6 research outputs found
Microtubule depolymerization by the kinesin-8 motor Kip3p: a mathematical model
Proteins from the kinesin-8 family promote microtubule (MT) depolymerization,
a process thought to be important for the control of microtubule length in
living cells. In addition to this MT shortening activity, kinesin 8s are motors
that show plus-end directed motility on MTs. Here we describe a simple model
that incorporates directional motion and destabilization of the MT plus end by
kinesin 8. Our model quantitatively reproduces the key features of
length-vs-time traces for stabilized MTs in the presence of purified kinesin 8,
including length-dependent depolymerization. Comparison of model predictions
with experiments suggests that kinesin 8 depolymerizes processively, i.e., one
motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in
MT length as a function of time are related to depolymerization processivity.
We have also determined the parameter regime in which the rate of MT
depolymerization is length dependent: length-dependent depolymerization occurs
only when MTs are sufficiently short; this crossover is sensitive to the bulk
motor concentration.Comment: 34 pages, 11 figure
Incorporating expression data in metabolic modeling: a case study of lactate dehydrogenase
Integrating biological information from different sources to understand
cellular processes is an important problem in systems biology. We use data from
mRNA expression arrays and chemical kinetics to formulate a metabolic model
relevant to K562 erythroleukemia cells. MAP kinase pathway activation alters
the expression of metabolic enzymes in K562 cells. Our array data show changes
in expression of lactate dehydrogenase (LDH) isoforms after treatment with
phorbol 12-myristate 13-acetate (PMA), which activates MAP kinase signaling. We
model the change in lactate production which occurs when the MAP kinase pathway
is activated, using a non-equilibrium, chemical-kinetic model of homolactic
fermentation. In particular, we examine the role of LDH isoforms, which
catalyze the conversion of pyruvate to lactate. Changes in the isoform ratio
are not the primary determinant of the production of lactate. Rather, the total
concentration of LDH controls the lactate concentration.Comment: In press, Journal of Theoretical Biology. 27 pages, 9 figure
Systems theory of Smad signaling
Transforming Growth Factor-beta (TGF-beta) signalling is an important
regulator of cellular growth and differentiation. The principal intracellular
mediators of TGF-beta signalling are the Smad proteins, which upon TGF-beta
stimulation accumulate in the nucleus and regulate transcription of target
genes. To investigate the mechanisms of Smad nuclear accumulation, we developed
a simple mathematical model of canonical Smad signalling. The model was built
using both published data and our experimentally determined cellular Smad
concentrations (isoforms 2, 3, and 4). We found in mink lung epithelial cells
that Smad2 (8.5-12 x 10^4 molecules/cell) was present in similar amounts to
Smad4 (9.3-12 x 10^4 molecules/cell), while both were in excess of Smad3
(1.1-2.0 x 10^4 molecules/cell). Variation of the model parameters and
statistical analysis showed that Smad nuclear accumulation is most sensitive to
parameters affecting the rates of RSmad phosphorylation and dephosphorylation
and Smad complex formation/dissociation in the nucleus. Deleting Smad4 from the
model revealed that rate-limiting phospho-R-Smad dephosphorylation could be an
important mechanism for Smad nuclear accumulation. Furthermore, we observed
that binding factors constitutively localised to the nucleus do not efficiently
mediate Smad nuclear accumulation if dephosphorylation is rapid. We therefore
conclude that an imbalance in the rates of R-Smad phosphorylation and
dephosphorylation is likely an important mechanism of Smad nuclear accumulation
during TGF-beta signalling.Comment: To appear in IEE Proceedings Systems Biology. 12 pages of text, 36
pages tota
The Role of Kinesin-8 Proteins in Kinetochore Movements and Spindle Dynamics in Fission Yeast
Elasticity of Short DNA Molecules: Theory and Experiment for Contour Lengths of 0.6–7 μm
The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters—the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm–7.03 μm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length pwlc depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the “finite wormlike chain (FWLC),” to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of pwlc on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of pfwlc on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules