mechanisms under quiet-standing and dynamic conditions.

Related Publications
 

M. Lauk, C.C. Chow, A.E. Pavlik and J.J. Collins. "Human balance out of equilibrium: nonequilibrium statistical mechanics in posture control", Physical Review Letters 80: 413-416 (1998).

Lauk, Chow and Collins recently developed a postural stiffness measure that is extracted from foot center-of-pressure (COP) trajectories from quietly standing individuals (reference above). . In a follow-on study, Lauk, Chow, Susan Mitchell (Harvard Medical School), Lew Lipsitz (Harvard Medical School) and Collins applied this measure to patients with Parkinson's disease (PD). They correlated the postural stiffness measure with different clinical rating scales, obtained from 18 patients, to test the hypothesis that the measure can be used to characterize quantitatively some of the major motor impairments associated with PD. It was found that the stiffness measure was highly correlated with rigidity, bradykinesia, posture impairment, gait and leg agility, respectively, as rated by the Unified Parkinson's Disease Rating Scale. These results provide further evidence that a higher intrinsic muscle stiffness may contribute to the aforementioned clinically defined symptoms. From a clinical standpoint, this work indicates that the proposed postural stiffness measure may be useful as an assessment tool for the evaluation of PD patients subsequent to pharmacological and surgical treatment.

Related Publications
 

M. Lauk, C.C. Chow, L.A. Lipsitz, S.L. Mitchell and J.J. Collins (1999) "Assessing muscle stiffness from quiet stance in Parkinson's disease", Muscle and Nerve 22:635-639.

Galvanic vestibular stimulation serves to modulate the continuous firing level of the peripheral vestibular afferents. It has been shown that the application of sinusoidally-varying bipolar galvanic currents to the vestibular system can lead to sinusoidally-varying postural sway. Recently, Pavlik, Tim Inglis (University of British Columbia), Lauk, Lars Oddsson, and Collins showed that stochastic galvanic vestibular stimulation can lead to coherent stochastic postural sway. These findings indicate that subjects can act as "responders" to galvanic vestibular stimulation. This work suggests that time-varying galvanic vestibular stimulation could be used as the basis for an artificial vestibular control system to reduce or eliminate certain types of pathological postural sway.

Related Publications
 

A.E. Pavlik, J.T. Inglis, M. Lauk, L. Oddsson and J.J. Collins (1999) "The effects of stochastic galvanic vestibular stimulation on human postural sway", Exp. Brain Res. 124: 273-280.

2. Controlling cell cycle dynamics

Recently, Tim Gardner, Milos Dolnik and Collins developed and demonstrated, using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved with this scheme by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, they showed that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

Related Publications
 

T.S. Gardner, M. Dolnik and J.J. Collins. "A theory for controlling cell cycle dynamics using a reversibly binding inhibitor" (1998) Proc. of the Nat. Acad. of Sci. USA 95: 14190-14195.

3. Frequency control of an oscillatory reaction

The speed and efficiency of many chemical and biochemical systems depend strongly on the pH of the reaction environment. Optimization of these reactions is often achieved by regulating the hydrogen ion concentration with a pH buffer. Although the maintenance of a stable pH is desirable in many applications, in some cases, such as drug delivery, the controlled periodic variation of pH is preferred. Past theoretical studies suggest that a buffer of one the reacting species can reduce the frequency of chemical oscillations. Recently, Dolnik, Gardner, Irv Epstein (Brandeis) and Collins showed, through experiments and numerical simulation, that the addition of a buffer solution can increase, as well as decrease, the frequency of pH oscillations in the mixed Landolt reaction. Moreover, they showed that oscillations can be completely suppressed, or alternatively induced, by buffers of appropriate composition. This simple buffering scheme could provide a useful method for controlling the oscillations of a variety of chemical and biochemical systems.

Related Publications
 

M. Dolnik, T.S. Gardner, I.R. Epstein and J.J. Collins. "Frequency control of an oscillatory reaction by reversible binding of an autocatalyst " (1999) Phys. Rev. Lett. 82: 1582-1585.

4. Gene dynamics

For several years, genetic engineering has been used to manipulate cellular function. These techniques have proven to be extremely powerful in basic biological research and have even shown promise in clinical gene therapies. Though these techniques have become increasingly advanced, they are generally limited to the deletion, modification or cross-organism transplantation of existing cellular functions. The de novo design and synthesis of complex genetic and cellular functions is beyond the current capabilities of genetic engineering. Currently, Tim Gardner and Jim Collins are using techniques from nonlinear dynamics, neural network theory, and statistical mechanics to develop a theory for the design and construction of "genetic applets". A genetic applet is essentially an artificial virus that, once delivered into a cell, would coordinate the sequential expression of multiple genes. These genes could be used to execute a series of specific tasks that would either repair, enhance or modify cell function. The genetic applets would be constructed from a network of regulatory, structural and metabolic genes. Thus, they could be "programmed" into DNA and delivered into a cell as cellular "software."

David McMillen, Nancy Kopell, Jeff Hasty, and Jim Collins designed a synthetic gene network in E. coli which acts as a relaxation oscillator, and uses an intercell signaling mechanism to couple the oscillators and induce synchronous oscillations. They modeled the system and showed that the proposed coupling scheme leads to synchronous behavior across a population of cells. They provided an analytical treatment of the synchronization process, the dominant mechanism of which is "fast threshold modulation."

Jeff Hasty, Milos Dolnik (Brandeis University, CBD alumni), Vivi Rottschaffer and Jim Collins developed a model for a synthetic gene oscillator and considered the coupling of the oscillator to a periodic process that is intrinsic to cells. They investigated the synchronization properties of the coupled system, and showed how the oscillator can be constructed to yield a significant amplification of cellular oscillations. They reduced the driven oscillator equations to a normal form, and analytically determined the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally-occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.

Stephen Yeung, Jesper Tegner and Jim Collins developed a scheme to reverse-engineer gene networks on a genome-wide scale using a relatively small amount of gene expression data from microarray experiments. This method is based on the empirical observation that such networks are typically large and sparse. It uses singular value decomposition to construct a family of candidate solutions and then uses robust regressions to identify the solution with the smallest number of connections as the most likely solution. This approach was tested and validated in a series of in numero experiments on model gene networks. Jesper Tegner, Stephen Yeung, Jeff Hasty and Jim Collins showed how the perturbation of carefully chosen genes in a microarray experiment can be used to generate an algorithm capable of revealing the architecture of an underlying gene regulatory network. This iterative scheme identifies the network topology by analyzing the steady-state changes in gene expression resulting from the systematic perturbation of a particular node in the network. The validity of the algorithm was highlighted through the successful deduction of the topology of a linear in numero network and a recently reported model for the segmentation polarity network in Drosphila melanogaster. This novel method may prove useful in identifying and validating specific drug targets and in deconvolving the effects of chemical compounds.

Related Publications
 

Hasty J., Isaacs F., Dolnik M., McMillen D. and Collins J.J. "Designer gene networks: towards fundamental cellular control" CHAOS 11: 207-220 (2001).

Hasty J., McMillen D., Isaacs F. and Collins J.J. "Computational studies of gene regulatory networks: in numero molecular biology" Nature Reviews Genetics 2: 268--279 (2001).

Hasty J. and Collins J.J. "Protein interactions: unspinning the web" Nature 411: 30-31 (2001).

McMillen D., Kopell N., Hasty J. and Collins J.J. "Synchronizing genetic relaxation oscillators with intercell signaling" Proceedings of the National Academy of Sciences USA 99: 679-684 (2002).

Hasty J., Dolnik M., Rottschafer V. and Collins J.J. "A synthetic gene network for entraining and amplifying cellular oscillations" Physical Review Letters 88: 148101 (2002).

Yeung MKS, Tegner J. and Collins J.J. "Reverse engineering gene networks using singular value decomposition and robust regression" Proceedings of the National Academy of Sciences USA 99: 6163-6168 (2002).

Hasty J. and Collins J.J. "Translating the noise" Nature Genetics 31: 13-14 (2002).

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