Page 2 of 2

Everything is Markovian; nothing is Markovian

The Markov model, without question, is one of the most powerful and elegant tools available in many fields of biological modeling and beyond.  In my world of molecular simulation, Markov models have provided analyses more insightful than would be possible with direct simulation alone.  And I’m a user, too.  Markov models, in their chemical-kinetics guise, play a prominent role in illustrating cellular biophysics in my online book, Physical Lens on the Cell.

Yet it’s fair to say that everything is Markovian and nothing is Markovian – and we need to understand this.

If you’re new to the business, a quick word on what “Markovian” means.  A Markov process is a stochastic process where the future (i.e., the distribution of future outcomes) depends only on the present state of the system.  Good examples would be chemical kinetics models with transition probabilities governed by rate constants or simple Monte Carlo simulation (a.k.a. Markov-chain Monte Carlo).  To determine the next state of the system, we don’t care about the past: only the present state matters.

Continue reading

“Proof” of the Hill Relation Between Probability Flux and Mean First-Passage Time

The “Hill relation” is a key result for anyone interested in calculating rates from trajectories of any kind, whether molecular simulations or otherwise.  I am not aware of any really clear explanation, including Hill’s original presentation.  Hopefully this go-around will make sense.

Continue reading

Why Hair Gel Matters to Statistical Biophysicists

I was worried that a discussion of hair gel would have a certain bias toward men, but my wife assures me that women are just as likely to use a leave-in hair product.  I’m going to rely on that unstatistical assurance and roll right on.

Continue reading

A hello: The point of this blog

Statistical physics governs the behavior of biological systems from the molecular scale (think protein stability and fluctuations) to the cellular scale (including heterogeneity and stochasticity of cellular behavior).  This is not a claim that understanding statistical physics, a.k.a. statistical mechanics, implies an understanding of cell biology.  But I do claim that cell biology cannot be understood without statistical physics.

Continue reading